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As a follow-up to the first IEEE Transactions on Medical Imaging (TMI) special issue on the theme of deep tomographic reconstruction, the second special issue is assembled to reflect the status and momentum of this rapidly emerging field. In this editorial, we provide a brief background illustrating the motivation for the development of network-based, data-driven, and learning-oriented reconstruction methods, summarize the included papers, and report our verification of the shared deep learning codes. Finally, we discuss several important research topics to facilitate further investigation and collaboration. [ABSTRACT FROM AUTHOR]

Introduction: Ringer's Lactate (RL), a crystalloid is the most common co-loading fluid used to limit haemodynamic complications following the Subarachnoid Block (SAB). Colloids like Hydroxyethyl Starches (HES) are occasionally used as the co-loading fluid despite controversies due to its better haemodynamic effect and are not written-off to date. So knowledge of the effect of co-loading fluid is of paramount importance if it contributes to hyperglycaemia, a detrimental factor for the outcome. Aim: To compare the Blood Sugar Levels (BSL) in different preparations of HES and to that of RL when administered as co-loading fluid following SAB. Materials and Methods: Eighty-nine patients were randomly allocated into three groups, namely HES 200, HES 130, and RL, and were co-loaded with either 20 mL/kg body weight of HES 200/0.5, 20 mL/kg body weight of HES 130/0.4 or 20 mL/kg body weight of RL respectively. BSL for each subject was recorded at 0, 15, 30, 45, 60, 120, 180, 240 min (post-hoc analysis was done with Tukey's test). Results: In all the three groups, there was a statistically significant rise in BSL from baseline. The BSL in the RL group reached its peak at 45 minutes and gradually dropped down to baseline. BSL increased more gradually with HES 130/0.4 reaching a peak value at 60 minutes, and at around 240 minutes for HES 200/0.5. Conclusion: HES causes an increase in BSL, though within physiological limits. [ABSTRACT FROM AUTHOR]

Background and Objective: Phenylephrine bolus or infusion is used to maintain arterial blood pressure during the subarachnoid block (SAB) for cesarean section. The objective was to assess the clinical efficacy of prophylactic phenylephrine infusion or bolus doses for maternal hemodynamics maintenance and its effect on fetal outcomes. Materials and Methods: Sixty parturients were randomized to receive either a continuous prophylactic IV infusion of phenylephrine (n = 30, group A) at a dose of 0.50 μg.kg−1.min−1 or phenylephrine (n = 30, Group B) 50 μg bolus dose after the systolic blood pressure (SBP) fell by 20% from the baseline. The changes in hemodynamics, ill effects, neonatal APGAR scores, and fetal acidosis were recorded at different time intervals. Results: SBP was significantly higher over time in group A. Group A showed a significant fall in heart rate from baseline after giving SAB and remained significantly low throughout the intraoperative period (P < 0.05). In group A, 12 patients showed a fall in blood pressure of >20% from the baseline; however, hypotension was observed in 21 patients in group B (P < 0.03). The number of hypotensive episodes was higher in the group B. Incidence of hypotension in Group A was 40% (12 out of 30 patients) and 70% (21 out of 30 patients) in Group B (P < 0.037). Episodes of reactive hypertension, defined as a rise in SBP >20% of baseline value, were noted in 3 out of 30 patients in the Group A. There was also a statistically nonsignificant trend toward a less frequent incidence of nausea and vomiting in the group A (P < 0.29). There was no significant difference between the two groups in APGAR scores at 1 and 5 min after delivery (P < 0.56, 0.13). The incidence of neonatal acidosis was similar in the two groups. Conclusion: Prophylactic phenylephrine infusion is superior to therapeutic phenylephrine bolus dose for control of hemodynamics. [ABSTRACT FROM AUTHOR]

The presence of missing entries in data often creates challenges for pattern recognition algorithms. Traditional algorithms for clustering data assume that all the feature values are known for every data point. We propose a method to cluster data in the presence of missing information. Unlike conventional clustering techniques where every feature is known for each point, our algorithm can handle cases where a few feature values are unknown for every point. For this more challenging problem, we provide theoretical guarantees for clustering using a $l_0$ fusion penalty based optimization problem. Furthermore, we propose an algorithm to solve a relaxation of this problem using saturating non-convex fusion penalties. It is observed that this algorithm produces solutions that degrade gradually with an increase in the fraction of missing feature values. We demonstrate the utility of the proposed method using a simulated dataset, the Wine dataset and the ASL dataset. It is shown that the proposed method is a promising clustering technique for datasets with large fractions of missing entries. [ABSTRACT FROM AUTHOR]

Background and Aims: Shivering after spinal anesthesia is a common complication and can occur in as many as 40%–70% of patients after regional anesthesia. This shivering, apart from its physiological and hemodynamic effects, has been described as even worse than surgical pain. The aim of the study was to evaluate and compare the effectiveness of prophylactic use of intravenous (IV) ketamine, dexmedetomidine, and tramadol for prevention of shivering after spinal anesthesia. Material and Methods: Two hundred American Society of Anesthesiologists physical status I and II patients subjected to spinal anesthesia were included in the study. The subjects were randomly divided into four groups to receive either ketamine 0.5 mg/kg IV or tramadol 0.5 mg/kg IV or dexmedetomidine 0.5 microgm/kg IV or 10 mL of 0.9% normal saline (NS). All the drugs/NS were administered as IV infusion over 10 min immediately before giving spinal anesthesia. Temperature (core and surface), heart rate, systolic blood pressure, diastolic blood pressure, and mean arterial pressure, peripheral oxygen saturation were assessed before giving the intrathecal injection and thereafter at 5 min intervals. Important side effects related to study drugs were also noted. Results: Shivering after spinal anesthesia was comparatively better controlled in group receiving dexmedetomidine as compared to other groups (P = 0.022). However, the use of dexmedetomidine was associated with significant hypotension which responded to single dose of mephentermine (3 mg IV). Dexmedetomidine is a better agent for prevention of shivering after spinal anesthesia as compared to ketamine and tramadol. It also provides adequate sedation and improves the surgical conditions. Conclusion: Dexmedetomidine is effective and comparably better than tramadol or ketamine in preventing shivering after spinal anesthesia. Dexmedetomidine also provides sedation without respiratory depression and favorable surgical conditions. However, with its use a fall in blood pressure and heart rate is anticipated. [ABSTRACT FROM AUTHOR]

Background: Pain associated with laparoscopic cholecystectomy is most severe during the first 24 h and the port sites are the most painful. Recent multimodal approaches target incisional pain instead of visceral pain which has led to the emergence of abdominal fascial plane blocks. This study embraces a novel combination of two independently effective fascial plane blocks, namely rectus sheath block and subcostal transversus abdominis plane (TAP) block to alleviate postoperative pain. Study Objective: The aim is to evaluate the effectiveness of the combination of rectus sheath block and subcostal TAP block, to compare its efficacy with that of subcostal TAP block alone and with conventional port site infiltration (PSI) in alleviating postoperative pain in patients undergoing laparoscopic cholecystectomy. Methodology: This prospective, randomized control, pilot study included 61 patients scheduled for elective laparoscopic cholecystectomy and distributed among three groups, namely Group 1: Combined subcostal TAP block with rectus sheath block (n = 20); Group 2: Oblique subcostal TAP block alone (n = 21); and Group 3: PSI group as an active control (n = 20). Results: Combined group had significantly lower pain scores, higher satisfaction scores, and reduced rescue analgesia both in early and late postoperative periods than the conventional PSI group. Conclusion: Ultrasound-guided combined fascial plane blocks is a novel intervention in pain management of patients undergoing laparoscopic cholecystectomy and should become the standard of care. [ABSTRACT FROM AUTHOR]

We introduce a novel algorithm to recover real time dynamic MR images from highly under-sampled k- t space measurements. The proposed scheme models the images in the dynamic dataset as points on a smooth, low dimensional manifold in high dimensional space. We propose to exploit the non-linear and non-local redundancies in the dataset by posing its recovery as a manifold smoothness regularized optimization problem. A navigator acquisition scheme is used to determine the structure of the manifold, or equivalently the associated graph Laplacian matrix. The estimated Laplacian matrix is used to recover the dataset from undersampled measurements. The utility of the proposed scheme is demonstrated by comparisons with state of the art methods in multi-slice real-time cardiac and speech imaging applications. [ABSTRACT FROM AUTHOR]

Highlights: [•] Novel NUFFT approximations for iterative non-Cartesian MRI reconstruction. [•] Better reconstructed image quality with less approximation error. [•] Considerably less memory demand compared to current algorithms, enabling implementations on GPUs. [Copyright &y& Elsevier]

We propose a novel blind compressive sensing (BCS) frame work to recover dynamic magnetic resonance images from undersampled measurements. This scheme models the dynamic signal as a sparse linear combination of temporal basis functions, chosen from a large dictionary. In contrast to classical compressed sensing, the BCS scheme simultaneously estimates the dictionary and the sparse coefficients from the undersampled measurements. Apart from the sparsity of the coefficients, the key difference of the BCS scheme with current low rank methods is the nonorthogonal nature of the dictionary basis functions. Since the number of degrees-of-freedom of the BCS model is smaller than that of the low-rank methods, it provides improved reconstructions at high acceleration rates. We formulate the reconstruction as a constrained optimization problem; the objective function is the linear combination of a data consistency term and sparsity promoting \ell1 prior of the coefficients. The Frobenius norm dictionary constraint is used to avoid scale ambiguity. We introduce a simple and efficient majorize–minimize algorithm, which decouples the original criterion into three simpler subproblems. An alternating minimization strategy is used, where we cycle through the minimization of three simpler problems. This algorithm is seen to be considerably faster than approaches that alternates between sparse coding and dictionary estimation, as well as the extension of K-SVD dictionary learning scheme. The use of the \ell1 penalty and Frobenius norm dictionary constraint enables the attenuation of insignificant basis functions compared to the \ell0 norm and column norm constraint assumed in most dictionary learning algorithms; this is especially important since the number of basis functions that can be reliably estimated is restricted by the available measurements. We also observe that the proposed scheme is more robust to local minima compared to K-SVD method, which relies on greedy sparse coding. Our phase transition experiments demonstrate that the BCS scheme provides much better recovery rates than classical Fourier-based CS schemes, while being only marginally worse than the dictionary aware setting. Since the overhead in additionally estimating the dictionary is low, this method can be very useful in dynamic magnetic resonance imaging applications, where the signal is not sparse in known dictionaries. We demonstrate the utility of the BCS scheme in accelerating contrast enhanced dynamic data. We observe superior reconstruction performance with the BCS scheme in comparison to existing low rank and compressed sensing schemes. [ABSTRACT FROM AUTHOR]

We introduce novel image regularization penalties to overcome the practical problems associated with the classical total variation (TV) scheme. Motivated by novel reinterpretations of the classical TV regularizer, we derive two families of functionals involving higher degree partial image derivatives; we term these families as isotropic and anisotropic higher degree TV (HDTV) penalties, respectively. The isotropic penalty is the L1 - L2 mixed norm of the directional image derivatives, while the anisotropic penalty is the separable L1 norm of directional derivatives. These functionals inherit the desirable properties of standard TV schemes such as invariance to rotations and translations, preservation of discontinuities, and convexity. The use of mixed norms in isotropic penalties encourages the joint sparsity of the directional derivatives at each pixel, thus encouraging isotropic smoothing. In contrast, the fully separable norm in the anisotropic penalty ensures the preservation of discontinuities, while continuing to smooth along the linelike features; this scheme thus enhances the linelike image characteristics analogous to standard TV. We also introduce efficient majorize–minimize algorithms to solve the resulting optimization problems. The numerical comparison of the proposed scheme with classical TV penalty, current second-degree methods, and wavelet algorithms clearly demonstrate the performance improvement. Specifically, the proposed algorithms minimize the staircase and ringing artifacts that are common with TV and wavelet schemes, while better preserving the singularities. We also observe that anisotropic HDTV penalty provides consistently improved reconstructions compared with the isotropic HDTV penalty. [ABSTRACT FROM PUBLISHER]

We introduce a novel algorithm to address the challenges in magnetic resonance (MR) spectroscopic imaging. In contrast to classical sequential data processing schemes, the proposed method combines the reconstruction and postprocessing steps into a unified algorithm. This integrated approach enables us to inject a range of prior information into the data processing scheme, thus constraining the reconstructions. We use high resolution, 3-D estimate of the magnetic field inhomogeneity map to generate an accurate forward model, while a high resolution estimate of the fat/water boundary is used to minimize spectral leakage artifacts. We parameterize the spectrum at each voxel as a sparse linear combination of spikes and polynomials to capture the metabolite and baseline components, respectively. The constrained model makes the problem better conditioned in regions with significant field inhomogeneity, thus enabling the recovery even in regions with high field map variations. To exploit the high resolution MR information, we formulate the problem as an anatomically constrained total variation optimization scheme on a grid with the same spacing as the magnetic resonance imaging data. We analyze the performance of the proposed scheme using phantom and human subjects. Quantitative and qualitative comparisons indicate a significant improvement in spectral quality and lower leakage artifacts. [ABSTRACT FROM AUTHOR]

The main focus of this paper is to derive a memory efficient approximation to the nonuniform Fourier transform of a support limited sequence. We show that the standard nonuniform fast Fourier transform (NUFFT) scheme is a shift invariant approximation of the exact Fourier transform. Based on the theory of shift-invariant representations, we derive an exact expression for the worst-case mean square approximation error. Using this metric, we evaluate the optimal scale-factors and the interpolator that provides the least approximation error. We also derive the upper-bound for the error component due to the lookup table based evaluation of the interpolator; we use this metric to ensure that this component is not the dominant one. Theoretical and experimental comparisons with standard NUFFT schemes clearly demonstrate the significant improvement in accuracy over conventional schemes, especially when the size of the uniform fast Fourier transform (FFT) is small. Since the memory requirement of the algorithm is dependent on the size of the uniform FFT, the proposed developments can lead to iterative signal reconstruction algorithms with significantly lower memory demands. [ABSTRACT FROM AUTHOR]

The decomposition of magnetic resonance imaging (MRI) data to generate water and fat images has several applications in medical imaging, including fat suppression and quantification of visceral fat. We introduce a novel algorithm to overcome some of the problems associated with current analytical and iterative decomposition schemes. In contrast to traditional analytical schemes, our approach is general enough to accommodate any uniform echo-shift pattern, any number of metabolites and signal samples. In contrast to region-growing method that use a smooth field-map initialization to resolve the ambiguities with the IDEAL algorithm, we propose to use an explicit smoothness constraint on the final fleldmap estimate. Towards this end, we estimate the number of feasible solutions at all the voxels, prior to the evaluation of the roots. This approach enables the algorithm to evaluate all the feasible roots, thus avoiding the convergence to the wrong solution. The estimation procedure is based on a modification of the harmonic retrieval (HR) framework to account for the chemical shift dependence in the frequencies. In contrast to the standard linear HR framework, we obtain the frequency shift as the common root of a set of quadratic equations. On most of the pixels with multiple feasible solutions, the correct solution can be identified by a simple sorting of the solutions. We use a region-merging algorithm to resolve the remaining ambiguity and phase-wrapping. Experimental results indicate that the proposed algebraic scheme eliminates most of the difficulties with the current schemes, without compromising the noise performance. Moreover, the proposed algorithm is also computationally more efficient. [ABSTRACT FROM AUTHOR]

Model-based techniques have the potential to reduce the artifacts and improve resolution in magnetic resonance spectroscopic imaging, without sacrificing the signal-to-noise ratio. However, the current approaches have a few drawbacks that limit their performance in practical applications. Specifically, the classical schemes use less flexible image models that lead to model misfit, thus resulting in artifacts. Moreover, the performance of the current approaches is negatively affected by the magnetic field inhomogeneity and spatial mismatch between the anatomical references and spectroscopic imaging data. In this paper, we propose efficient solutions to overcome these problems. We introduce a more flexible image model that represents the signal as a linear combination of compartmental and local basis functions. The former set represents the signal variations within the compartments, while the latter captures the local perturbations resulting from lesions or segmentation errors. Since the combined set is redundant, we obtain the reconstructions using sparsity penalized optimization. To compensate for the artifacts resulting from field inhomogeneity, we estimate the field map using alternate scans and use it in the reconstruction. We model the spatial mismatch as an affine transformation, whose parameters are estimated from the spectroscopy data. [ABSTRACT FROM AUTHOR]

We introduce a three-dimensional (3-D) parametric active contour algorithm for the shape estimation of DNA molecules from stereo cryo-electron micrographs. We estimate the shape by matching the projections of a 3-D global shape model with the micrographs; we choose the global model as a 3-D filament with a B-spline skeleton and a specified radial profile. The active contour algorithm iteratively updates the B-spline coefficients, which requires us to evaluate the projections and match them with the micrographs at every iteration. Since the evaluation of the projections of the global model is computationally expensive, we propose a fast algorithm based on locally approximating it by elongated blob-like templates. We introduce the concept of projection-steerability and derive a projection-steerable elongated template. Since the two-dimensional projections of such a blob at any 3-D orientation can be expressed as a linear combination of a few basis functions, matching the projections of such a 3-D template involves evaluating a weighted sum of inner products between the basis functions and the micrographs. The weights are simple functions of the 3-D orientation and the inner-products are evaluated efficiently by separable filtering. We choose an internal energy term that penalizes the average curvature magnitude. Since the exact length of the DNA molecule is known a priori, we intro- duce a constraint energy term that forces the curve to have this specified length. The sum of these energies along with the image energy derived from the matching process is minimized using the conjugate gradients algorithm. We validate the algorithm using real, as well as simulated, data and show that it performs well. [ABSTRACT FROM AUTHOR]

Compressive sampling has the potential to dramatically accelerate the pace of data collection in two-dimensional infrared (2D IR) spectroscopy. We have previously introduced the Generic Iteratively Reweighted Annihilating Filter (GIRAF) reconstruction algorithm to solve the reconstruction in 2D IR compressive sampling. Here, we report a thorough assessment of this method and comparison to our earlier efforts using the Total Variation (TV) algorithm. We show that the GIRAF algorithm has some distinct advantages over TV. Although it is no better or worse in terms of ameliorating the impacts of compressive sampling on the measured 2D IR line shape, we find that the nature of those effects is different for GIRAF than they were for TV. In addition to assessing the impacts on the line shape of a single oscillator, we also test the ability of the algorithm to reconstruct spectra that have transitions from more than one oscillator, such as the coupled carbonyl oscillators in rhodium dicarbonyl. Finally, and perhaps most importantly, we show that the GIRAF algorithm has a distinct denoising effect on the signal-to-noise ratio (SNR) of the 2D IR spectra that can increase the SNR by as much as 4× without any additional signal averaging and collecting fewer data points, which should further enhance the acceleration of data collection that can be achieved using compressive sampling and enable even more challenging experimental measurements. [ABSTRACT FROM AUTHOR]

Parametric active contour models are one of the preferred approaches for image segmentation because of their computational efficiency and simplicity. However, they have a few drawbacks which limit their performance. In this paper, we identify some of these problems and propose efficient solutions to get around them. The widely-used gradient magnitude-based energy is parameter dependent; its use will negatively affect the parametrization of the curve and, consequently, its stiffness. Hence, we introduce a new edge-based energy that is independent of the parameterization. It is also more robust since it takes into account the gradient direction as well. We express this energy term as a surface integral, thus unifying it naturally with the region-based schemes. The unified framework enables the user to tune the image energy to the application at hand. We show that parametric snakes can guarantee low curvature curves, but only if they are described in the curvilinear abscissa. Since normal curve evolution do not ensure constant are-length, we propose a new internal energy term that will force this configuration. The curve evolution can sometimes give rise to closed loops in the contour, which will adversely interfere with the optimization algorithm. We propose a curve evolution scheme that prevents this condition. [ABSTRACT FROM AUTHOR]

We propose a general approach for the design of 2D feature detectors from a class of steerable functions based on the optimization of a Canny-like criterion. In contrast with previous computational designs, our approach is truly 2D and provides filters that have closed-form expressions. It also yields operators that have a belier orientation selectivity than the classical gradient or Hessian- based detectors. We illustrate the method with the design of operators for edge and ridge detection. We present some experimental results that demonstrate the performance improvement of these new feature detectors. We propose computationally efficient local optimization algorithms for the estimation of feature orientation. We also introduce the notion of shape-adaptable feature detection and use it for the detection of image corners. [ABSTRACT FROM AUTHOR]

Presents an expression for the L[sub2] error that occurs when one approximates a periodic signal in a basis of shifted and scaled versions of a generating function. Overview of classical sampling theory; Fourier series representation; Computation of the square error; Experimental verification of the error formula.

Structured low-rank (SLR) algorithms, which exploit annihilation relations between the Fourier samples of a signal resulting from different properties, is a powerful image reconstruction framework in several applications. This scheme relies on low-rank matrix completion to estimate the annihilation relations from the measurements. The main challenge with this strategy is the high computational complexity of matrix completion. We introduce a deep learning (DL) approach to significantly reduce the computational complexity. Specifically, we use a convolutional neural network (CNN)-based filterbank that is trained to estimate the annihilation relations from imperfect (under-sampled and noisy) k-space measurements of Magnetic Resonance Imaging (MRI). The main reason for the computational efficiency is the pre-learning of the parameters of the non-linear CNN from exemplar data, compared to SLR schemes that learn the linear filterbank parameters from the dataset itself. Experimental comparisons show that the proposed scheme can enable calibration-less parallel MRI; it can offer performance similar to SLR schemes while reducing the runtime by around three orders of magnitude. Unlike pre-calibrated and self-calibrated approaches, the proposed uncalibrated approach is insensitive to motion errors and affords higher acceleration. The proposed scheme also incorporates image domain priors that are complementary, thus significantly improving the performance over that of SLR schemes. [ABSTRACT FROM AUTHOR]

The article presents a case study 40-year-old asymptomatic patient that was found to have a very high blood pressure (BP) during routine medical examination. It mentions that his systemic examination was essentially normal and routine investigations did not reveal any abnormality. It also mentions that epidural anaesthesia can alleviate ischaemic pain after transcatheter arterial embolisation (TAE) of tumour, after ensuring stringent haemodynamic monitoring.

We introduce a model-based deep learning architecture termed MoDL-MUSSELS for the correction of phase errors in multishot diffusion-weighted echo-planar MR images. The proposed algorithm is a generalization of the existing MUSSELS algorithm with similar performance but significantly reduced computational complexity. In this work, we show that an iterative re-weighted least-squares implementation of MUSSELS alternates between a multichannel filter bank and the enforcement of data consistency. The multichannel filter bank projects the data to the signal subspace, thus exploiting the annihilation relations between shots. Due to the high computational complexity of the self-learned filter bank, we propose replacing it with a convolutional neural network (CNN) whose parameters are learned from exemplary data. The proposed CNN is a hybrid model involving a multichannel CNN in the k-space and another CNN in the image space. The k-space CNN exploits the annihilation relations between the shot images, while the image domain network is used to project the data to an image manifold. The experiments show that the proposed scheme can yield reconstructions that are comparable to state-of-the-art methods while offering several orders of magnitude reduction in run-time. [ABSTRACT FROM AUTHOR]

We introduce a continuous domain framework for the recovery of a planar curve from a few samples. We model the curve as the zero level set of a trigonometric polynomial. We show that the exponential feature maps of the points on the curve lie on a low-dimensional subspace. We show that the null-space vector of the feature matrix can be used to uniquely identify the curve, given a sufficient number of samples. The worst-case theoretical guarantees show that the number of samples required for unique recovery depends on the bandwidth of the underlying trigonometric polynomial, which is a measure of the complexity of the curve. We introduce an iterative algorithm that relies on the low-rank property of the feature maps to recover the curves when the samples are noisy or when the true bandwidth of the curve is unknown. We also demonstrate the preliminary utility of the proposed curve representation in the context of image segmentation. [ABSTRACT FROM AUTHOR]

We introduce a local manifold regularization approach to recover dynamic MRI data from highly undersampled measurements. The proposed scheme relies on the manifold structure of local image patches at the same spatial location in a free-breathing cardiac MRI dataset; this approach is a generalization of the SmooThness Regularization on Manifolds (SToRM) scheme that exploits the global manifold structure of images in the dataset. Since the manifold structure of the patches varies depending on the spatial location and is often considerably simpler than the global one, this approach significantly reduces the data demand, facilitating the recovery from shorter scans. Since the navigator-based estimation of manifold structure pursued in SToRM is not feasible in this setting, a reformulation of SToRM is introduced. Specifically, the regularization term of the cost function involves the sum of robust distances between images sub-patches in the dataset. The optimization algorithm alternates between updating the images and estimating the manifold structure of the image patches. The utility of the proposed scheme is demonstrated in the context of $\textit {in-vivo}$ prospective free-breathing cardiac CINE MRI imaging with multichannel acquisitions and simulated phantoms. The new framework facilitates a reduction in scan time, as compared to the SToRM strategy. [ABSTRACT FROM AUTHOR]

Recent theory of mapping an image into a structured low-rank Toeplitz or Hankel matrix has become an effective method to restore images. In this paper, we introduce a generalized structured low-rank algorithm to recover images from their undersampled Fourier coefficients using infimal convolution regularizations. The image is modeled as the superposition of a piecewise constant component and a piecewise linear component. The Fourier coefficients of each component satisfy an annihilation relation, which results in a structured Toeplitz matrix. We exploit the low-rank property of the matrices to formulate a combined regularized optimization problem. In order to solve the problem efficiently and to avoid the high-memory demand resulting from the large-scale Toeplitz matrices, we introduce a fast and a memory-efficient algorithm based on the half-circulant approximation of the Toeplitz matrix. We demonstrate our algorithm in the context of single and multi-channel MR images recovery. Numerical experiments indicate that the proposed algorithm provides improved recovery performance over the state-of-the-art approaches. [ABSTRACT FROM AUTHOR]

We consider the problem of recovering the superposition of |$R$| distinct complex exponential functions from compressed non-uniform time-domain samples. Total variation (TV) minimization or atomic norm minimization was proposed in the literature to recover the |$R$| frequencies or the missing data. However, it is known that in order for TV minimization and atomic norm minimization to recover the missing data or the frequencies, the underlying |$R$| frequencies are required to be well separated, even when the measurements are noiseless. This paper shows that the Hankel matrix recovery approach can super-resolve the |$R$| complex exponentials and their frequencies from compressed non-uniform measurements, regardless of how close their frequencies are to each other. We propose a new concept of orthonormal atomic norm minimization (OANM), and demonstrate that the success of Hankel matrix recovery in separation-free super-resolution comes from the fact that the nuclear norm of a Hankel matrix is an orthonormal atomic norm. More specifically, we show that, in traditional atomic norm minimization, the underlying parameter values must be well separated to achieve successful signal recovery, if the atoms are changing continuously with respect to the continuously valued parameter. In contrast, for the OANM, it is possible the OANM is successful even though the original atoms can be arbitrarily close. As a byproduct of this research, we provide one matrix-theoretic inequality of nuclear norm, and give its proof using the theory of compressed sensing. [ABSTRACT FROM AUTHOR]

We introduce a structured low rank algorithm for the calibration-free compensation of field inhomogeneity artifacts in echo planar imaging (EPI) MRI data. We acquire the data using two EPI readouts that differ in echo-time. Using time segmentation, we reformulate the field inhomogeneity compensation problem as the recovery of an image time series from highly undersampled Fourier measurements. The temporal profile at each pixel is modeled as a single exponential, which is exploited to fill in the missing entries. We show that the exponential behavior at each pixel, along with the spatial smoothness of the exponential parameters, can be exploited to derive a 3-D annihilation relation in the Fourier domain. This relation translates to a low rank property on a structured multi-fold Toeplitz matrix, whose entries correspond to the measured k-space samples. We introduce a fast two-step algorithm for the completion of the Toeplitz matrix from the available samples. In the first step, we estimate the null space vectors of the Toeplitz matrix using only its fully sampled rows. The null space is then used to estimate the signal subspace, which facilitates the efficient recovery of the time series of images. We finally demonstrate the proposed approach on spherical MR phantom data and human data and show that the artifacts are significantly reduced. [ABSTRACT FROM AUTHOR]

We introduce a model-based image reconstruction framework with a convolution neural network (CNN)-based regularization prior. The proposed formulation provides a systematic approach for deriving deep architectures for inverse problems with the arbitrary structure. Since the forward model is explicitly accounted for, a smaller network with fewer parameters is sufficient to capture the image information compared to direct inversion approaches. Thus, reducing the demand for training data and training time. Since we rely on end-to-end training with weight sharing across iterations, the CNN weights are customized to the forward model, thus offering improved performance over approaches that rely on pre-trained denoisers. Our experiments show that the decoupling of the number of iterations from the network complexity offered by this approach provides benefits, including lower demand for training data, reduced risk of overfitting, and implementations with significantly reduced memory footprint. We propose to enforce data-consistency by using numerical optimization blocks, such as conjugate gradients algorithm within the network. This approach offers faster convergence per iteration, compared to methods that rely on proximal gradients steps to enforce data consistency. Our experiments show that the faster convergence translates to improved performance, primarily when the available GPU memory restricts the number of iterations. [ABSTRACT FROM AUTHOR]

We consider the recovery of a continuous domain piecewise constant image from its nonuniform Fourier samples using a convex matrix completion algorithm. We assume the discontinuities/edges of the image are localized to the zero level set of a bandlimited function. This assumption induces linear dependencies between the Fourier coefficients of the image, which results in a two-fold block Toeplitz matrix constructed from the Fourier coefficients being low rank. The proposed algorithm reformulates the recovery of the unknown Fourier coefficients as a structured low-rank matrix completion problem, where the nuclear norm of the matrix is minimized subject to structure and data constraints. We show that the exact recovery is possible with high probability when the edge set of the image satisfies an incoherency property. We also show that the incoherency property is dependent on the geometry of the edge set curve, implying higher sampling burden for smaller curves. This paper generalizes recent work on the super-resolution recovery of isolated Diracs or signals with finite rate of innovation to the recovery of piecewise constant images. [ABSTRACT FROM AUTHOR]

We introduce a structured low rank matrix completion algorithm to recover a series of images from their under-sampled measurements, where the signal along the parameter dimension at every pixel is described by a linear combination of exponentials. We exploit the exponential behavior of the signal at every pixel, along with the spatial smoothness of the exponential parameters to derive an annihilation relation in the Fourier domain. This relation translates to a low-rank property on a structured matrix constructed from the Fourier samples. We enforce the low-rank property of the structured matrix as a regularization prior to recover the images. Since the direct use of current low rank matrix recovery schemes to this problem is associated with high computational complexity and memory demand, we adopt an iterative re-weighted least squares algorithm, which facilitates the exploitation of the convolutional structure of the matrix. Novel approximations involving 2-D fast Fourier transforms are introduced to drastically reduce the memory demand and computational complexity, which facilitates the extension of structured low-rank methods to large scale 3-D problems. We demonstrate our algorithm in the MR parameter mapping setting and show improvement over the state-of-the-art methods. [ABSTRACT FROM PUBLISHER]

The main focus of this work is to introduce a single free-breathing and ungated imaging protocol to jointly estimate cardiac function and myocardial T 1 maps. We reconstruct a time series of images corresponding to k-space data from a free-breathing and ungated inversion recovery gradient echo sequence using a manifold algorithm. We model each image in the time series as a non-linear function of three variables: cardiac and respiratory phases and inversion time. The non-linear function is realized using a convolutional neural networks (CNN) generator, while the CNN parameters, as well as the phase information, are estimated from the measured k-t space data. We use a dense conditional auto-encoder to estimate the cardiac and respiratory phases from the central multi-channel k-space samples acquired at each frame. The latent vectors of the auto-encoder are constrained to be bandlimited functions with appropriate frequency bands, which enables the disentanglement of the latent vectors into cardiac and respiratory phases, even when the data are acquired with intermittent inversion pulses. Once the phases are estimated, we pose the image recovery as the learning of the parameters of the CNN generator from the measured k-t space data. The learned CNN generator is used to generate synthetic data on demand by feeding it with appropriate latent vectors. The proposed approach capitalizes on the synergies between cine MRI and T 1 mapping to reduce the scan time and improve patient comfort. The framework also enables the generation of synthetic breath-held cine movies with different inversion contrasts, which improves the visualization of the myocardium. In addition, the approach also enables the estimation of the T 1 maps with specific phases, which is challenging with breath-held approaches. [ABSTRACT FROM AUTHOR]

Two-dimensional infrared (2D IR) spectroscopy is a powerful tool to investigate molecular structures and dynamics on femtosecond to picosecond time scales and is applied to diverse systems. Current technologies allow for the acquisition of a single 2D IR spectrum in a few tens of milliseconds using a pulse shaper and an array detector, but demanding applications require spectra for many waiting times and involve considerable signal averaging, resulting in data acquisition times that can be many days or weeks of laboratory measurement time. Using compressive sampling, we show that we can reduce the time for collection of a 2D IR data set in a particularly demanding application from 8 to 2 days, a factor of 4 x, without changing the apparatus and while accurately reproducing the line-shape information that is most relevant to this application. This result is a potent example of the potential of compressive sampling to enable challenging new applications of 2D IR. [ABSTRACT FROM AUTHOR]

Current deep learning-based manifold learning algorithms such as the variational autoencoder (VAE) require fully sampled data to learn the probability density of real-world datasets. However, fully sampled data is often unavailable in a variety of problems, including the recovery of dynamic and high-resolution magnetic resonance imaging (MRI). We introduce a novel variational approach to learn a manifold from undersampled data. The VAE uses a decoder fed by latent vectors, drawn from a conditional density estimated from the fully sampled images using an encoder. Since fully sampled images are not available in our setting, we approximate the conditional density of the latent vectors by a parametric model whose parameters are estimated from the undersampled measurements using back-propagation. We use the framework for the joint alignment and recovery of multi-slice free breathing and ungated cardiac MRI data from highly undersampled measurements. Experimental results demonstrate the utility of the proposed scheme in dynamic imaging alignment and reconstructions. [ABSTRACT FROM AUTHOR]

Bilinear models such as low-rank and dictionary methods, which decompose dynamic data to spatial and temporal factor matrices are powerful and memory-efficient tools for the recovery of dynamic MRI data. Current bilinear methods rely on sparsity and energy compaction priors on the factor matrices to regularize the recovery. Motivated by deep image prior, we introduce a novel bilinear model, whose factor matrices are generated using convolutional neural networks (CNNs). The CNN parameters, and equivalently the factors, are learned from the undersampled data of the specific subject. Unlike current unrolled deep learning methods that require the storage of all the time frames in the dataset, the proposed approach only requires the storage of the factors or compressed representation; this approach allows the direct use of this scheme to large-scale dynamic applications, including free breathing cardiac MRI considered in this work. To reduce the run time and to improve performance, we initialize the CNN parameters using existing factor methods. We use sparsity regularization of the network parameters to minimize the overfitting of the network to measurement noise. Our experiments on free-breathing and ungated cardiac cine data acquired using a navigated golden-angle gradient-echo radial sequence show the ability of our method to provide reduced spatial blurring as compared to classical bilinear methods as well as a recent unsupervised deep-learning approach. [ABSTRACT FROM AUTHOR]

Objective. We introduce an unsupervised motion-compensated reconstruction scheme for high-resolution free-breathing pulmonary magnetic resonance imaging. Approach. We model the image frames in the time series as the deformed version of the 3D template image volume. We assume the deformation maps to be points on a smooth manifold in high-dimensional space. Specifically, we model the deformation map at each time instant as the output of a CNN-based generator that has the same weight for all time-frames, driven by a low-dimensional latent vector. The time series of latent vectors account for the dynamics in the dataset, including respiratory motion and bulk motion. The template image volume, the parameters of the generator, and the latent vectors are learned directly from the k-t space data in an unsupervised fashion. Main results. Our experimental results show improved reconstructions compared to state-of-the-art methods, especially in the context of bulk motion during the scans. Significance. The proposed unsupervised motion-compensated scheme jointly estimates the latent vectors that capture the motion dynamics, the corresponding deformation maps, and the reconstructed motion-compensated images from the raw k-t space data of each subject. Unlike current motion-resolved strategies, the proposed scheme is more robust to bulk motion events during the scan. [ABSTRACT FROM AUTHOR]

We introduce a fast iterative shrinkage algorithm for patch-smoothness regularization of inverse problems in medical imaging. This approach is enabled by the reformulation of current non-local regularization schemes as an alternating algorithm to minimize a global criterion. The proposed algorithm alternates between evaluating the denoised inter-patch differences by shrinkage and computing an image that is consistent with the denoised inter-patch differences and measured data. We derive analytical shrinkage rules for several penalties that are relevant in non-local regularization. The redundancy in patch comparisons used to evaluate the shrinkage steps are exploited using convolution operations. The resulting algorithm is observed to be considerably faster than current alternating non-local algorithms. The proposed scheme is applicable to a large class of inverse problems including deblurring, denoising, and Fourier inversion. The comparisons of the proposed scheme with state-of-the-art regularization schemes in the context of recovering images from undersampled Fourier measurements demonstrate a considerable reduction in alias artifacts and preservation of edges. [ABSTRACT FROM PUBLISHER]

We propose a novel deformation corrected compressed sensing (DC-CS) framework to recover contrast enhanced dynamic magnetic resonance images from undersampled measurements. We introduce a formulation that is capable of handling a wide class of sparsity/compactness priors on the deformation corrected dynamic signal. In this work, we consider example compactness priors such as sparsity in temporal Fourier domain, sparsity in temporal finite difference domain, and nuclear norm penalty to exploit low rank structure. Using variable splitting, we decouple the complex optimization problem to simpler and well understood sub problems; the resulting algorithm alternates between simple steps of shrinkage-based denoising, deformable registration, and a quadratic optimization step. Additionally, we employ efficient continuation strategies to reduce the risk of convergence to local minima. The decoupling enabled by the proposed scheme enables us to apply this scheme to contrast enhanced MRI applications. Through experiments on numerical phantom and in vivo myocardial perfusion MRI datasets, we observe superior image quality of the proposed DC-CS scheme in comparison to the classical k-t FOCUSS with motion estimation/correction scheme, and demonstrate reduced motion artifacts over classical compressed sensing schemes that utilize the compact priors on the original deformation uncorrected signal. [ABSTRACT FROM AUTHOR]

We introduce a generative smoothness regularization on manifolds (SToRM) model for the recovery of dynamic image data from highly undersampled measurements. The model assumes that the images in the dataset are non-linear mappings of low-dimensional latent vectors. We use the deep convolutional neural network (CNN) to represent the non-linear transformation. The parameters of the generator as well as the low-dimensional latent vectors are jointly estimated only from the undersampled measurements. This approach is different from traditional CNN approaches that require extensive fully sampled training data. We penalize the norm of the gradients of the non-linear mapping to constrain the manifold to be smooth, while temporal gradients of the latent vectors are penalized to obtain a smoothly varying time-series. The proposed scheme brings in the spatial regularization provided by the convolutional network. The main benefit of the proposed scheme is the improvement in image quality and the orders-of-magnitude reduction in memory demand compared to traditional manifold models. To minimize the computational complexity of the algorithm, we introduce an efficient progressive training-in-time approach and an approximate cost function. These approaches speed up the image reconstructions and offers better reconstruction performance. [ABSTRACT FROM AUTHOR]

We introduce a novel algorithm to recover sparse and low-rank matrices from noisy and undersampled measurements. We pose the reconstruction as an optimization problem, where we minimize a linear combination of data consistency error, nonconvex spectral penalty, and nonconvex sparsity penalty. We majorize the nondifferentiable spectral and sparsity penalties in the criterion by quadratic expressions to realize an iterative three-step alternating minimization scheme. Since each of these steps can be evaluated either analytically or using fast schemes, we obtain a computationally efficient algorithm. We demonstrate the utility of the algorithm in the context of dynamic magnetic resonance imaging (MRI) reconstruction from sub-Nyquist sampled measurements. The results show a significant improvement in signal-to-noise ratio and image quality compared with classical dynamic imaging algorithms. We expect the proposed scheme to be useful in a range of applications including video restoration and multidimensional MRI. [ABSTRACT FROM PUBLISHER]

Abstract: We introduce a novel noniterative algorithm for the fast and accurate reconstruction of nonuniformly sampled MRI data. The proposed scheme derives the reconstructed image as the nonuniform inverse Fourier transform of a compensated dataset. We derive each sample in the compensated dataset as a weighted linear combination of a few measured k-space samples. The specific k-space samples and the weights involved in the linear combination are derived such that the reconstruction error is minimized. The computational complexity of the proposed scheme is comparable to that of gridding. At the same time, it provides significantly improved accuracy and is considerably more robust to noise and undersampling. The advantages of the proposed scheme makes it ideally suited for the fast reconstruction of large multidimensional datasets, which routinely arise in applications such as f-MRI and MR spectroscopy. The comparisons with state-of-the-art algorithms on numerical phantoms and MRI data clearly demonstrate the performance improvement. [Copyright &y& Elsevier]

Magnetic resonance spectroscopy imaging (MRSI) is an attractive tool for medical imaging. However, its practical use is often limited by the intrinsic low spatial resolution and long acquisition time. Spectral localization by imaging (SLIM) has been proposed as a non-Fourier reconstruction algorithm that incorporates spatial a priori information about spectroscopically uniform compartments. Unfortunately, the influence of the magnetic field inhomogeneity—in particular, the susceptibility effects at tissues' boundaries—undermines the validity of the compartmental model. Therefore, we propose BSLIM as an extension of SLIM with field inhomogeneity compensation. A B0-field inhomogeneity map, which can be acquired rapidly and at high resolution, is used by the new algorithm as additional a priori information. We show that the proposed method is distinct from the generalized SLIM (GSLIM) framework. Experimental results of a two-compartment phantom demonstrate the feasibility of the method and the importance of inhomogeneity compensation. [ABSTRACT FROM AUTHOR]

Side experiments are performed on radiomics models to improve their reproducibility. We measure the impact of myocardial masks, radiomic side experiments and data augmentation for information transfer (DAFIT) approach to differentiate patients with and without pulmonary hypertension (PH) using cardiac MRI (CMRI) derived radiomics. Feature extraction was performed from the left ventricle (LV) and right ventricle (RV) myocardial masks using CMRI in 82 patients (42 PH and 40 controls). Various side study experiments were evaluated: Original data without and with intraclass correlation (ICC) feature-filtering and DAFIT approach (without and with ICC feature-filtering). Multiple machine learning and feature selection strategies were evaluated. Primary analysis included all PH patients with subgroup analysis including PH patients with preserved LVEF (≥ 50%). For both primary and subgroup analysis, DAFIT approach without feature-filtering was the highest performer (AUC 0.957–0.958). ICC approaches showed poor performance compared to DAFIT approach. The performance of combined LV and RV masks was superior to individual masks alone. There was variation in top performing models across all approaches (AUC 0.862–0.958). DAFIT approach with features from combined LV and RV masks provide superior performance with poor performance of feature filtering approaches. Model performance varies based upon the feature selection and model combination. [ABSTRACT FROM AUTHOR]

We introduce a kernel low-rank algorithm to recover free-breathing and ungated dynamic MRI from spiral acquisitions without explicit k-space navigators. It is often challenging for low-rank methods to recover free-breathing and ungated images from undersampled measurements; extensive cardiac and respiratory motion often results in the Casorati matrix not being sufficiently low-rank. Therefore, we exploit the non-linear structure of the dynamic data, which gives the low-rank kernel matrix. Unlike prior work that rely on navigators to estimate the manifold structure, we propose a kernel low-rank matrix completion method to directly fill in the missing k-space data from variable density spiral acquisitions. We validate the proposed scheme using simulated data and in-vivo data. Our results show that the proposed scheme provides improved reconstructions compared to the classical methods such as low-rank and XD-GRASP. The comparison with breath-held cine data shows that the quantitative metrics agree, whereas the image quality is marginally lower. [ABSTRACT FROM AUTHOR]

An abstract of the conference paper "Accelerated imaging of rest and stress myocardial perfusion MRI using multi-coil k-t SLR: A feasibility study," by Sajan Goud Lingala and colleagues is presented.

Hyperspectral image (HSI) restoration is an important preprocessing step in HSI data analysis to improve the image quality for subsequent applications of HSI. In this article, we introduce a spatial–spectral patch-based nonconvex sparsity and low-rank regularization method for HSI restoration. In contrast to traditional approaches based on convex penalties or nonconvex spectral penalty alone, we consider the sparsity of HSI in the spatial–spectral domain and combine the nonconvex low-rank penalty and the nonconvex 3-D total variation (TV)-like sparsity regularization to fully exploit the correlations in both spatial–spectral dimensions of the HSI data set. In addition, we propose a fast iterative variable splitting-based algorithm to effectively solve the corresponding optimization problem. Numerical experiments on both simulated and real HSI data sets demonstrate that the proposed nonconvex low-rank and TV (NonLRTV) method significantly improves the recovered image quality compared with the state-of-the-art algorithms. [ABSTRACT FROM AUTHOR]

Clustering is a challenging problem in unsupervised learning. In lieu of a gold standard, stability has become a valuable surrogate to performance and robustness. In this work, we propose a non-parametric bootstrapping approach to estimating the stability of a clustering method, which also captures stability of the individual clusters and observations. This flexible framework enables different types of comparisons between clusterings and can be used in connection with two possible bootstrap approaches for stability. The first approach, scheme 1, can be used to assess confidence (stability) around clustering from the original dataset based on bootstrap replications. A second approach, scheme 2, searches over the bootstrap clusterings for an optimally stable partitioning of the data. The two schemes accommodate different model assumptions that can be motivated by an investigator's trust (or lack thereof) in the original data and additional computational considerations. We propose a hierarchical visualization extrapolated from the stability profiles that give insights into the separation of groups, and projected visualizations for the inspection of the stability of individual operations. Our approaches show good performance in simulation and on real data. These approaches can be implemented using the R package bootcluster that is available on the Comprehensive R Archive Network (CRAN). [ABSTRACT FROM AUTHOR]

Validation is arguably the bottleneck in the diffusion magnetic resonance imaging (MRI) community. This paper evaluates and compares 20 algorithms for recovering the local intra-voxel fiber structure from diffusion MRI data and is based on the results of the “HARDI reconstruction challenge” organized in the context of the “ISBI 2012” conference. Evaluated methods encompass a mixture of classical techniques well known in the literature such as diffusion tensor, Q-Ball and diffusion spectrum imaging, algorithms inspired by the recent theory of compressed sensing and also brand new approaches proposed for the first time at this contest. To quantitatively compare the methods under controlled conditions, two datasets with known ground-truth were synthetically generated and two main criteria were used to evaluate the quality of the reconstructions in every voxel: correct assessment of the number of fiber populations and angular accuracy in their orientation. This comparative study investigates the behavior of every algorithm with varying experimental conditions and highlights strengths and weaknesses of each approach. This information can be useful not only for enhancing current algorithms and develop the next generation of reconstruction methods, but also to assist physicians in the choice of the most adequate technique for their studies. [ABSTRACT FROM AUTHOR]

The clinical utility of myocardial perfusion MR imaging (MPI) is often restricted by the inability of current acquisition schemes to simultaneously achieve high spatio-temporal resolution, good volume coverage, and high signal to noise ratio. Moreover, many subjects often find it difficult to hold their breath for sufficiently long durations making it difficult to obtain reliable MPI data. Accelerated acquisition of free breathing MPI data can overcome some of these challenges. Recently, an algorithm termed as k − t SLR has been proposed to accelerate dynamic MRI by exploiting sparsity and low rank properties of dynamic MRI data. The main focus of this paper is to further improve k − t SLR and demonstrate its utility in considerably accelerating free breathing MPI. We extend its previous implementation to account for multi-coil radial MPI acquisitions. We perform k − t sampling experiments to compare different radial trajectories and determine the best sampling pattern. We also introduce a novel augmented Lagrangian framework to considerably improve the algorithm’s convergence rate. The proposed algorithm is validated using free breathing rest and stress radial perfusion data sets from two normal subjects and one patient with ischemia. k − t SLR was observed to provide faithful reconstructions at high acceleration levels with minimal artifacts compared to existing MPI acceleration schemes such as spatio-temporal constrained reconstruction and k − t SPARSE/SENSE. [ABSTRACT FROM AUTHOR]

We introduce a novel algorithm to reconstruct dynamic magnetic resonance imaging (MRI) data from under-sampled k-t space data. In contrast to classical model based cine MRI schemes that rely on the sparsity or banded structure in Fourier space, we use the compact representation of the data in the Karhunen Louve transform (KLT) domain to exploit the correlations in the dataset. The use of the data-dependent KL transform makes our approach ideally suited to a range of dynamic imaging problems, even when the motion is not periodic. In comparison to current KLT-based methods that rely on a two-step approach to first estimate the basis functions and then use it for reconstruction, we pose the problem as a spectrally regularized matrix recovery problem. By simultaneously determining the temporal basis functions and its spatial weights from the entire measured data, the proposed scheme is capable of providing high quality reconstructions at a range of accelerations. In addition to using the compact representation in the KLT domain, we also exploit the sparsity of the data to further improve the recovery rate. Validations using numerical phantoms and in vivo cardiac perfusion MRI data demonstrate the significant improvement in performance offered by the proposed scheme over existing methods. [ABSTRACT FROM AUTHOR]