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The articles in this special section focus on computational magnetic resonance imaging (MRI) using compressed sensing applications. Presents recent developments in computational MRI. These developments are pushing the frontier of computational imaging beyond CS. Similar to CS, most of these algorithms rely on image representation in one form or another. However, the common recent thread is the departure from handcrafted image representations to learning-based image representations. These learned representations are seamlessly combined with clever measurement strategies to significantly advance the state of the art in a number of areas. Several exciting applications including significantly improved spatial and temporal resolution, a considerable reduction in scan time, measurement of biophysical parameters directly from highly undersampled data, and direct measurement of very high-dimensional data are reviewed in this special issue of SPM. This issue describes key ideas underlying the computational approaches used in MRI. These approaches range from CS algorithms that rely on fixed transforms or dictionaries, to adaptive or shallow-learning algorithms that adapt the image representation to the data to recent deep-learning methods that learn a highly nonlinear representation from exemplar data. The articles provide insight into the capabilities of the current algorithms, their limitations, and their utility in challenging MRI problems.

In portable, three dimensional, and ultra-fast ultrasound imaging systems, there is an increasing demand for the reconstruction of high quality images from a limited number of radio-frequency (RF) measurements due to receiver (Rx) or transmit (Xmit) event sub-sampling. However, due to the presence of side lobe artifacts from RF sub-sampling, the standard beamformer often produces blurry images with less contrast, which are unsuitable for diagnostic purposes. Existing compressed sensing approaches often require either hardware changes or computationally expensive algorithms, but their quality improvements are limited. To address this problem, here we propose a novel deep learning approach that directly interpolates the missing RF data by utilizing redundancy in the Rx-Xmit plane. Our extensive experimental results using sub-sampled RF data from a multi-line acquisition B-mode system confirm that the proposed method can effectively reduce the data rate without sacrificing image quality., The title has been changed. This version will appear in IEEE Trans. on Medical Imaging

Time-of-flight magnetic resonance angiography (TOF-MRA) is one of the most widely used non-contrast MR imaging methods to visualize blood vessels, but due to the 3-D volume acquisition highly accelerated acquisition is necessary. Accordingly, high quality reconstruction from undersampled TOF-MRA is an important research topic for deep learning. However, most existing deep learning works require matched reference data for supervised training, which are often difficult to obtain. By extending the recent theoretical understanding of cycleGAN from the optimal transport theory, here we propose a novel two-stage unsupervised deep learning approach, which is composed of the multi-coil reconstruction network along the coronal plane followed by a multi-planar refinement network along the axial plane. Specifically, the first network is trained in the square-root of sum of squares (SSoS) domain to achieve high quality parallel image reconstruction, whereas the second refinement network is designed to efficiently learn the characteristics of highly-activated blood flow using double-headed projection discriminator. Extensive experiments demonstrate that the proposed learning process without matched reference exceeds performance of state-of-the-art compressed sensing (CS)-based method and provides comparable or even better results than supervised learning approaches.

Recently, deep learning based approaches for accelerated MRI have been extensively studied due to its high performance and reduced run time complexity. The existing deep learning methods for accelerated MRI are mostly supervised methods, where matched subsampled k-space data and fully sampled k-space data are necessary. However, it is hard to acquire fully sampled k-space data because of long scan time of MRI. Therefore, unsupervised method without matched label data has become a very important research topic. In this paper, we propose an unsupervised method using a novel cycle-consistent generative adversarial network (cycleGAN) with a single deep generator. We show that the proposed cy-cleGAN architecture can be derived from a dual formulation of the optimal transport with the penalized least squares cost. The results of experiments show that our method can remove aliasing patterns in downsampled MR images without the matched reference data.

Parallel MRI (pMRI) and compressed sensing MRI (CS-MRI) have been considered as two distinct reconstruction problems. Inspired by recent k-space interpolation methods, an annihilating filter based low-rank Hankel matrix approach (ALOHA) is proposed as a general framework for sparsity-driven k-space interpolation method which unifies pMRI and CS-MRI. Specifically, our framework is based on the fundamental duality between the transform domain sparsity in the primary space and the low-rankness of weighted Hankel matrix in the reciprocal space, which converts pMRI and CS-MRI to a k-space interpolation problem using structured matrix completion. Using theoretical results from the latest compressed sensing literatures, we showed that the required sampling rates for ALOHA may achieve the optimal rate. Experimental results with in vivo data for single/multi-coil imaging as well as dynamic imaging confirmed that the proposed method outperforms the state-of-the-art pMRI and CS-MRI.

The field of medical image reconstruction has seen roughly four types of methods. The first type tended to be analytical methods, such as filtered back-projection (FBP) for X-ray computed tomography (CT) and the inverse Fourier transform for magnetic resonance imaging (MRI), based on simple mathematical models for the imaging systems. These methods are typically fast, but have suboptimal properties such as poor resolution-noise trade-off for CT. A second type is iterative reconstruction methods based on more complete models for the imaging system physics and, where appropriate, models for the sensor statistics. These iterative methods improved image quality by reducing noise and artifacts. The FDA-approved methods among these have been based on relatively simple regularization models. A third type of methods has been designed to accommodate modified data acquisition methods, such as reduced sampling in MRI and CT to reduce scan time or radiation dose. These methods typically involve mathematical image models involving assumptions such as sparsity or low-rank. A fourth type of methods replaces mathematically designed models of signals and systems with data-driven or adaptive models inspired by the field of machine learning. This paper focuses on the two most recent trends in medical image reconstruction: methods based on sparsity or low-rank models, and data-driven methods based on machine learning techniques., To appear in the Proceedings of the IEEE, Special Issue on Biomedical Imaging and Analysis in the Age of Sparsity, Big Data, and Deep Learning

Purpose Magnetic resonance imaging (MRI) artifacts are originated from various sources including instability of an magnetic resonance (MR) system, patient motion, inhomogeneities of gradient fields, and so on. Such MRI artifacts are usually considered as irreversible, so additional artifact-free scan or navigator scan is necessary. To overcome these limitations, this article proposes a novel compressed sensing-based approach for removal of various MRI artifacts. Theory Recently, the annihilating filter based low-rank Hankel matrix approach was proposed. The annihilating filter based low-rank Hankel matrix exploits the duality between the low-rankness of weighted Hankel structured matrix and the sparsity of signal in a transform domain. Because MR artifacts usually appeared as sparse k-space components, the low-rank Hankel matrix from underlying artifact-free k-space data can be exploited to decompose the sparse outliers. Methods The sparse + low-rank decomposition framework using Hankel matrix was proposed for removal of MRI artifacts. Alternating direction method of multipliers algorithm was employed for the minimization of associated cost function with the initialized matrices from a factorization-based matrix completion. Results Experimental results demonstrated that the proposed algorithm can correct MR artifacts including herringbone (crisscross), motion, and zipper artifacts without image distortion. Conclusion The proposed method may be a robust correction solution for various MRI artifacts that can be represented as sparse outliers. Magn Reson Med 78:327-340, 2017. © 2016 International Society for Magnetic Resonance in Medicine.

Recently, balanced steady-state free precession (bSSFP) readout has been proposed for arterial spin labeling (ASL) perfusion imaging to reduce susceptibility artifacts at a relatively high spatial resolution and signal-to-noise ratio (SNR). However, the main limitation of bSSFP-ASL is the low spatial coverage. In this work, methods to increase the spatial coverage of bSSFP-ASL are proposed for distortion-free, high-resolution, whole-brain perfusion imaging. Three strategies of (i) segmentation, (ii) compressed sensing (CS) and (iii) a hybrid approach combining the two methods were tested to increase the spatial coverage of pseudo-continuous ASL (pCASL) with three-dimensional bSSFP readout. The spatial coverage was increased by factors of two, four and six using each of the three approaches, whilst maintaining the same total scan time (5.3 min). The number of segments and/or CS acceleration rate (R) correspondingly increased to maintain the same bSSFP readout time (1.2 s). The segmentation approach allowed whole-brain perfusion imaging for pCASL-bSSFP with no penalty in SNR and/or total scan time. The CS approach increased the spatial coverage of pCASL-bSSFP whilst maintaining the temporal resolution, with minimal impact on the image quality. The hybrid approach provided compromised effects between the two methods. Balanced SSFP-based ASL allows the acquisition of perfusion images with wide spatial coverage, high spatial resolution and SNR, and reduced susceptibility artifacts, and thus may become a good choice for clinical and neurological studies. Copyright © 2015 John Wiley & Sons, Ltd.

A multiple measurement vector problem (MMV) is a generalization of the compressed sensing problem that addresses the recovery of a set of jointly sparse signal vectors. One of the important contributions of this paper is to show that the seemingly least related state-of-the-art MMV joint sparse recovery algorithms—the M-SBL (multiple sparse Bayesian learning) and subspace-based hybrid greedy algorithms—have a very important link. More specifically, we show that replacing the $\log\det(\,{\cdot}\,)$ term in the M-SBL by a rank surrogate that exploits the spark reduction property discovered in the subspace-based joint sparse recovery algorithms provides significant improvements. In particular, if we use the Schatten- $p$ quasi-norm as the corresponding rank surrogate, the global minimizer of the cost function in the proposed algorithm becomes identical to the true solution as $p \rightarrow 0$ . Furthermore, under regularity conditions, we show that convergence to a local minimizer is guaranteed using an alternating minimization algorithm that has closed form expressions for each of the minimization steps, which are convex. Numerical simulations under a variety of scenarios in terms of SNR and the condition number of the signal amplitude matrix show that the proposed algorithm consistently outperformed the M-SBL and other state-of-the art algorithms.

The annihilating filter-based low-rank Hankel matrix approach (ALOHA) is one of the state-of-the-art compressed sensing approaches that directly interpolates the missing k-space data using low-rank Hankel matrix completion. The success of ALOHA is due to the concise signal representation in the k-space domain thanks to the duality between structured low-rankness in the k-space domain and the image domain sparsity. Inspired by the recent mathematical discovery that links convolutional neural networks to Hankel matrix decomposition using data-driven framelet basis, here we propose a fully data-driven deep learning algorithm for k-space interpolation. Our network can be also easily applied to non-Cartesian k-space trajectories by simply adding an additional regridding layer. Extensive numerical experiments show that the proposed deep learning method consistently outperforms the existing image-domain deep learning approaches., Accepted to IEEE Transactions on Medical Imaging

Accelerated magnetic resonance (MR) scan acquisition with compressed sensing (CS) and parallel imaging is a powerful method to reduce MR imaging scan time. However, many reconstruction algorithms have high computational costs. To address this, we investigate deep residual learning networks to remove aliasing artifacts from artifact corrupted images. The proposed deep residual learning networks are composed of magnitude and phase networks that are separately trained. If both phase and magnitude information are available, the proposed algorithm can work as an iterative k-space interpolation algorithm using framelet representation. When only magnitude data is available, the proposed approach works as an image domain post-processing algorithm. Even with strong coherent aliasing artifacts, the proposed network successfully learned and removed the aliasing artifacts, whereas current parallel and CS reconstruction methods were unable to remove these artifacts. Comparisons using single and multiple coil show that the proposed residual network provides good reconstruction results with orders of magnitude faster computational time than existing compressed sensing methods. The proposed deep learning framework may have a great potential for accelerated MR reconstruction by generating accurate results immediately., Comment: This paper will appear in IEEE Trans. Biomedical Engineering, Special Section on Deep Learning

In our recent theoretical work, we have provided a complete 1-D theory for restoring signals with finite rate of innovations (FRI) from sparse Fourier measurements using low-rank Fourier interpolation. In this work, we are expanding this theory for restoring common sparse signals where the singularity of the FRI signals is at the same position, while the unknown weights are different for each channel. We consider two situations: one for the same Fourier sampling pattern, which corresponds to the multiple measurement vector problems (MMV), and the other for different sampling patterns. We will derive performance guarantees: one for the algebraic guraantee and the other for probabilistic guarantee from randomly sampled Fourier measurements. We will discuss the relationship between the newly derived bounds and those of multiple signal classification (MUSIC) algorithm and single channel low-rank Fourier interpolation.

Compressed sensing (CS) enables significant reduction of MR acquisition time with performance guarantee. However, computational complexity of CS is usually expensive. To address this, here we propose a novel deep residual learning algorithm to reconstruct MR images from sparsely sampled k-space data. In particular, based on the observation that coherent aliasing artifacts from downsampled data has topologically simpler structure than the original image data, we formulate a CS problem as a residual regression problem and propose a deep convolutional neural network (CNN) to learn the aliasing artifacts. Experimental results using single channel and multi channel MR data demonstrate that the proposed deep residual learning outperforms the existing CS and parallel imaging algorithms. Moreover, the computational time is faster in several orders of magnitude.

Compressed sensing provided a data-acquisition paradigm for sparse signals. Remarkably, it has been shown that practical algorithms provide robust recovery from noisy linear measurements acquired at a near optimal sampling rate. In many real-world applications, a signal of interest is typically sparse not in the canonical basis but in a certain transform domain, such as wavelets or the finite difference. The theory of compressed sensing was extended to the analysis sparsity model but known extensions are limited to specific choices of sensing matrix and sparsifying transform. In this paper, we propose a unified theory for robust recovery of sparse signals in a general transform domain by convex programming. In particular, our results apply to general acquisition and sparsity models and show how the number of measurements for recovery depends on properties of measurement and sparsifying transforms. Moreover, we also provide extensions of our results to the scenarios where the atoms in the transform has varying incoherence parameters and the unknown signal exhibits a structured sparsity pattern. In particular, for the partial Fourier recovery of sparse signals over a circulant transform, our main results suggest a uniformly random sampling. Numerical results demonstrate that the variable density random sampling by our main results provides superior recovery performance over known sampling strategies., 42 pages, 3 figures

In a multiple measurement vector problem (MMV), where multiple signals share a common sparse support and are sampled by a common sensing matrix, we can expect joint sparsity to enable a further reduction in the number of required measurements. While a diversity gain from joint sparsity had been demonstrated earlier in the case of a convex relaxation method using an $l_1/l_2$ mixed norm penalty, only recently was it shown that similar diversity gain can be achieved by greedy algorithms if we combine greedy steps with a MUSIC-like subspace criterion. However, the main limitation of these hybrid algorithms is that they often require a large number of snapshots or a high signal-to-noise ratio (SNR) for an accurate subspace as well as partial support estimation. One of the main contributions of this work is to show that the noise robustness of these algorithms can be significantly improved by allowing sequential subspace estimation and support filtering, even when the number of snapshots is insufficient. Numerical simulations show that a novel sequential compressive MUSIC (sequential CS-MUSIC) that combines the sequential subspace estimation and support filtering steps significantly outperforms the existing greedy algorithms and is quite comparable with computationally expensive state-of-art algorithms.

Recently, an annihilating filter based low-rank Hankel matrix approach (ALOHA) was proposed as a general framework for sparsity-driven k-space interpolation method for compressed sensing MRI (CS-MRI). The principle of ALOHA framework is based on the fundamental duality between the transform domain sparsity in the primary space and the low-rankness of weighted Hankel matrix in Fourier domain, which converts CS-MRI to a k-space interpolation problem using structured matrix completion. In this review, we explain the theory behind ALOHA. Experimental results with in vivo data for multi-coil dynamic imaging, parametric mapping as well as Nyquist ghost correction confirmed that the proposed method has potential to be a general solution of various MR imaging problems.

To reduce data rate for power-limited portable ultrasound imaging systems, various compressed sensing approaches have been investigated. However, most of the existing approaches require either hardware changes or computationally expensive forward modeling of wave propagation. To overcome these limitations, here we propose a novel low rank interpolation method that exploits the annihilation property of ultrasound measurements. Specifically, based on the observation that the pre-beamformed signals from a ultrasound probe have significant redundancy in spatial domain, only random subset of scan line measurements are obtained and the missing data are interpolated using a recently proposed annihilating filter-based low-rank Hankel matrix approach (ALOHA). Moreover, we exploit temporal correlation between the measurements from consecutive frames by augmenting Hankel matrix side by side for a low rank matrix completion. Reconstruction results confirmed that the proposed method can effectively reduce the data rate for ultrasound acquisition without sacrificing the image quality.

The multiple measurement vector (MMV) problem addresses the identification of unknown input vectors that share common sparse support. Even though MMV problems have been traditionally addressed within the context of sensor array signal processing, the recent trend is to apply compressive sensing (CS) due to its capability to estimate sparse support even with an insufficient number of snapshots, in which case classical array signal processing fails. However, CS guarantees the accurate recovery in a probabilistic manner, which often shows inferior performance in the regime where the traditional array signal processing approaches succeed. The apparent dichotomy between the probabilistic CS and deterministic sensor array signal processing has not been fully understood. The main contribution of the present article is a unified approach that revisits the link between CS and array signal processing first unveiled in the mid 1990s by Feng and Bresler. The new algorithm, which we call compressive MUSIC, identifies the parts of support using CS, after which the remaining supports are estimated using a novel generalized MUSIC criterion. Using a large system MMV model, we show that our compressive MUSIC requires a smaller number of sensor elements for accurate support recovery than the existing CS methods and that it can approach the optimal -bound with finite number of snapshots even in cases where the signals are linearly dependent.

Diffuse optical tomography (DOT) is a sensitive and relatively low cost imaging modality that reconstructs optical properties of a highly scattering medium. However, due to the diffusive nature of light propagation, the problem is severely ill-conditioned and highly nonlinear. Even though nonlinear iterative methods have been commonly used, they are computationally expensive especially for three dimensional imaging geometry. Recently, compressed sensing theory has provided a systematic understanding of high resolution reconstruction of sparse objects in many imaging problems; hence, the goal of this paper is to extend the theory to the diffuse optical tomography problem. The main contributions of this paper are to formulate the imaging problem as a joint sparse recovery problem in a compressive sensing framework and to propose a novel noniterative and exact inversion algorithm that achieves the l(0) optimality as the rank of measurement increases to the unknown sparsity level. The algorithm is based on the recently discovered generalized MUSIC criterion, which exploits the advantages of both compressive sensing and array signal processing. A theoretical criterion for optimizing the imaging geometry is provided, and simulation results confirm that the new algorithm outperforms the existing algorithms and reliably reconstructs the optical inhomogeneities when we assume that the optical background is known to a reasonable accuracy.

Cardiac T(2) mapping is a promising method for quantitative assessment of myocardial edema and iron overload. We have developed a new multiecho fast spin echo (ME-FSE) pulse sequence for breath-hold T(2) mapping with acceptable spatial resolution. We propose to further accelerate this new ME-FSE pulse sequence using k-t focal underdetermined system solver adapted with a framework that uses both compressed sensing and parallel imaging (e.g., sensitivity encoding) to achieve higher spatial resolution. We imaged 12 control subjects in midventricular short-axis planes and compared the accuracy of T(2) measurements obtained using ME-FSE with generalized autocalibrating partially parallel acquisitions and ME-FSE with k-t focal underdetermined system solver. For image reconstruction, we used a bootstrapping two-step approach, where in the first step fast Fourier transform was used as the sparsifying transform and in the final step principal component analysis was used as the sparsifying transform. When compared with T(2) measurements obtained using generalized autocalibrating partially parallel acquisitions, T(2) measurements obtained using k-t focal underdetermined system solver were in excellent agreement (mean difference = 0.04 msec; upper/lower 95% limits of agreement were 2.26/-2.19 msec, respectively). The proposed accelerated ME-FSE pulse sequence with k-t focal underdetermined system solver is a promising investigational method for rapid T(2) measurement of the heart with relatively high spatial resolution (1.7 × 1.7 mm(2) ).

Metal artifact removal (MAR) is one of the most important issues in x-ray CT reconstruction. Various methods have been suggested for metal artifact removal, among which projection modification and iterative methods are most popular. While those methods mainly focus on removing background artifacts, for some applications such as dental CT the correct reconstruction of metallic inserts is also important. For this application, we formulate the MAR problem as a sparse recovery problem since metallic inserts usually occupy very little volume within a field of view. One of the main advantages of this approach is to overcome the inconsistency of sinograms from metal artifacts by imposing a geometric constraint, "sparsity". As a side product of this formulation, a significant reduction of the sample views is feasible for metal part reconstruction without sacrificing quality, thanks to the compressed sensing theory, which minimizes the additional computational overhead. Numerical results confirm that metallic inserts can be accurately reconstructed with a significant reduction of computation time.

A compressed sensing dynamic MR technique called k-t FOCUSS (k-t FOCal Underdetermined System Solver) has been recently proposed. It outperforms the conventional k-t BLAST/SENSE (Broad-use Linear Acquisition Speed-up Technique/SENSitivity Encoding) technique by exploiting the sparsity of x-f signals. This paper applies this idea to radial trajectories for high-resolution cardiac cine imaging. Radial trajectories are more suitable for high-resolution dynamic MRI than Cartesian trajectories since there is smaller tradeoff between spatial resolution and number of views if streaking artifacts due to limited views can be resolved. As shown for Cartesian trajectories, k-t FOCUSS algorithm efficiently removes artifacts while preserving high temporal resolution. k-t FOCUSS algorithm applied to radial trajectories is expected to enhance dynamic MRI quality. Rather than using an explicit gridding method, which transforms radial k-space sampling data to Cartesian grid prior to applying k-t FOCUSS algorithms, we use implicit gridding during FOCUSS iterations to prevent k-space sampling errors from being propagated. In addition, motion estimation and motion compensation after the first FOCUSS iteration were used to further sparsify the residual image. By applying an additional k-t FOCUSS step to the residual image, improved resolution was achieved. In vivo experimental results show that this new method can provide high spatiotemporal resolution even from a very limited radial data set.

A model-based dynamic MRI called k-t BLAST/SENSE has drawn significant attention from the MR imaging community because of its improved spatio-temporal resolution. Recently, we showed that the k-t BLAST/SENSE corresponds to the special case of a new dynamic MRI algorithm called k-t FOCUSS that is optimal from a compressed sensing perspective. The main contribution of this article is an extension of k-t FOCUSS to a more general framework with prediction and residual encoding, where the prediction provides an initial estimate and the residual encoding takes care of the remaining residual signals. Two prediction methods, RIGR and motion estimation/compensation scheme, are proposed, which significantly sparsify the residual signals. Then, using a more sophisticated random sampling pattern and optimized temporal transform, the residual signal can be effectively estimated from a very small number of k-t samples. Experimental results show that excellent reconstruction can be achieved even from severely limited k-t samples without aliasing artifacts. Magn Reson Med 61:103–116, 2009.

Recent theory of compressed sensing informs us that near-exact recovery of an unknown sparse signal is possible from a very limited number of Fourier samples by solving a convex L1 optimization problem. The main contribution of the present letter is a compressed sensing-based novel nonparametric shape estimation framework and a computational algorithm for binary star shape objects, whose radius functions belong to the space of bounded-variation functions. Specifically, in contrast with standard compressed sensing, the present approach involves directly reconstructing the shape boundary under sparsity constraint. This is done by converting the standard pixel-based reconstruction approach into estimation of a nonparametric shape boundary on a wavelet basis. This results in an L1 minimization under a nonlinear constraint, which makes the optimization problem nonconvex. We solve the problem by successive linearization and application of one-dimensional L1 minimization, which significantly reduces the number of sampling requirements as well as the computational burden. Fourier imaging simulation results demonstrate that high quality reconstruction can be quickly obtained from a very limited number of samples. Furthermore, the algorithm outperforms the standard compressed sensing reconstruction approach using the total variation norm.

The dynamic MR imaging of time-varying objects, such as beating hearts or brain hemodynamics, requires a significant reduction of the data acquisition time without sacrificing spatial resolution. The classical approaches for this goal include parallel imaging, temporal filtering and their combinations. Recently, model-based reconstruction methods called k-t BLAST and k-t SENSE have been proposed which largely overcome the drawbacks of the conventional dynamic imaging methods without a priori knowledge of the spectral support. Another recent approach called k-t SPARSE also does not require exact knowledge of the spectral support. However, unlike k-t BLAST/SENSE, k-t SPARSE employs the so-called compressed sensing (CS) theory rather than using training. The main contribution of this paper is a new theory and algorithm that unifies the above mentioned approaches while overcoming their drawbacks. Specifically, we show that the celebrated k-t BLAST/SENSE are the special cases of our algorithm, which is asymptotically optimal from the CS theory perspective. Experimental results show that the new algorithm can successfully reconstruct a high resolution cardiac sequence and functional MRI data even from severely limited k-t samples, without incurring aliasing artifacts often observed in conventional methods.

In this paper, we review joint sparse recovery based reconstruction approach for inverse scattering problems that can solve the nonlnear inverse scattering probleme without linearization or iterative Green's function update. The main idea is to exploit the common support conditions of anomalies during multiple illumination or current injections, after which unknown potential or field can be estimated using recursive integral equation relationship. Explicit derivation for electric impedance tomography and diffuse optical tomography are discussed.

Conventional functional magnetic resonance imaging (fMRI) technique known as gradient-recalled echo (GRE) echo-planar imaging (EPI) is sensitive to image distortion and degradation caused by local magnetic field inhomogeneity at high magnetic fields. Non-EPI sequences such as spoiled gradient echo and balanced steady-state free precession (bSSFP) have been proposed as an alternative high-resolution fMRI technique; however, the temporal resolution of these sequences is lower than the typically used GRE-EPI fMRI. One potential approach to improve the temporal resolution is to use compressed sensing (CS). In this study, we tested the feasibility ofk-tFOCUSS—one of the high performance CS algorithms for dynamic MRI—for non-EPI fMRI at 9.4T using the model of rat somatosensory stimulation. To optimize the performance of CS reconstruction, different sampling patterns andk-tFOCUSS variations were investigated. Experimental results show that an optimizedk-tFOCUSS algorithm with acceleration by a factor of 4 works well for non-EPI fMRI at high field under various statistical criteria, which confirms that a combination of CS and a non-EPI sequence may be a good solution for high-resolution fMRI at high fields.

In this paper, we propose a novel k-space method called ALOHA (Annihilating filter based LOw-rank Hankel matrix Approach) that unifies parallel imaging and compressed sensing as a k-space data interpolation problem. Specifically, ALOHA employs annihilating filter relationships originated from the intrinsic image property originated from the finite rate of innovation model, as well as the multi-coil acquisition physics. By interchanging the annihilating filter with the k-space measurement, a rank-deficient block Hankel structured matrix can be obtained, whose missing elements can be restored by a low rank matrix completion algorithm. To exploit the low rank Hankel structure, we develop an alternating direction method of multiplier (ADMM) method with initialisation from low rank matrix fitting (LMaFit) algorithm. Additionally, we develop a novel pyramidal representation of the Hankel structured matrix to reduce the computational complexity of the algorithm. ALOHA can be universally applied to compressed sensing MRI as well as parallel imaging for both static and dynamic applications. Experimental results with real in vivo data confirmed that ALOHA outperforms the existing state-of-the-art parallel and compressed sensing MRI.

The combination of the PI with CS reconstruction has been an important research topic in MR community due to its potential for further acceleration in MR acquisition. In particular, the application to the 3D volumetric imaging has great potential due to the introduction of additional dimension along slice direction. In this work, we propose a combined approach of dynamic compressed sensing (CS) and parallel imaging (PI) for dynamic simultaneous multislice (SMS) imaging using multi-band RF pulses. The proposed algorithm is tested to dynamic contrast-enhanced angiography to observe brain tissue dynamics. SMS image of slice-direction acceleration factor of 2,4 and 8 with in-plane acceleration of 2 are reconstructed by the proposed multi-band dynamic CS algorithm. The reconstructed results show that a proper combination of CS and parallel imaging can effectively suppress noise propagation and provide improved spatio-temporal resolution under high acceleration factor.

One of important applications of dynamic contrast-enhanced (DCE) MRI is to observe brain tissue dynamics. In this work, we applied a combined approach of dynamic compressed sensing (CS) and parallel imaging for volumetric DCE-MRI. The combination of the parallel imaging with CS reconstruction has been a topic of significant interest in MR community due to its potential for further acceleration in MR acquisition. In particular, the application to the 3D volumetric imaging has great potential due to the introduction of additional dimension along slice direction. Here, we proposed two different combinations depending on their encoding schemes: i.e. 3D encoding and simultaneous multislice imaging (SMS) using multiband RF pulses. Experiments show that a proper combination of CS and parallel imaging can effectively suppress noise propagation and provide improved spatio-temporal resolution.

One of the technical challenges in cine magnetic resonance imaging (MRI) is to reduce the acquisition time to enable the high spatio-temporal resolution imaging of a cardiac volume within a short scan time. Recently, compressed sensing approaches have been investigated extensively for highly accelerated cine MRI by exploiting transform domain sparsity using linear transforms such as wavelets, and Fourier. However, in cardiac cine imaging, the cardiac volume changes significantly between frames, and there often exist abrupt pixel value changes along time. In order to effectively sparsify such temporal variations, it is necessary to exploit temporal redundancy along motion trajectories. This paper introduces a novel patch-based reconstruction method to exploit geometric similarities in the spatio-temporal domain. In particular, we use a low rank constraint for similar patches along motion, based on the observation that rank structures are relatively less sensitive to global intensity changes, but make it easier to capture moving edges. A Nash equilibrium formulation with relaxation is employed to guarantee convergence. Experimental results show that the proposed algorithm clearly reconstructs important anatomical structures in cardiac cine image and provides improved image quality compared to existing state-of-the-art methods such as k-t FOCUSS, k-t SLR, and MASTeR.

In this paper, a novel patch-based signal processing algorithm for motion estimated/compensated compressed sensing dynamic MR imaging is proposed. More specifically, we impose a non-convex patch-based low-rank penalty that exploits self-similarities within the images. This penalty is shown to favor capturing geometric features such as edges rather than reconstructing the background noises. To solve the resulting non-convex optimization problem, we propose a globally convergent concave-convex procedure (CCCP) using convex conju- gate, which has closed form solution at each sub-iteration. Experimental results demonstrate that the proposed algorithm outperforms the existing ones.

Compressed sensing (CS) may be useful for accelerating data acquisitions in high-resolution fMRI. However, due to the inherent slow temporal dynamics of the hemodynamic signals and concerns of potential statistical power loss, the CS approach for fMRI (CS–fMRI) has not been extensively investigated. To evaluate the utility of CS in fMRI application, we systematically investigated the properties of CS–fMRI using computer simulations and in vivo experiments of rat forepaw sensory and odor stimulations with gradient-recalled echo (GRE) and echo planar imaging (EPI) sequences. Various undersampling patterns along the phase-encoding direction were studied and k–t FOCUSS was used as the CS reconstruction algorithm, which exploits the temporal redundancy of images. Functional sensitivity, specificity, and time courses were compared between fully-sampled and CS–fMRI with reduction factors of 2 and 4. CS–fMRI with GRE, but not with EPI, improves the statistical sensitivity for activation detection over the fully sampled data when the ratio of the fMRI signal change to noise is low. CS improves the temporal resolution and reduces temporal noise correlations. While CS reduces the functional response amplitudes, the noise variance is also reduced to make the overall activation detection more sensitive. Consequently, CS is a valuable fMRI acceleration approach, especially for GRE fMRI studies.

The multiple measurement vector problem (MMV) is a generalization of the compressed sensing problem that addresses the recovery of a set of jointly sparse signal vectors. One of the important contributions of this paper is to reveal that the seemingly least related state-of-art MMV joint sparse recovery algorithms - M-SBL (multiple sparse Bayesian learning) and subspace-based hybrid greedy algorithms - have a very important link. More specifically, we show that replacing the log det(·) term in M-SBL by a log det(·) rank proxy that exploits the spark reduction property discovered in subspace-based joint sparse recovery algorithms, provides significant improvements. Theoretical analysis demonstrates that even thoughM-SBL is often unable to remove all localminimizers, the proposed method can do so under fairly mild conditions, without affecting the global minimizer.

One of the technical challenges of the predication/residual encoding in motion estimated and compensated k-t FOCUSS is that after the prediction, the energy of the residual measurement is significantly reduced compared to the original measurement. This implies that the residual measurement should be judiciously used to recover important geometric features rather than background noise during residual encoding stage. To address this, this paper proposes a novel patch-based residual encoding scheme to exploit geometric similarity in the residual images. In particular, this paper is interested in patch-based low rank constraint from similarity patches [1] since rank structures are relatively less sensitive to global intensity changes but easier to capture edges and etc. To address the nonconvexity and non-smoothess of the rank penalty, a concave-convex procedure is proposed. Experimental results show that the proposed algorithm clearly reconstructs important anatomic structures in cardiac cine image and provides significant performance improvement compared to the existing motion compensated k-t FOCUSS.

We study a multiple measurement vector problem (MMV), where multiple signals share a common sparse support and are sampled by a common sensing matrix. While a diversity gain from joint sparsity had been demonstrated earlier in the case of a convex relaxation method using a mixed norm, only recently was it shown that similar gain can be achieved by greedy algorithms if we combine greedy steps with a MUSIC-like subspace criterion. However, the main limitation of these hybrid algorithms is that they require a large number of snapshots or a high signal-to-noise ratio (SNR) for an accurate subspace as well as partial support estimation. Hence, in this work, we show that the noise robustness of these algorithms can be significantly improved by allowing sequential subspace estimation and support filtering, even when the number of snapshots is insufficient. Numerical simulations show that the proposed algorithms significantly outperform the existing greedy algorithms and are quite comparable with computationally expensive state-of-art algorithms.

Functional near infrared spectroscopy (fNIRS) is a non-invasive imaging modality to measure functional brain activities. Many researches have investigated diffuse optical tomography (DOT) to overcome the limitation of lack of depth information in fNIRS topographic approach. In this paper, we proposes a novel compressed sensing approach, especially using a 2-thresholding algorithm, that directly reconstructs statistical parameter maps by exploiting spatio-temporal sparsity of neural activation. The final reconstruction algorithm has very intuitive form which is similar to conventional fDOT with SPM analysis. However, the main advantage of the new algorithm is that the unknown weighting components in inversion kernel are iteratively updated for more accurate reconstruction which significantly improves the reconstruction performance. Experimental results demonstrated that the localization error using the proposed method is competitive with that of fMRI.

A non-local motion compensation algorithm combined with k-t FOCUSS for high resolution compressed sensing cardiac cine imaging is proposed in this paper. While conventional non-local means algorithms use self-similarity, our method collects similar blocks from another reference frame that is obtained during diastole phase. We show that this non-local motion compensation is optimal in MMSE sense, if the probability for each candidate patch is uniform. Experimental results show that the proposed algorithm clearly reconstructs important edge boundaries in cardiac cine imaging and provides significant performance improvement compared to the existing motion compensated k-t FOCUSS.

Dynamic tracking of sparse targets has been one of the important topics in array signal processing. Recently, compressed sensing (CS) approaches have been extensively investigated as a new tool for this problem using partial support information obtained by exploiting temporal redundancy. However, most of these approaches are formulated under single measurement vector compressed sensing (SMV-CS) framework, where the performance guarantees are only in a probabilistic manner. The main contribution of this paper is to allow deterministic tracking of time varying supports with multiple measurement vectors (MMV) by exploiting multi-sensor diversity. In particular, we show that a novel compressive MUSIC (CS-MUSIC) algorithm with optimized partial support selection not only allows removal of inaccurate portion of previous support estimation but also enables addition of newly emerged part of unknown support. Numerical results confirm the theory.

Recently, there has been increased interest in the usage of neuroimaging techniques to investigate what happens in the brain at rest. Functional imaging studies have revealed that the default-mode network activity is disrupted in Alzheimer's disease (AD). However, there is no consensus, as yet, on the choice of analysis method for the application of resting-state analysis for disease classification. This paper proposes a novel compressed sensing based resting-state fMRI analysis tool called Sparse-SPM. As the brain's functional systems has shown to have features of complex networks according to graph theoretical analysis, we apply a graph model to represent a sparse combination of information flows in complex network perspectives. In particular, a new concept of spatially adaptive design matrix has been proposed by implementing sparse dictionary learning based on sparsity. The proposed approach shows better performance compared to other conventional methods, such as independent component analysis (ICA) and seed-based approach, in classifying the AD patients from normal using resting-state analysis.

A novel data-driven sparse generalized linear model (GLM) and statistical analysis method for fMRI is developed. Although independent component analysis (ICA) has been broadly applied to fMRI to separate spatially or temporally independent components, recent studies show that ICA does not guarantee independence of simultaneously occurred distinct activity patterns in the brain and sparsity of the signal has been shown to be more important. Motivated from the ICA and biological findings such as sparse coding in the primary visual cortex simple cells, we propose a compressed sensing based data-driven sparse GLM solely based upon the sparsity of the signal. It enables estimation of spatially adaptive design matrix from sparse signal components that represent synchronous neural hemodynamics. Furthermore, an MDL based model order selection rule can determine unknown sparsity for sparse dictionary learning.

Since the advent of compressed sensing in dynamic MR imaging area, a number of l 1 -compressed sensing algorithms have been proposed to improve the resolution. Recently, it was shown that by solving an l p minimization problem with 0 ≤ p < 1, the number of required measurements for an exact sparse reconstruction is more reduced than in solving an l 1 minimization. However, when 0 ≤ p < 1, the problem is not convex and there exist many local minima. To deal with this problem, we adopted an empirical Bayesian approach called sparse Bayesian learning (SBL). The main contribution of this paper is to extend the idea for parallel dynamic MR imaging problems. By exploiting the simultaneous sparsity, the algorithm outperforms other methods, especially when the coil sensitivity map is not accurate. Numerical results confirms the theory.

For medical image analysis, the test statistic of the measurements is usually constructed at every voxels in space and thresholded to determine the regions of significant signals. This thresholding produces a small patch of regions around the critical values of the test statistic. It is known that the probability of the critical values bigger than a specific threshold can be computed as the expectation of the Euler characteristic of the patch. Motivated by this topological connection, we present a new computational framework of modeling various functional measurements as topological objects. The level set associated with functional measurements can be approximated using a simplicial complex consisting of nodes and links. The existence of links basically determine the underlying topological structure of the signal. The strength of links can be modeled using an underdetermined linear model. By incorporating sparsity into the model, the links can be sparsely obtained making interpretation and visualization of the simplicial complex easier. The main contribution of this paper is showing the relationship between sparse topological structures to the sparse regression framework. We apply this novel framework in constructing a structural brain network model.

Diffuse optical tomography (DOT) is an emerging imaging modality to reconstruct the optical parameters of a highly scattering medium. However, ill-posedness and nonlinearity of light scattering make the DOT problem very difficult. We showed that DOT problem can be formulated as a multiple measurement vector (MMV) problem, and compressive sensing approach like S-OMP can be used. However, for a limited number of illumination patterns, the conventional compressed sensing (CS) approach for DOT was not satisfactory. The main objective of this paper is to propose a new non-iterative and exact reconstruction algorithm for the diffuse optical tomography problem that outperforms the conventional compressive sensing approach, thanks to a recently invented generalized MUSIC algorithm. Simulation results confirm that the new algorithm outperforms the previous algorithms and reliably reconstructs optical inhomogeneities.

Multiple measurement vector (MMV) problem addresses the identification of unknown input vectors that share common sparse support. The MMV problems had been traditionally addressed either by sensor array signal processing or compressive sensing. However, recent breakthrough in this area such as compressive MUSIC (CS-MUSIC) or subspace-augumented MUSIC (SA-MUSIC) optimally combines the compressive sensing (CS) and array signal processing such that $k-r$ supports are first found by CS and the remaining $r$ supports are determined by generalized MUSIC criterion, where $k$ and $r$ denote the sparsity and the independent snapshots, respectively. Even though such hybrid approach significantly outperforms the conventional algorithms, its performance heavily depends on the correct identification of $k-r$ partial support by compressive sensing step, which often deteriorate the overall performance. The main contribution of this paper is, therefore, to show that as long as $k-r+1$ correct supports are included in any $k$-sparse CS solution, the optimal $k-r$ partial support can be found using a subspace fitting criterion, significantly improving the overall performance of CS-MUSIC. Furthermore, unlike the single measurement CS counterpart that requires infinite SNR for a perfect support recovery, we can derive an information theoretic sufficient condition for the perfect recovery using CS-MUSIC under a {\em finite} SNR scenario., Comment: 9 pages, 2 figures

We propose a novel statistical analysis method for functional magnetic resonance imaging (fMRI) to overcome the drawbacks of conventional data-driven methods such as the independent component analysis (ICA). Although ICA has been broadly applied to fMRI due to its capacity to separate spatially or temporally independent components, the assumption of independence has been challenged by recent studies showing that ICA does not guarantee independence of simultaneously occurring distinct activity patterns in the brain. Instead, sparsity of the signal has been shown to be more promising. This coincides with biological findings such as sparse coding in V1 simple cells, electrophysiological experiment results in the human medial temporal lobe, etc. The main contribution of this paper is, therefore, a new data driven fMRI analysis that is derived solely based upon the sparsity of the signals. A compressed sensing based data-driven sparse generalized linear model is proposed that enables estimation of spatially adaptive design matrix as well as sparse signal components that represent synchronous, functionally organized and integrated neural hemodynamics. Furthermore, a minimum description length (MDL)-based model order selection rule is shown to be essential in selecting unknown sparsity level for sparse dictionary learning. Using simulation and real fMRI experiments, we show that the proposed method can adapt individual variation better compared to the conventional ICA methods.