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Image Quality Assessment (IQA) is essential in various Computer Vision tasks such as image deblurring and super-resolution. However, most IQA methods require reference images, which are not always available. While there are some reference-free IQA metrics, they have limitations in simulating human perception and discerning subtle image quality variations. We hypothesize that the JPEG quality factor is representatives of image quality measurement, and a well-trained neural network can learn to accurately evaluate image quality without requiring a clean reference, as it can recognize image degradation artifacts based on prior knowledge. Thus, we developed a reference-free quality evaluation network, dubbed "Quality Factor (QF) Predictor", which does not require any reference. Our QF Predictor is a lightweight, fully convolutional network comprising seven layers. The model is trained in a self-supervised manner: it receives JPEG compressed image patch with a random QF as input, is trained to accurately predict the corresponding QF. We demonstrate the versatility of the model by applying it to various tasks. First, our QF Predictor can generalize to measure the severity of various image artifacts, such as Gaussian Blur and Gaussian noise. Second, we show that the QF Predictor can be trained to predict the undersampling rate of images reconstructed from Magnetic Resonance Imaging (MRI) data.

Although deep learning (DL) methods are powerful for solving inverse problems, their reliance on high-quality training data is a major hurdle. This is significant in high-dimensional (dynamic/volumetric) magnetic resonance imaging (MRI), where acquisition of high-resolution fully sampled k-space data is impractical. We introduce a novel mathematical framework, dubbed k-band, that enables training DL models using only partial, limited-resolution k-space data. Specifically, we introduce training with stochastic gradient descent (SGD) over k-space subsets. In each training iteration, rather than using the fully sampled k-space for computing gradients, we use only a small k-space portion. This concept is compatible with different sampling strategies; here we demonstrate the method for k-space "bands", which have limited resolution in one dimension and can hence be acquired rapidly. We prove analytically that our method stochastically approximates the gradients computed in a fully-supervised setup, when two simple conditions are met: (i) the limited-resolution axis is chosen randomly-uniformly for every new scan, hence k-space is fully covered across the entire training set, and (ii) the loss function is weighed with a mask, derived here analytically, which facilitates accurate reconstruction of high-resolution details. Numerical experiments with raw MRI data indicate that k-band outperforms two other methods trained on limited-resolution data and performs comparably to state-of-the-art (SoTA) methods trained on high-resolution data. k-band hence obtains SoTA performance, with the advantage of training using only limited-resolution data. This work hence introduces a practical, easy-to-implement, self-supervised training framework, which involves fast acquisition and self-supervised reconstruction and offers theoretical guarantees.

Purpose: To introduce a simple system exploitation with the potential to turn MRI scanners into general-purpose RF motion monitoring systems. Methods: Inspired by Pilot Tone (PT), this work proposes Beat Pilot Tone (BPT), in which two or more RF tones at arbitrary frequencies are transmitted continuously during the scan. These tones create motion-modulated standing wave patterns that are sensed by the receiver coil array, incidentally mixed by intermodulation in the receiver chain, and digitized simultaneously with the MRI data. BPT can operate at almost any frequency as long as the intermodulation products lie within the bandwidth of the receivers. BPT's mechanism is explained in electromagnetic simulations and validated experimentally. Results: Phantom and volunteer experiments over a range of transmit frequencies suggest that BPT may offer frequency-dependent sensitivity to motion. Using a semi-flexible body receiver array, BPT appears to sense cardiac-induced body vibrations at microwave frequencies (1.2 GHz and greater). At lower frequencies, it exhibits a similar cardiac signal shape to PT, likely due to blood volume changes. Other volunteer experiments with respiratory, bulk, and head motion show that BPT can achieve greater sensitivity to motion than PT and greater separability between motion types. Basic multiple-input multiple-output (4x22 MIMO) operation with simultaneous PT and BPT in head motion is demonstrated using two transmit antennas and a 22-channel head-neck coil. Conclusion: BPT may offer a rich source of motion information that is frequency-dependent, simultaneous, and complementary to PT and the MRI exam., Comment: Accepted by the journal Magnetic Resonance in Medicine, April 2024

Magnetic Resonance Fingerprinting (MRF) is an efficient quantitative MRI technique that can extract important tissue and system parameters such as T1, T2, B0, and B1 from a single scan. This property also makes it attractive for retrospectively synthesizing contrast-weighted images. In general, contrast-weighted images like T1-weighted, T2-weighted, etc., can be synthesized directly from parameter maps through spin-dynamics simulation (i.e., Bloch or Extended Phase Graph models). However, these approaches often exhibit artifacts due to imperfections in the mapping, the sequence modeling, and the data acquisition. Here we propose a supervised learning-based method that directly synthesizes contrast-weighted images from the MRF data without going through the quantitative mapping and spin-dynamics simulation. To implement our direct contrast synthesis (DCS) method, we deploy a conditional Generative Adversarial Network (GAN) framework and propose a multi-branch U-Net as the generator. The input MRF data are used to directly synthesize T1-weighted, T2-weighted, and fluid-attenuated inversion recovery (FLAIR) images through supervised training on paired MRF and target spin echo-based contrast-weighted scans. In-vivo experiments demonstrate excellent image quality compared to simulation-based contrast synthesis and previous DCS methods, both visually as well as by quantitative metrics. We also demonstrate cases where our trained model is able to mitigate in-flow and spiral off-resonance artifacts that are typically seen in MRF reconstructions and thus more faithfully represent conventional spin echo-based contrast-weighted images., Comment: 19 pages, 8 figures

Medical electrophysiological sensors that can study the body and diagnose diseases depend on consistently low impedance electrode-skin interfaces. Clinical-standard wet electrodes use hydrogels and skin abrasion to improve the interface and thus the recorded signal quality. These electrodes are challenging to self-administer and impede in-home care. Wearable dry electrodes are more practical; however, they show higher impedances than wet electrodes and are costly to customize. This work presents a fabrication method for rapidly producing low impedance, anatomically fit dry electrodes that do not require hydrogels. By using electroless copper and gold plating with 3D printing, biocompatible electrodes can be optimized for individuals at a fraction of the cost of existing vacuum deposition-based techniques. Example 3D dry electrodes made with this process are evaluated alongside clinical-standard devices in typical scenarios to compare electrical performance and comfort. The resulting dry electrodes exhibited an average electrode-skin impedance of 66.7 k{\Omega} at 50Hz and DC offset of -20 mV without any hydrogel, which, when area normalized, is within the range achieved by wet electrodes without skin abrasion.

While open databases are an important resource in the Deep Learning (DL) era, they are sometimes used "off-label": data published for one task are used for training algorithms for a different one. This work aims to highlight that in some cases, this common practice may lead to biased, overly-optimistic results. We demonstrate this phenomenon for inverse problem solvers and show how their biased performance stems from hidden data preprocessing pipelines. We describe two preprocessing pipelines typical of open-access databases and study their effects on three well-established algorithms developed for Magnetic Resonance Imaging (MRI) reconstruction: Compressed Sensing (CS), Dictionary Learning (DictL), and DL. In this large-scale study we performed extensive computations. Our results demonstrate that the CS, DictL and DL algorithms yield systematically biased results when naively trained on seemingly-appropriate data: the Normalized Root Mean Square Error (NRMSE) improves consistently with the preprocessing extent, showing an artificial increase of 25%-48% in some cases. Since this phenomenon is generally unknown, biased results are sometimes published as state-of-the-art; we refer to that as subtle data crimes. This work hence raises a red flag regarding naive off-label usage of Big Data and reveals the vulnerability of modern inverse problem solvers to the resulting bias., Comment: 16 pages, 7 figures, two tables. Submitted to a journal

Purpose: To improve reconstruction fidelity of fine structures and textures in deep learning (DL) based reconstructions. Methods: A novel patch-based Unsupervised Feature Loss (UFLoss) is proposed and incorporated into the training of DL-based reconstruction frameworks in order to preserve perceptual similarity and high-order statistics. The UFLoss provides instance-level discrimination by mapping similar instances to similar low-dimensional feature vectors and is trained without any human annotation. By adding an additional loss function on the low-dimensional feature space during training, the reconstruction frameworks from under-sampled or corrupted data can reproduce more realistic images that are closer to the original with finer textures, sharper edges, and improved overall image quality. The performance of the proposed UFLoss is demonstrated on unrolled networks for accelerated 2D and 3D knee MRI reconstruction with retrospective under-sampling. Quantitative metrics including NRMSE, SSIM, and our proposed UFLoss were used to evaluate the performance of the proposed method and compare it with others. Results: In-vivo experiments indicate that adding the UFLoss encourages sharper edges and more faithful contrasts compared to traditional and learning-based methods with pure l2 loss. More detailed textures can be seen in both 2D and 3D knee MR images. Quantitative results indicate that reconstruction with UFLoss can provide comparable NRMSE and a higher SSIM while achieving a much lower UFLoss value. Conclusion: We present UFLoss, a patch-based unsupervised learned feature loss, which allows the training of DL-based reconstruction to obtain more detailed texture, finer features, and sharper edges with higher overall image quality under DL-based reconstruction frameworks., Comment: 35 pages, 13 figures

The Shinnar-Le-Roux (SLR) algorithm is widely used to design frequency selective pulses with large flip angles. We improve its design process to generate pulses with lower energy (by as much as 26%) and more accurate phase profiles. Concretely, the SLR algorithm consists of two steps: (1) an invertible transform between frequency selective pulses and polynomial pairs that represent Cayley-Klein (CK) parameters and (2) the design of the CK polynomial pair to match the desired magnetization profiles. Because the CK polynomial pair is bi-linearly coupled, the original algorithm sequentially solves for each polynomial instead of jointly. This results in sub-optimal pulses. Instead, we leverage a convex relaxation technique, commonly used for low rank matrix recovery, to address the bi-linearity. Our numerical experiments show that the resulting pulses are almost always globally optimal in practice. For slice excitation, the proposed algorithm results in more accurate linear phase profiles. And in general the improved pulses have lower energy than the original SLR pulses., Comment: Frank Ong and Zheng Zhong make equal contributions to the work. Submitted to IEEE Transactions on Medical Imaging

Deep learning (DL) based unrolled reconstructions have shown state-of-the-art performance for under-sampled magnetic resonance imaging (MRI). Similar to compressed sensing, DL can leverage high-dimensional data (e.g. 3D, 2D+time, 3D+time) to further improve performance. However, network size and depth are currently limited by the GPU memory required for backpropagation. Here we use a memory-efficient learning (MEL) framework which favorably trades off storage with a manageable increase in computation during training. Using MEL with multi-dimensional data, we demonstrate improved image reconstruction performance for in-vivo 3D MRI and 2D+time cardiac cine MRI. MEL uses far less GPU memory while marginally increasing the training time, which enables new applications of DL to high-dimensional MRI., Comment: 14 pages, 8 figures

The goal of this tutorial is to explain step-by-step how to implement physics-based learning for the rapid prototyping of a computational imaging system. We provide a basic overview of physics-based learning, the construction of a physics-based network, and its reduction to practice. Specifically, we advocate exploiting the auto-differentiation functionality twice, once to build a physics-based network and again to perform physics-based learning. Thus, the user need only implement the forward model process for their system, speeding up prototyping time. We provide an open-source Pytorch implementation of a physics-based network and training procedure for a generic sparse recovery problem, Comment: 3 pages, 2 figures, linked repository https://github.com/kellman/physics_based_learning

Critical aspects of computational imaging systems, such as experimental design and image priors, can be optimized through deep networks formed by the unrolled iterations of classical model-based reconstructions (termed physics-based networks). However, for real-world large-scale inverse problems, computing gradients via backpropagation is infeasible due to memory limitations of graphics processing units. In this work, we propose a memory-efficient learning procedure that exploits the reversibility of the network's layers to enable data-driven design for large-scale computational imaging systems. We demonstrate our method on a small-scale compressed sensing example, as well as two large-scale real-world systems: multi-channel magnetic resonance imaging and super-resolution optical microscopy., Comment: 9 pages, 8 figures. See also relate NeurIPS 2019 presentation arXiv:1912.05098

Purpose, To develop a high scanning efficiency, motion corrected imaging strategy for free-breathing pulmonary MRI by combining a motion compensation reconstruction with a UTE acquisition, called iMoCo UTE. Methods, An optimized golden angle ordering radial UTE sequence was used to continuously acquire data for 5 minutes. All readouts were grouped to different respiratory motion states based on self-navigator signals, then motion resolved data was reconstructed by XD Golden angle RAdial Sparse Parallel reconstruction (XD GRASP). One state from the motion resolved images was selected as a reference, and motion fields from the other states to the reference were derived via non-rigid registration. Finally, all motion resolved data and motion fields were reconstructed by using an iterative motion compensation reconstruction with a total generalized variation sparse constraint. Results, The iMoCo UTE strategy was evaluated in volunteers and non-sedated pediatric patient(4-6 y/o) studies. Images reconstructed with iMoCo UTE provided sharper anatomical lung structures, and higher apparent SNR and CNR, compared to using other motion correction strategies, such as soft-gating, motion resolved reconstruction, and non-rigid motion compensation(MoCo). iMoCo UTE also showed promising results in an infant study. Conclusions, The proposed iMoCo UTE combines self-navigation, motion modeling, and a compressed sensing reconstruction to increase scan efficiency, SNR, and reduce respiratory motion in lung MRI. This proposed strategy shows improvements in free breathing lung MRI scans, especially in very challenging application situations, such as pediatric MRI studies.

Computational imaging systems jointly design computation and hardware to retrieve information which is not traditionally accessible with standard imaging systems. Recently, critical aspects such as experimental design and image priors are optimized through deep neural networks formed by the unrolled iterations of classical physics-based reconstructions (termed physics-based networks). However, for real-world large-scale systems, computing gradients via backpropagation restricts learning due to memory limitations of graphical processing units. In this work, we propose a memory-efficient learning procedure that exploits the reversibility of the network's layers to enable data-driven design for large-scale computational imaging. We demonstrate our methods practicality on two large-scale systems: super-resolution optical microscopy and multi-channel magnetic resonance imaging., Comment: 5 pages, 2 figures, presented at NeurIPS 2019 Deep Inverse workshop

Basis pursuit is a compressed sensing optimization in which the l1-norm is minimized subject to model error constraints. Here we use a deep neural network prior instead of l1-regularization. Using known noise statistics, we jointly learn the prior and reconstruct images without access to ground-truth data. During training, we use alternating minimization across an unrolled iterative network and jointly solve for the neural network weights and training set image reconstructions. At inference, we fix the weights and pass the measurements through the network. We compare reconstruction performance between unsupervised and supervised (i.e. with ground-truth) methods. We hypothesize this technique could be used to learn reconstruction when ground-truth data are unavailable, such as in high-resolution dynamic MRI., Comment: https://deep-inverse.org/

Purpose: To develop a framework to reconstruct large-scale volumetric dynamic MRI from rapid continuous and non-gated acquisitions, with applications to pulmonary and dynamic contrast enhanced (DCE) imaging. Theory and Methods: The problem considered here requires recovering hundred-gigabytes of dynamic volumetric image data from a few gigabytes of k-space data, acquired continuously over several minutes. This reconstruction is vastly under-determined, heavily stressing computing resources as well as memory management and storage. To overcome these challenges, we leverage intrinsic three dimensional (3D) trajectories, such as 3D radial and 3D cones, with ordering that incoherently cover time and k-space over the entire acquisition. We then propose two innovations: (1) A compressed representation using multi-scale low rank matrix factorization that constrains the reconstruction problem, and reduces its memory footprint. (2) Stochastic optimization to reduce computation, improve memory locality, and minimize communications between threads and processors. We demonstrate the feasibility of the proposed method on DCE imaging acquired with a golden-angle ordered 3D cones trajectory and pulmonary imaging acquired with a bit-reversed ordered 3D radial trajectory. We compare it with "soft-gated" dynamic reconstruction for DCE and respiratory resolved reconstruction for pulmonary imaging. Results: The proposed technique shows transient dynamics that are not seen in gating based methods. When applied to datasets with irregular, or non-repetitive motions, the proposed method displays sharper image features. Conclusion: We demonstrated a method that can reconstruct massive 3D dynamic image series in the extreme undersampling and extreme computation setting., Comment: Accepted to Magnetic Resonance in Medicine

Compressed sensing takes advantage of low-dimensional signal structure to reduce sampling requirements far below the Nyquist rate. In magnetic resonance imaging (MRI), this often takes the form of sparsity through wavelet transform, finite differences, and low rank extensions. Though powerful, these image priors are phenomenological in nature and do not account for the mechanism behind the image formation. On the other hand, MRI signal dynamics are governed by physical laws, which can be explicitly modeled and used as priors for reconstruction. {1}These explicit and implicit signal priors can be synergistically combined in an inverse problem framework to recover sharp, multi-contrast images from highly accelerated scans. Furthermore, the physics-based constraints provide a recipe for recovering quantitative, bio-physical parameters from the data. This article introduces physics-based modeling constraints in MRI and shows how they can be used in conjunction with compressed sensing for image reconstruction and quantitative imaging. We describe model-based quantitative MRI, as well as its linear subspace approximation. We also discuss approaches to selecting user-controllable scan parameters given knowledge of the physical model. We present several MRI applications that take advantage of this framework for the purpose of multi-contrast imaging and quantitative mapping.

We propose a k-space preconditioning formulation for accelerating the convergence of iterative Magnetic Resonance Imaging (MRI) reconstructions from non-uniformly sampled k-space data. Existing methods either use sampling density compensations which sacrifice reconstruction accuracy, or circulant preconditioners which increase per-iteration computation. Our approach overcomes both shortcomings. Concretely, we show that viewing the reconstruction problem in the dual formulation allows us to precondition in k-space using density-compensation-like operations. Using the primal-dual hybrid gradient method, the proposed preconditioning method does not have inner loops and are competitive in accelerating convergence compared to existing algorithms. We derive l2-optimized preconditioners, and demonstrate through experiments that the proposed method converges in about ten iterations in practice., Comment: Accepted to IEEE Transaction on Medical Imaging

Purpose: Parallel imaging methods in MRI have resulted in faster acquisition times and improved noise performance. ESPIRiT is one such technique that estimates coil sensitivity maps from the auto-calibration region using an eigenvalue-based method. This method requires choosing several parameters for the the map estimation. Even though ESPIRiT is fairly robust to these parameter choices, occasionally, poor selection can result in reduced performance. The purpose of this work is to automatically select parameters in ESPIRiT for more robust and consistent performance across a variety of exams. Theory and Methods: Stein's unbiased risk estimate (SURE) is a method of calculating an unbiased estimate of the mean squared error of an estimator under certain assumptions. We show that this can be used to estimate the performance of ESPIRiT. We derive and demonstrate the use of SURE to optimize ESPIRiT parameter selection. Results: Simulations show SURE to be an accurate estimator of the mean squared error. SURE is then used to optimize ESPIRiT parameters to yield maps that are optimal in a denoising/data-consistency sense. This improves g-factor performance without causing undesirable attenuation. In-vivo experiments verify the reliability of this method. Conclusion: Simulation experiments demonstrate that SURE is an accurate estimate of expected mean squared error. Using SURE to determine ESPIRiT parameters allows for automatic parameter selections.In-vivo results are consistent with simulation and theoretical results.

Magnetic resonance imaging is capable of producing volumetric images without ionizing radiation. Nonetheless, long acquisitions lead to prohibitively long exams. Compressed sensing (CS) can enable faster scanning via sub-sampling with reduced artifacts. However, CS requires significantly higher reconstruction computation, limiting current clinical applications to 2D/3D or limited-resolution dynamic imaging. Here we analyze the practical limitations to T2 Shuffling, a four-dimensional CS-based acquisition, which provides sharp 3D-isotropic-resolution and multi-contrast images in a single scan. Our improvements to the pipeline on a single machine provide a 3x overall reconstruction speedup, which allowed us to add algorithmic changes improving image quality. Using four machines, we achieved additional 2.1x improvement through distributed parallelization. Our solution reduced the reconstruction time in the hospital to 90 seconds on a 4-node cluster, enabling its use clinically. To understand the implications of scaling this application, we simulated running our reconstructions with a multiple scanner setup typical in hospitals.

Purpose: To develop a general phase regularized image reconstruction method, with applications to partial Fourier imaging, water-fat imaging and flow imaging. Theory and Methods: The problem of enforcing phase constraints in reconstruction was studied under a regularized inverse problem framework. A general phase regularized reconstruction algorithm was proposed to enable various joint reconstruction of partial Fourier imaging, water-fat imaging and flow imaging, along with parallel imaging (PI) and compressed sensing (CS). Since phase regularized reconstruction is inherently non-convex and sensitive to phase wraps in the initial solution, a reconstruction technique, named phase cycling, was proposed to render the overall algorithm invariant to phase wraps. The proposed method was applied to retrospectively under-sampled in vivo datasets and compared with state of the art reconstruction methods. Results: Phase cycling reconstructions showed reduction of artifacts compared to reconstructions with- out phase cycling and achieved similar performances as state of the art results in partial Fourier, water-fat and divergence-free regularized flow reconstruction. Joint reconstruction of partial Fourier + water-fat imaging + PI + CS, and partial Fourier + divergence-free regularized flow imaging + PI + CS were demonstrated. Conclusion: The proposed phase cycling reconstruction provides an alternative way to perform phase regularized reconstruction, without the need to perform phase unwrapping. It is robust to the choice of initial solutions and encourages the joint reconstruction of phase imaging applications.

The task of MRI fingerprinting is to identify tissue parameters from complex-valued MRI signals. The prevalent approach is dictionary based, where a test MRI signal is compared to stored MRI signals with known tissue parameters and the most similar signals and tissue parameters retrieved. Such an approach does not scale with the number of parameters and is rather slow when the tissue parameter space is large. Our first novel contribution is to use deep learning as an efficient nonlinear inverse mapping approach. We generate synthetic (tissue, MRI) data from an MRI simulator, and use them to train a deep net to map the MRI signal to the tissue parameters directly. Our second novel contribution is to develop a complex-valued neural network with new cardioid activation functions. Our results demonstrate that complex-valued neural nets could be much more accurate than real-valued neural nets at complex-valued MRI fingerprinting., Comment: Accepted in Proc. IEEE International Conference on Image Processing (ICIP), 2017

Robustness against data inconsistencies, imaging artifacts and acquisition speed are crucial factors limiting the possible range of applications for magnetic resonance imaging (MRI). Therefore, we report a novel calibrationless parallel imaging technique which simultaneously estimates coil profiles and image content in a relaxed forward model. Our method is robust against a wide class of data inconsistencies, minimizes imaging artifacts and is comparably fast combining important advantages of many conceptually different state-of-the-art parallel imaging approaches. Depending on the experimental setting, data can be undersampled well below the Nyquist limit. Here, even high acceleration factors yield excellent imaging results while being robust to noise and the occurrence of phase singularities in the image domain, as we show on different data. Moreover, our method successfully reconstructs acquisitions with insufficient field-of-view. We further compare our approach to ESPIRiT and SAKE using spin-echo and gradient echo MRI data from the human head and knee. In addition, we show its applicability to non-Cartesian imaging on radial FLASH cardiac MRI data. Using theoretical considerations, we show that ENLIVE can be related to a low-rank formulation of blind multi-channel deconvolution, explaining why it inherently promotes low-rank solutions., Comment: 17 pages, 10 figures

Purpose: Spatio-temporal encoding (SPEN) experiments can deliver single-scan MR images without folding complications and with robustness to chemical shift and susceptibility artifacts. It is here shown that further resolution improvements can arise by relying on multiple receivers, to interpolate the sampled data along the low-bandwidth dimension. The ensuing multiple-sensor interpolation is akin to recently introduced SPEN interleaving procedures, albeit without requiring multiple shots. Methods: By casting SPEN's spatial rasterization in k-space, it becomes evident that local k-data interpolations enabled by multiple receivers are akin to real-space interleaving of SPEN images. The practical implementation of such resolution-enhancing procedure becomes similar to those normally used in SMASH or SENSE, yet relaxing these methods' fold-over constraints. Results: Experiments validating the theoretical expectations were carried out on phantoms and human volunteers on a 3T scanner. The experiments showed the expected resolution enhancement, at no cost in the sequence's complexity. With the addition of multibanding and stimulated echo procedures, 48-slices full-brain coverage could be recorded free from distortions at sub-mm resolution, in 3 sec. Conclusion: Super-resolved SPEN with SENSE (SUSPENSE) achieves the goals of multi-shot SPEN interleaving within one single scan, delivering single-shot sub-mm in-plane resolutions in scanners equipped with suitable multiple sensors., Comment: 7 figs in main text; 2 in Supplementary Information; 0 tables

In Fourier-based medical imaging, sampling below the Nyquist rate results in an underdetermined system, in which linear reconstructions will exhibit artifacts. Another consequence of under-sampling is lower signal to noise ratio (SNR) due to fewer acquired measurements. Even if an oracle provided the information to perfectly disambiguate the underdetermined system, the reconstructed image could still have lower image quality than a corresponding fully sampled acquisition because of the reduced measurement time. The effects of lower SNR and the underdetermined system are coupled during reconstruction, making it difficult to isolate the impact of lower SNR on image quality. To this end, we present an image quality prediction process that reconstructs fully sampled, fully determined data with noise added to simulate the loss of SNR induced by a given under-sampling pattern. The resulting prediction image empirically shows the effect of noise in under-sampled image reconstruction without any effect from an underdetermined system. We discuss how our image quality prediction process can simulate the distribution of noise for a given under-sampling pattern, including variable density sampling that produces colored noise in the measurement data. An interesting consequence of our prediction model is that we can show that recovery from underdetermined non-uniform sampling is equivalent to a weighted least squares optimization that accounts for heterogeneous noise levels across measurements. Through a series of experiments with synthetic and in vivo datasets, we demonstrate the efficacy of the image quality prediction process and show that it provides a better estimation of reconstruction image quality than the corresponding fully-sampled reference image., Comment: 24 pages, 7 figures

\textit{In vivo} spin spin relaxation time ($T_2$) heterogeneity of hyperpolarized \textsuperscript{13}C urea in the rat kidney was investigated. Selective quenching of the vascular hyperpolarized \textsuperscript{13}C signal with a macromolecular relaxation agent revealed that a long-$T_2$ component of the \textsuperscript{13}C urea signal originated from the renal extravascular space, thus allowing the vascular and renal filtrate contrast agent pools of the \textsuperscript{13}C urea to be distinguished via multi-exponential analysis. The $T_2$ response to induced diuresis and antidiuresis was performed with two imaging agents: hyperpolarized \textsuperscript{13}C urea and a control agent hyperpolarized bis-1,1-(hydroxymethyl)-1-\textsuperscript{13}C-cyclopropane-$^2\textrm{H}_8$. Large $T_2$ increases in the inner-medullar and papilla were observed with the former agent and not the latter during antidiuresis suggesting that $T_2$ relaxometry may be used to monitor the inner-medullary urea transporter (UT)-A1 and UT-A3 mediated urea concentrating process. Two high resolution imaging techniques - multiple echo time averaging and ultra-long echo time sub-2 mm$^3$ resolution 3D imaging - were developed to exploit the particularly long relaxation times observed.

We present a natural generalization of the recent low rank + sparse matrix decomposition and consider the decomposition of matrices into components of multiple scales. Such decomposition is well motivated in practice as data matrices often exhibit local correlations in multiple scales. Concretely, we propose a multi-scale low rank modeling that represents a data matrix as a sum of block-wise low rank matrices with increasing scales of block sizes. We then consider the inverse problem of decomposing the data matrix into its multi-scale low rank components and approach the problem via a convex formulation. Theoretically, we show that under various incoherence conditions, the convex program recovers the multi-scale low rank components \revised{either exactly or approximately}. Practically, we provide guidance on selecting the regularization parameters and incorporate cycle spinning to reduce blocking artifacts. Experimentally, we show that the multi-scale low rank decomposition provides a more intuitive decomposition than conventional low rank methods and demonstrate its effectiveness in four applications, including illumination normalization for face images, motion separation for surveillance videos, multi-scale modeling of the dynamic contrast enhanced magnetic resonance imaging and collaborative filtering exploiting age information.

Purpose: To develop an ESPIRiT-based method to estimate coil sensitivities with image phase as a building block for efficient and robust image reconstruction with phase constraints. Theory and Methods: ESPIRiT is a new framework for calibration of the coil sensitivities and reconstruction in parallel Magnetic Resonance Imaging (MRI). Applying ESPIRiT to a combined set of physical and virtual conjugate coils (VCC-ESPIRiT) implicitly exploits conjugate symmetry in k-space similar to VCC-GRAPPA. Based on this method, a new post-processing step is proposed for the explicit computation of coil sensitivities that include the absolute phase of the image. The accuracy of the computed maps is directly validated using a test based on projection onto fully sampled coil images and also indirectly in phase-constrained parallel-imaging reconstructions. Results: The proposed method can estimate accurate sensitivities which include low-resolution image phase. In case of high-frequency phase variations VCC-ESPIRiT yields an additional set of maps that indicates the existence of a high-frequency phase component. Taking this additional set of maps into account can improve the robustness of phase-constrained parallel imaging. Conclusion: The extended VCC-ESPIRiT is a useful tool for phase-constrained imaging., Comment: 15 pages, 5 figures