Physics-driven deep learning (PD-DL) models have proven to be a powerful approach for improved reconstruction of rapid MRI scans. In order to train these models in scenarios where fully-sampled reference data is unavailable, self-supervised learning has gained prominence. However, its application at high acceleration rates frequently introduces artifacts, compromising image fidelity. To mitigate this shortcoming, we propose a novel way to train PD-DL networks via carefully-designed perturbations. In particular, we enhance the k-space masking idea of conventional self-supervised learning with a novel consistency term that assesses the model's ability to accurately predict the added perturbations in a sparse domain, leading to more reliable and artifact-free reconstructions. The results obtained from the fastMRI knee and brain datasets show that the proposed training strategy effectively reduces aliasing artifacts and mitigates noise amplification at high acceleration rates, outperforming state-of-the-art self-supervised methods both visually and quantitatively.

Physics-driven deep learning (PD-DL) approaches have become popular for improved reconstruction of fast magnetic resonance imaging (MRI) scans. Though PD-DL offers higher acceleration rates than existing clinical fast MRI techniques, their use has been limited outside specialized MRI centers. A key challenge is generalization to rare pathologies or different populations, noted in multiple studies, with fine-tuning on target populations suggested for improvement. However, current approaches for PD-DL training require access to raw k-space measurements, which is typically only available at specialized MRI centers that have research agreements for such data access. This is especially an issue for rural and under-resourced areas, where commercial MRI scanners only provide access to a final reconstructed image. To tackle these challenges, we propose Compressibility-inspired Unsupervised Learning via Parallel Imaging Fidelity (CUPID) for high-quality PD-DL training using only routine clinical reconstructed images exported from an MRI scanner. CUPID evaluates output quality with a compressibility-based approach while ensuring that the output stays consistent with the clinical parallel imaging reconstruction through well-designed perturbations. Our results show CUPID achieves similar quality to established PD-DL training that requires k-space data while outperforming compressed sensing (CS) and diffusion-based generative methods. We further demonstrate its effectiveness in a zero-shot training setup for retrospectively and prospectively sub-sampled acquisitions, attesting to its minimal training burden. As an approach that radically deviates from existing strategies, CUPID presents an opportunity to provide broader access to fast MRI for remote and rural populations in an attempt to reduce the obstacles associated with this expensive imaging modality. Code is available at https://github.com/ualcalar17/CUPID.

Algorithm unrolling methods have proven powerful for solving the regularized least squares problem in computational magnetic resonance imaging (MRI). These approaches unfold an iterative algorithm with a fixed number of iterations, typically alternating between a neural network-based proximal operator for regularization, a data fidelity operation and auxiliary updates with learnable parameters. While the connection to optimization methods dictate that the proximal operator network should be shared across unrolls, this can introduce artifacts or blurring. Heuristically, practitioners have shown that using distinct networks may be beneficial, but this significantly increases the number of learnable parameters, making it challenging to prevent overfitting. To address these shortcomings, by taking inspirations from proximal operators with varying thresholds in approximate message passing (AMP) and the success of time-embedding in diffusion models, we propose a time-embedded algorithm unrolling scheme for inverse problems. Specifically, we introduce a novel perspective on the iteration-dependent proximal operation in vector AMP (VAMP) and the subsequent Onsager correction in the context of algorithm unrolling, framing them as a time-embedded neural network. Similarly, the scalar weights in the data fidelity operation and its associated Onsager correction are cast as time-dependent learnable parameters. Our extensive experiments on the fastMRI dataset, spanning various acceleration rates and datasets, demonstrate that our method effectively reduces aliasing artifacts and mitigates noise amplification, achieving state-of-the-art performance. Furthermore, we show that our time-embedding strategy extends to existing algorithm unrolling approaches, enhancing reconstruction quality without increasing the computational complexity significantly. Code available at https://github.com/JN-Yun/TE-Unrolling-MRI.

Infrared (IR) imaging is commonly used in various scenarios, including autonomous driving, fire safety and defense applications. Thus, semantic segmentation of such images is of great interest. However, this task faces several challenges, including data scarcity, differing contrast and input channel number compared to natural images, and emergence of classes not represented in databases in certain scenarios, such as defense applications. Few-shot segmentation (FSS) provides a framework to overcome these issues by segmenting query images using a few labeled support samples. However, existing FSS models for IR images require paired visible RGB images, which is a major limitation since acquiring such paired data is difficult or impossible in some applications. In this work, we develop new strategies for FSS of IR images by using generative modeling and fusion techniques. To this end, we propose to synthesize auxiliary data to provide additional channel information to complement the limited contrast in the IR images, as well as IR data synthesis for data augmentation. Here, the former helps the FSS model to better capture the relationship between the support and query sets, while the latter addresses the issue of data scarcity. Finally, to further improve the former aspect, we propose a novel fusion ensemble module for integrating the two different modalities. Our methods are evaluated on different IR datasets, and improve upon the state-of-the-art (SOTA) FSS models.

Physics-driven deep learning (PD-DL) techniques have recently emerged as a powerful means for improved computational imaging, including in MRI applications. These methods use the physics information by incorporating the known forward model for data fidelity, while performing regularization using neural networks. There has been substantial progress in the training of PD-DL reconstruction methods, ranging from simple supervised learning to more practical self-supervised learning and generative models that allow training without reference data. Similarly, efforts have been made to characterize the errors associated with PD-DL methods via uncertainty quantification, mostly focusing on generative models. In this work, we devise an uncertainty estimation process that primarily focuses on the data fidelity component of PD-DL by characterizing the cyclic consistency between different forward models. Subsequently, we use this uncertainty estimate to guide the training of the PD-DL method. Results show that the proposed uncertainty-guided PD-DL strategy improves reconstruction quality.

Physics-guided deep learning (PG-DL) via algorithm unrolling has received significant interest for improved image reconstruction, including MRI applications. These methods unroll an iterative optimization algorithm into a series of regularizer and data consistency units. The unrolled networks are typically trained end-to-end using a supervised approach. Current supervised PG-DL approaches use all of the available sub-sampled measurements in their data consistency units. Thus, the network learns to fit the rest of the measurements. In this study, we propose to improve the performance and robustness of supervised training by utilizing randomness by retrospectively selecting only a subset of all the available measurements for data consistency units. The process is repeated multiple times using different random masks during training for further enhancement. Results on knee MRI show that the proposed multi-mask supervised PG-DL enhances reconstruction performance compared to conventional supervised PG-DL approaches.

Sampling lies at the heart of signal processing. The celebrated Shan-non - Nyquist theorem states that in order to reconstruct a continuous or discrete time signal from uniform samples one must sample at a rate twice the highest frequency present in the signal. Numerous signals and images of interest, however, are not even approximately bandlimited. While much progress has happened in recent years, reconstruction from sub-Nyquist samples still hinges on the use of random / incoherent (aggregate) sampling patterns, instead of uniform or regular sampling, which is far more simple, practical, and natural in many applications. In this work, we study regular sampling and reconstruction of three- or higher-dimensional signals (tensors). We prove that exact tensor reconstruction from regular samples is feasible under mild conditions on the rank of the tensor. Furthermore we cast the functional magnetic resonance imaging (fMRI) acceleration task as a regular tensor sampling problem and provide an algorithmic framework that effectively handles the reconstruction task. Experiments based on synthetic data and real fMRI data showcase the effectiveness of our approach.

Segmentation of ventricles from cardiac magnetic resonance (MR) images is a key step to obtaining clinical parameters useful for prognosis of cardiac pathologies. To improve upon the performance of existing fully convolutional network (FCN) based automatic right ventricle (RV) segmentation approaches, a multi-task deep neural network (DNN) architecture is proposed. The multi-task model can employ any FCN as a building block, allows for leveraging shared features between different tasks, and can be efficiently trained end-to-end. Specifically, a multi-task U-net is developed and implemented using the Tensorflow framework. Numerical tests on real datasets showcase the merits of the proposed approach and in particular its ability to offer improved segmentation performance for small-size RVs.

Magnetic Resonance Imaging (MRI) is one of the leading modalities for medical imaging, providing excellent soft-tissue contrast without exposure to ionizing radiation. Despite continuing advances in MRI, long scan times remain a major limitation in clinical applications. Parallel imaging is a technique for scan time acceleration in MRI, which utilizes the spatial variations in the reception profiles of receiver coil arrays to reconstruct images from undersampled Fourier space, i.e. k-space. One of the most commonly used parallel imaging techniques employs interpolation of missing k-space information by using linear shift-invariant convolutional kernels. These kernels are trained on a limited amount of autocalibration signal (ACS) for each scan. We propose a novel method for parallel imaging,Robust Artificial-neural-networks for k-space Interpolation (RAKI), which uses scan-specific convolutional neural networks (CNNs) to perform improved k-space interpolation. Three-layer CNNs are trained using only scan-specific ACS data, alleviating the need for large training databases. The proposed method was tested in ultra-high resolution brain MRI and quantitative cardiac MRI, acquired with various acceleration rates. Improved noise resilience as compared to existing parallel imaging methods was observed for high acceleration rates or in the presence of low signal-to-noise ratio (SNR). Furthermore, RAKI successfully reconstructed images for quantitative cardiac MRI, even when using the same CNN across images with varying contrasts. These results indicate that RAKI achieves improved noise performance without overfitting to specific image contents, and offers great promise for improved acceleration in a wide range of MRI applications.

A linear-time algorithm termed SPARse Truncated Amplitude flow (SPARTA) is developed for the phase retrieval (PR) of sparse signals. Upon formulating the sparse PR as a non-convex empirical loss minimization task, SPARTA emerges as an iterative solver consisting of two components: s1) a sparse orthogonality-promoting initialization leveraging support recovery and principal component analysis; and, s2) a series of refinements by hard thresholding based truncated gradient iterations. SPARTA is simple, scalable, and fast. It recovers any k-sparse n-dimensional signal (k ≪ n) of large enough minimum (in modulus) nonzero entries from about k2log n measurements with high probability; this is achieved at computational complexity of order k2n log n, improving upon the state-of-the-art by at least a factor of k. SPARTA is robust against bounded additive noise. Simulated tests corroborate the merits of SPARTA relative to existing alternatives.

We consider the problem of exact sparse signal recovery from a combination of linear and magnitude-only (phaseless) measurements. A k-sparse signal x ∈ ℂnis measured as r = Bx and y = |Cx |, where B ∈ ℂm1 ×nand C ∈ ℂm2 ×nare measurement matrices and |·| is the element-wise absolute value. We show that if max(2m1,1) + m2≥ 4k - 1, then a set of generic measurements are sufficient to recover every k-sparse x exactly, establishing the trade-off between the number of linear and magnitude-only measurements.

In this paper, we consider an undersampling system model of the form y = A(T(x, θ)) + n, where x is a k-sparse signal, T(·, · is a (possibly non-linear) function specified by a parameter vector θ and acting on x, A is a sensing matrix, and n is additive measurement noise. We consider an information theoretic decoder that aims to recover the sparse signal and the transformation parameter vector jointly, and study the achievability conditions for estimating the underlying signal within a specified ℓ2distortion for Gaussian sensing matrices. We compare the achievable distortion of the joint estimation process to that of the standard noisy compressed sensing model, where the sparse signal is directly measured with a sensing matrix with the same number of measurements. We also provide a numerical example to illustrate potential applications.

Coronary magnetic resonance imaging (MRI) is a noninvasive imaging modality for diagnosis of coronary artery disease. One of the limitations of coronary MRI is its long acquisition time due to the need of imaging with high spatial resolution and constraints on respiratory and cardiac motions. Compressed sensing (CS) has been recently utilized to accelerate image acquisition in MRI. In this paper, we develop an improved CS reconstruction method, Bayesian least squares-Gaussian scale mixture (BLS-GSM), that uses dependencies of wavelet domain coefficients to reduce the observed blurring and reconstruction artifacts in coronary MRI using traditional l(1) regularization. Images of left and right coronary MRI was acquired in 7 healthy subjects with fully-sampled k-space data. The data was retrospectively undersampled using acceleration rates of 2, 4, 6, and 8 and reconstructed using l(1) thresholding, l(1) minimization and BLS-GSM thresholding. Reconstructed right and left coronary images were compared with fully-sampled reconstructions in vessel sharpness and subjective image quality (1-4 for poor-excellent). Mean square error (MSE) was also calculated for each reconstruction. There were no significant differences between the fully sampled image score versus rate 2, 4, or 6 for BLS-GSM for both right and left coronaries (=N.S.). However, for l(1) thresholding significant differences were observed for rates higher than 2 and 4 for right and left coronaries respectively. l(1) minimization also yields images with lower scores compared to the reference for rates higher than 4 for both coronaries. These results were consistent with the quantitative vessel sharpness readings. BLS-GSM allows acceleration of coronary MRI with acceleration rates beyond what can be achieved with l(1) regularization.

We consider the compressive sensing of a sparse or compressible signal x ∈ ℝM. We explicitly construct a class of measurement matrices, referred to as the low density frames, and develop decoding algorithms that produce an accurate estimate x even in the presence of additive noise. Low density frames are sparse matrices and have small storage requirements. Our decoding algorithms for these frames can be implemented in O(Mdvdc) complexity, where dcand dvare the row and column weight of the frame respectively. Simulation results are provided, demonstrating that our approach significantly outperforms state-of-the-art recovery algorithms for numerous cases of interest.

In this paper, we study the number of measurements required to recover a sparse signal in CMwith L nonzero coefficients from compressed samples in the presence of noise. We consider a number of different recovery criteria, including the exact recovery of the support of the signal, which was previously considered in the literature, as well as new criteria for the recovery of a large fraction of the support of the signal, and the recovery of a large fraction of the energy of the signal. For these recovery criteria, we prove that O(L) (an asymptotically linear multiple of L) measurements are necessary and sufficient for signal recovery, whenever L grows linearly as a function of M. This improves on the existing literature that is mostly focused on variants of a specific recovery algorithm based on convex programming, for which O(L log(M - L)) measurements are required. In contrast, the implementation of our proof method would have a higher complexity. We also show that O(L log(M - L)) measurements are required in the sublinear regime (L - o(M)). For our sufficiency proofs, we introduce a Shannon-theoretic decoder based on joint typicality, which allows error events to be defined in terms of a single random variable in contrast to previous information-theoretic work, where comparison of random variables are required. We also prove concentration results for our error bounds implying that a randomly selected Gaussian matrix will suffice with high probability. For our necessity proofs, we rely on results from channel coding and rate-distortion theory.

We consider approximations of signals by the elements of a frame in a complex vector space of dimension N and formulate both the noiseless and the noisy sparse representation problems. The noiseless representation problem is to find sparse representations of a signal r given that such representations exist. In this case, we explicitly construct a frame, referred to as the Vandermonde frame, for which the noiseless sparse representation problem can be solved uniquely using O(N2) operations, as long as the number of non-zero coefficients in the sparse representation of r is isinN for some 0 les isin les 0.5, thus improving on a result of Candes and Tao [3]. We also show that isin les 0.5 cannot be relaxed without violating uniqueness. The noisy sparse representation problem is to find sparse representations of a signal r satisfying a distortion criterion. In this case, we establish a lower bound on the trade-off between the sparsity of the representation, the underlying distortion and the redundancy of any given frame.

We consider sparse representations of signals with at most L nonzero coefficients using a frame F of size M in CN. For any F, we establish a universal numerical lower bound on the average distortion of the representation as a function of the sparsity epsiv = L/N of the representation and redundancy (tau - 1) = M/N - 1 of F. In low dimensions (e.g., N = 6, 8.10), this bound is much stronger than the analytical and asymptotic bounds given in another of our papers. In contrast, it is much less straightforward to compute. We then compare the performance of randomly generated frames to this numerical lower bound and to the analytical and asymptotic bounds given in the aforementioned paper. In low dimensions, it is shown that randomly generated frames perform about 2 dB away from the theoretical lower bound, when the optimal sparse representation algorithm is used. In higher dimensions, we evaluate the performance of randomly generated frames using the greedy orthogonal matching pursuit (OMP) algorithm. The results indicate that for small values of epsiv, OMP performs close to the lower bound and suggest that the loss of the suboptimal search using orthogonal matching pursuit algorithm grows as a function of epsiv. In all cases, the performance of randomly generated frames hardens about their average as N grows, even when using the OMP algorithm.