Compressed sensing (CS) MRI relies on adequate undersampling of the k-space to accelerate the acquisition without compromising image quality. Consequently, the design of optimal sampling patterns for these k-space coefficients has received significant attention, with many CS MRI methods exploiting variable-density probability distributions. Realizing that an optimal sampling pattern may depend on the downstream task (e.g. image reconstruction, segmentation, or classification), we here propose joint learning of both task-adaptive k-space sampling and a subsequent model-based proximal-gradient recovery network. The former is enabled through a probabilistic generative model that leverages the Gumbel-softmax relaxation to sample across trainable beliefs while maintaining differentiability. The proposed combination of a highly flexible sampling model and a model-based (sampling-adaptive) image reconstruction network facilitates exploration and efficient training, yielding improved MR image quality compared to other sampling baselines.
Nanchang University（南昌大学）；Medical AI Research Center, Shenzhen Institutes of Advanced Technology, Chinese Academy of Sciences（中国科学院深圳先进技术研究院医学人工智能研究中心）
To improve the compressive sensing MRI (CS-MRI) approaches in terms of fine structure loss under high acceleration factors, we have proposed an iterative feature refinement model (IFR-CS), equipped with fixed transforms, to restore the meaningful structures and details. Nevertheless, the proposed IFR-CS still has some limitations, such as the selection of hyper-parameters, a lengthy reconstruction time, and the fixed sparsifying transform. To alleviate these issues, we unroll the iterative feature refinement procedures in IFR-CS to a supervised model-driven network, dubbed IFR-Net. Equipped wi…
The CSGM framework (Bora-Jalal-Price-Dimakis'17) has shown that deep generative priors can be powerful tools for solving inverse problems. However, to date this framework has been empirically successful only on certain datasets (for example, human faces and MNIST digits), and it is known to perform poorly on out-of-distribution samples. In this paper, we present the first successful application of the CSGM framework on clinical MRI data. We train a generative prior on brain scans from the fastMRI dataset, and show that posterior sampling via Langevin dynamics achieves high quality reconstructi…
University of Illinois, Urbana-Champaign（伊利诺伊大学厄巴纳-香槟分校）
Natural signals and images are well-known to be approximately sparse in transform domains such as Wavelets and DCT. This property has been heavily exploited in various applications in image processing and medical imaging. Compressed sensing exploits the sparsity of images or image patches in a transform domain or synthesis dictionary to reconstruct images from undersampled measurements. In this work, we focus on blind compressed sensing, where the underlying sparsifying transform is a priori unknown, and propose a framework to simultaneously reconstruct the underlying image as well as the spar…
Magnetic resonance image (MRI) reconstruction is a severely ill-posed linear inverse task demanding time and resource intensive computations that can substantially trade off {\it accuracy} for {\it speed} in real-time imaging. In addition, state-of-the-art compressed sensing (CS) analytics are not cognizant of the image {\it diagnostic quality}. To cope with these challenges we put forth a novel CS framework that permeates benefits from generative adversarial networks (GAN) to train a (low-dimensional) manifold of diagnostic-quality MR images from historical patients. Leveraging a mixture of l…
In this paper, we propose majority voting neural networks for sparse signal recovery in binary compressed sensing. The majority voting neural network is composed of several independently trained feedforward neural networks employing the sigmoid function as an activation function. Our empirical study shows that a choice of a loss function used in training processes for the network is of prime importance. We found a loss function suitable for sparse signal recovery, which includes a cross entropy-like term and an $L_1$ regularized term. From the experimental results, we observed that the majorit…
The structure of Magnetic Resonance Images (MRI) and especially their compressibility in an appropriate representation basis enables the application of the compressive sensing theory, which guarantees exact image recovery from incomplete measurements. According to recent theoretical conditions on the reconstruction guarantees, the optimal strategy is to downsample the k-space using an independent drawing of the acquisition basis entries. Here, we first bring a novel answer to the synthesis problem, which amounts to deriving the op- timal distribution (according to a given criterion) from which…
We develop a Bayesian nonparametric model for reconstructing magnetic resonance images (MRI) from highly undersampled k-space data. We perform dictionary learning as part of the image reconstruction process. To this end, we use the beta process as a nonparametric dictionary learning prior for representing an image patch as a sparse combination of dictionary elements. The size of the dictionary and the patch-specific sparsity pattern are inferred from the data, in addition to other dictionary learning variables. Dictionary learning is performed directly on the compressed image, and so is tailor…
We adopt data structure in the form of cover trees and iteratively apply approximate nearest neighbour (ANN) searches for fast compressed sensing reconstruction of signals living on discrete smooth manifolds. Levering on the recent stability results for the inexact Iterative Projected Gradient (IPG) algorithm and by using the cover tree's ANN searches, we decrease the projection cost of the IPG algorithm to be logarithmically growing with data population for low dimensional smooth manifolds. We apply our results to quantitative MRI compressed sensing and in particular within the Magnetic Reson…
In this paper we introduce a new optimization formulation for sparse regression and compressed sensing, called CLOT (Combined L-One and Two), wherein the regularizer is a convex combination of the $\ell_1$- and $\ell_2$-norms. This formulation differs from the Elastic Net (EN) formulation, in which the regularizer is a convex combination of the $\ell_1$- and $\ell_2$-norm squared. It is shown that, in the context of compressed sensing, the EN formulation does not achieve robust recovery of sparse vectors, whereas the new CLOT formulation achieves robust recovery. Also, like EN but unlike LASSO…
University of Michigan（密歇根大学）；University of Illinois, Urbana-Champaign（伊利诺伊大学厄巴纳-香槟分校）
Compressed sensing is a powerful tool in applications such as magnetic resonance imaging (MRI). It enables accurate recovery of images from highly undersampled measurements by exploiting the sparsity of the images or image patches in a transform domain or dictionary. In this work, we focus on blind compressed sensing (BCS), where the underlying sparse signal model is a priori unknown, and propose a framework to simultaneously reconstruct the underlying image as well as the unknown model from highly undersampled measurements. Specifically, our model is that the patches of the underlying image(s…
University of California San Diego（加州大学圣迭戈分校）；Google Research, India（谷歌印度研究院）
One-bit compressed sensing (1bCS) is an extremely quantized signal acquisition method that has been proposed and studied rigorously in the past decade. In 1bCS, linear samples of a high dimensional signal are quantized to only one bit per sample (sign of the measurement). Assuming the original signal vector to be sparse, existing results in 1bCS either aim to find the support of the vector, or approximate the signal allowing a small error. The focus of this paper is support recovery, which often also computationally facilitate approximate signal recovery. A {\em universal} measurement matrix f…
Compressed sensing techniques enable efficient acquisition and recovery of sparse, high-dimensional data signals via low-dimensional projections. In this work, we propose Uncertainty Autoencoders, a learning framework for unsupervised representation learning inspired by compressed sensing. We treat the low-dimensional projections as noisy latent representations of an autoencoder and directly learn both the acquisition (i.e., encoding) and amortized recovery (i.e., decoding) procedures. Our learning objective optimizes for a tractable variational lower bound to the mutual information between th…
One-bit compressed sensing (1bCS) is an extreme-quantized signal acquisition method that has been intermittently studied in the past decade. In 1bCS, linear samples of a high dimensional signal are quantized to only one bit per sample (sign of the measurement). The extreme quantization makes it an interesting case study of the more general single-index or generalized linear models. At the same time it can also be thought of as a `design' version of learning a binary linear classifier or halfspace-learning. Assuming the original signal vector to be sparse, existing results in 1bCS either aim to…
Compressed sensing (CS) is an important theory for sub-Nyquist sampling and recovery of compressible data. Recently, it has been extended by Pham and Venkatesh to cope with the case where corruption to the CS data is modeled as impulsive noise. The new formulation, termed as robust CS, combines robust statistics and CS into a single framework to suppress outliers in the CS recovery. To solve the newly formulated robust CS problem, Pham and Venkatesh suggested a scheme that iteratively solves a number of CS problems, the solutions from which converge to the true robust compressed sensing soluti…
Compressed sensing (sparse signal recovery) has been a popular and important research topic in recent years. By observing that natural signals are often nonnegative, we propose a new framework for nonnegative signal recovery using Compressed Counting (CC). CC is a technique built on maximally-skewed p-stable random projections originally developed for data stream computations. Our recovery procedure is computationally very efficient in that it requires only one linear scan of the coordinates. Our analysis demonstrates that, when 0<p<=0.5, it suffices to use M= O(C/eps^p log N) measurements so …
Compressed sensing (sparse signal recovery) often encounters nonnegative data (e.g., images). Recently we developed the methodology of using (dense) Compressed Counting for recovering nonnegative K-sparse signals. In this paper, we adopt very sparse Compressed Counting for nonnegative signal recovery. Our design matrix is sampled from a maximally-skewed p-stable distribution (0<p<1), and we sparsify the design matrix so that on average (1-g)-fraction of the entries become zero. The idea is related to very sparse stable random projections (Li et al 2006 and Li 2007), the prior work for estimati…
In compressed sensing, a small number of linear measurements can be used to reconstruct an unknown signal. Existing approaches leverage assumptions on the structure of these signals, such as sparsity or the availability of a generative model. A domain-specific generative model can provide a stronger prior and thus allow for recovery with far fewer measurements. However, unlike sparsity-based approaches, existing methods based on generative models guarantee exact recovery only over their support, which is typically only a small subset of the space on which the signals are defined. We propose Sp…
This paper investigates the problem of recovering the support of structured signals via adaptive compressive sensing. We examine several classes of structured support sets, and characterize the fundamental limits of accurately recovering such sets through compressive measurements, while simultaneously providing adaptive support recovery protocols that perform near optimally for these classes. We show that by adaptively designing the sensing matrix we can attain significant performance gains over non-adaptive protocols. These gains arise from the fact that adaptive sensing can: (i) better mitig…
The goal of compressed sensing is to estimate a high dimensional vector from an underdetermined system of noisy linear equations. In analogy to classical compressed sensing, here we assume a generative model as a prior, that is, we assume the vector is represented by a deep generative model $G: \mathbb{R}^k \rightarrow \mathbb{R}^n$. Classical recovery approaches such as empirical risk minimization (ERM) are guaranteed to succeed when the measurement matrix is sub-Gaussian. However, when the measurement matrix and measurements are heavy-tailed or have outliers, recovery may fail dramatically. …
Given the superposition of a low-rank matrix plus the product of a known fat compression matrix times a sparse matrix, the goal of this paper is to establish deterministic conditions under which exact recovery of the low-rank and sparse components becomes possible. This fundamental identifiability issue arises with traffic anomaly detection in backbone networks, and subsumes compressed sensing as well as the timely low-rank plus sparse matrix recovery tasks encountered in matrix decomposition problems. Leveraging the ability of $\ell_1$- and nuclear norms to recover sparse and low-rank matrice…
Compressed sensing (CS) is a signal acquisition paradigm to simultaneously acquire and reduce dimension of signals that admit sparse representations. When such a signal is acquired according to the principles of CS, the measurements still take on values in the continuum. In today's "digital" world, a subsequent quantization step, where these measurements are replaced with elements from a finite set is crucial. We focus on one of the approaches that yield efficient quantizers for CS: $ΣΔ$ quantization, followed by a one-stage tractable reconstruction method, which was developed by Saab et al. w…
This paper establishes new restricted isometry conditions for compressed sensing and affine rank minimization. It is shown for compressed sensing that $δ_{k}^A+θ_{k,k}^A < 1$ guarantees the exact recovery of all $k$ sparse signals in the noiseless case through the constrained $\ell_1$ minimization. Furthermore, the upper bound 1 is sharp in the sense that for any $ε> 0$, the condition $δ_k^A + θ_{k, k}^A < 1+ε$ is not sufficient to guarantee such exact recovery using any recovery method. Similarly, for affine rank minimization, if $δ_{r}^\mathcal{M}+θ_{r,r}^\mathcal{M}< 1$ then all matrices wi…
Compressed sensing is a new methodology for constructing sensors which allow sparse signals to be efficiently recovered using only a small number of observations. The recovery problem can often be stated as the one of finding the solution of an underdetermined system of linear equations with the smallest possible support. The most studied relaxation of this hard combinatorial problem is the $l_1$-relaxation consisting of searching for solutions with smallest $l_1$-norm. In this short note, based on the ideas of Lagrangian duality, we introduce an alternating $l_1$ relaxation for the recovery p…
Greedy Pursuits are very popular in Compressed Sensing for sparse signal recovery. Though many of the Greedy Pursuits possess elegant theoretical guarantees for performance, it is well known that their performance depends on the statistical distribution of the non-zero elements in the sparse signal. In practice, the distribution of the sparse signal may not be known a priori. It is also observed that performance of Greedy Pursuits degrades as the number of available measurements decreases from a threshold value which is method dependent. To improve the performance in these situations, we intro…
University at Buffalo（布法罗大学）；INRIA（法国国家信息与自动化研究所）；Université Côte d’ Azur（蔚蓝海岸大学）；Stanford University（斯坦福大学）；Purdue University（普渡大学）
This paper puts forth a novel bi-linear modeling framework for data recovery via manifold-learning and sparse-approximation arguments and considers its application to dynamic magnetic-resonance imaging (dMRI). Each temporal-domain MR image is viewed as a point that lies onto or close to a smooth manifold, and landmark points are identified to describe the point cloud concisely. To facilitate computations, a dimensionality reduction module generates low-dimensional/compressed renditions of the landmark points. Recovery of the high-fidelity MRI data is realized by solving a non-convex minimizati…
Nanjing University of Information Science and Technology（南京信息工程大学）
Magnetic resonance imaging (MRI) reconstruction is an active inverse problem which can be addressed by conventional compressed sensing (CS) MRI algorithms that exploit the sparse nature of MRI in an iterative optimization-based manner. However, two main drawbacks of iterative optimization-based CSMRI methods are time-consuming and are limited in model capacity. Meanwhile, one main challenge for recent deep learning-based CSMRI is the trade-off between model performance and network size. To address the above issues, we develop a new multi-scale dilated network for MRI reconstruction with high s…
Sun Yat-sen University（中山大学）；The Chinese University of Hong Kong（香港中文大学）；Royal Brompton Hospital（皇家布朗普顿医院）；Imperial College London（伦敦帝国理工学院）
The long acquisition time has limited the accessibility of magnetic resonance imaging (MRI) because it leads to patient discomfort and motion artifacts. Although several MRI techniques have been proposed to reduce the acquisition time, compressed sensing in magnetic resonance imaging (CS-MRI) enables fast acquisition without compromising SNR and resolution. However, existing CS-MRI methods suffer from the challenge of aliasing artifacts. This challenge results in the noise-like textures and missing the fine details, thus leading to unsatisfactory reconstruction performance. To tackle this chal…
Cornell University（康奈尔大学）；Massachusetts Institute of Technology（麻省理工学院）；Massachusetts General Hospital（麻省总医院）
Compressed Sensing MRI (CS-MRI) has shown promise in reconstructing under-sampled MR images, offering the potential to reduce scan times. Classical techniques minimize a regularized least-squares cost function using an expensive iterative optimization procedure. Recently, deep learning models have been developed that model the iterative nature of classical techniques by unrolling iterations in a neural network. While exhibiting superior performance, these methods require large quantities of ground-truth images and have shown to be non-robust to unseen data. In this paper, we explore a novel st…
We investigated whether a combination of k-space undersampling and variable density averaging enhances image quality for low-SNR MRI acquisitions. We implemented 3D Cartesian k-space prospective undersampling with a variable number of averages for each k-line. The performance of this compressed sensing with variable-density averaging (CS-VDA) method was evaluated in retrospective analysis of fully sampled phantom MRI measurements, as well as for prospectively accelerated in vivo 3D brain and knee MRI scans. Both phantom and in vivo results showed that acquisitions using the CS-VDA approach res…
Cornell University（康奈尔大学）；Massachusetts Institute of Technology（麻省理工学院）；Massachusetts General Hospital（麻省总医院）；Harvard Medical School（哈佛医学院）
Reconstructing under-sampled k-space measurements in Compressed Sensing MRI (CS-MRI) is classically solved with regularized least-squares. Recently, deep learning has been used to amortize this optimization by training reconstruction networks on a dataset of under-sampled measurements. Here, a crucial design choice is the regularization function(s) and corresponding weight(s). In this paper, we explore a novel strategy of using a hypernetwork to generate the parameters of a separate reconstruction network as a function of the regularization weight(s), resulting in a regularization-agnostic rec…
Plug-and-play (PnP) methods that employ application-specific denoisers have been proposed to solve inverse problems, including MRI reconstruction. However, training application-specific denoisers is not feasible for many applications due to the lack of training data. In this work, we propose a PnP-inspired recovery method that does not require data beyond the single, incomplete set of measurements. The proposed method, called recovery with a self-calibrated denoiser (ReSiDe), trains the denoiser from the patches of the image being recovered. The denoiser training and a call to the denoising su…
Inspired by the first-order method of Malitsky and Pock, we propose a new variational framework for compressed MR image reconstruction which introduces the application of a rotation-invariant discretization of total variation functional into MR imaging while exploiting BM3D frame as a sparsifying transform. In the first step, we provide theoretical and numerical analysis establishing the exceptional rotation-invariance property of this total variation functional and observe its superiority over other well-known variational regularization terms in both upright and rotated imaging setups. Thereu…
Compressed sensing magnetic resonance imaging (CS-MRI) is a theoretical framework that can accurately reconstruct images from undersampled k-space data with a much lower sampling rate than the one set by the classical Nyquist-Shannon sampling theorem. Therefore, CS-MRI can efficiently accelerate acquisition time and relieve the psychological burden on patients while maintaining high imaging quality. The problems with traditional CS-MRI reconstruction are solved by iterative numerical solvers, which usually suffer from expensive computational cost and the lack of accurate handcrafted priori. In…
Bangladesh University of Engineering and Technology（孟加拉国工程技术大学）
Parallel imaging accelerates MRI data acquisition by acquiring additional sensitivity information with an array of receiver coils, resulting in fewer phase encoding steps. Because of fewer data requirements than parallel imaging, compressed sensing magnetic resonance imaging (CS-MRI) has gained popularity in the field of medical imaging. Parallel imaging and compressed sensing (CS) both reduce the amount of data captured in the k-space, which speeds up traditional MRI acquisition. As acquisition time is inversely proportional to sample count, forming an image from reduced k-space samples resul…
Optimizing Sampling Patterns for Compressed Sensing MRI with Diffusion Generative Models
Chandra Family Department of Electrical and Computer Engineering, The University of Texas at Austin（查德拉家族电子与计算机工程系，德克萨斯大学奥斯汀分校）；The University of Texas at Austin（德克萨斯大学奥斯汀分校）；Imaging Physics, MD Anderson Cancer Center, Houston, Texas, USA（影像物理，MD安德森癌症中心，休斯顿，德克萨斯州，美国）；Electrical Engineering and Computer Sciences, University of California, Berkeley（电气工程与计算机科学，加州大学伯克利分校）；Department of Diagnostic Medicine, Dell Medical School, Austin, Texas, USA（诊断医学系，德勒医学学院，奥斯汀，德克萨斯州，美国）
University at Buffalo（布法罗大学）；Stanford University（斯坦福大学）；Purdue University（普渡大学）
This paper establishes a kernel-based framework for reconstructing data on manifolds, tailored to fit the dynamic-(d)MRI-data recovery problem. The proposed methodology exploits simple tangent-space geometries of manifolds in reproducing kernel Hilbert spaces and follows classical kernel-approximation arguments to form the data-recovery task as a bi-linear inverse problem. Departing from mainstream approaches, the proposed methodology uses no training data, employs no graph Laplacian matrix to penalize the optimization task, uses no costly (kernel) pre-imaging step to map feature points back t…
In this work we introduce a new method that combines Parallel MRI and Compressed Sensing (CS) for accelerated image reconstruction from subsampled k-space data. The method first computes a convolved image, which gives the convolution between a user-defined kernel and the unknown MR image, and then reconstructs the image by CS-based image deblurring, in which CS is applied for removing the inherent blur stemming from the convolution process. This method is hence termed CORE-Deblur. Retrospective subsampling experiments with data from a numerical brain phantom and in-vivo 7T brain scans showed t…
University of Oxford（牛津大学）；Siemens Healthineers（西门子医疗）
Magnetic Resonance Imaging (MRI) has excellent soft tissue contrast but is hindered by an inherently slow data acquisition process. Compressed sensing, which reconstructs sparse signals from incoherently sampled data, has been widely applied to accelerate MRI acquisitions. Compressed sensing MRI requires one or more model parameters to be tuned, which is usually done by hand, giving sub-optimal tuning in general. To address this issue, we build on previous work by the authors on the single-coil Variable Density Approximate Message Passing (VDAMP) algorithm, extending the framework to multiple …
Recently, the finite-rate-of-innovation (FRI) based continuous domain regularization is emerging as an alternative to the conventional on-the-grid sparse regularization for the compressed sensing (CS) due to its ability to alleviate the basis mismatch between the true support of the shape in the continuous domain and the discrete grid. In this paper, we propose a new off-the-grid regularization for the CS-MRI reconstruction. Following the recent works on two dimensional FRI, we assume that the discontinuities/edges of the image are localized in the zero level set of a band-limited periodic fun…
Fluorine-19 (19F) MRI of injected perfluorocarbon emulsions (PFCs) allows for the non-invasive quantification of inflammation and cell tracking, but suffers from a low signal-to-noise ratio and extended scan time. To address this limitation, we tested the hypothesis that a 19F MRI pulse sequence that combines a specific undersampling regime with signal averaging has increased sensitivity and robustness against motion artifacts compared to a non-averaged fully-sampled dataset, when both are reconstructed with compressed sensing. To this end, numerical simulations and phantom experiments were pe…
Continuous K-space Recovery Network with Image Guidance for Fast MRI Reconstruction
The Shanghai Key Laboratory of Medical Image Computing and Computer Assisted Intervention（上海医学影像计算与计算机辅助介入重点实验室）；Academy of Engineering and Technology, Fudan University（复旦大学工程与技术学院）
The development of compressed sensing methods for magnetic resonance (MR) image reconstruction led to an explosion of research on models and optimization algorithms for MR imaging (MRI). Roughly 10 years after such methods first appeared in the MRI literature, the U.S. Food and Drug Administration (FDA) approved certain compressed sensing methods for commercial use, making compressed sensing a clinical success story for MRI. This review paper summarizes several key models and optimization algorithms for MR image reconstruction, including both the type of methods that have FDA approval for clin…
Facebook AI Research（Facebook人工智能研究）；fastMRI team（fastMRI团队）
Deep learning approaches to accelerated MRI take a matrix of sampled Fourier-space lines as input and produce a spatial image as output. In this work we show that by careful choice of the offset used in the sampling procedure, the symmetries in k-space can be better exploited, producing higher quality reconstructions than given by standard equally-spaced samples or randomized samples motivated by compressed sensing.
Eindhoven University of Technology（埃因霍温理工大学）；University of Amsterdam（阿姆斯特丹大学）；Philips Research（飞利浦研究院）
Limitations on bandwidth and power consumption impose strict bounds on data rates of diagnostic imaging systems. Consequently, the design of suitable (i.e. task- and data-aware) compression and reconstruction techniques has attracted considerable attention in recent years. Compressed sensing emerged as a popular framework for sparse signal reconstruction from a small set of compressed measurements. However, typical compressed sensing designs measure a (non)linearly weighted combination of all input signal elements, which poses practical challenges. These designs are also not necessarily task-o…
Technion - Israel Institute of Technology（以色列理工学院）
Magnetic Resonance Imaging (MRI) has long been considered to be among the gold standards of today's diagnostic imaging. The most significant drawback of MRI is long acquisition times, prohibiting its use in standard practice for some applications. Compressed sensing (CS) proposes to subsample the k-space (the Fourier domain dual to the physical space of spatial coordinates) leading to significantly accelerated acquisition. However, the benefit of compressed sensing has not been fully exploited; most of the sampling densities obtained through CS do not produce a trajectory that obeys the string…
