Recent advances in deep learning-based parallel compressed sensing magnetic resonance imaging (p-CSMRI) have significantly improved reconstruction quality. However, current p-CSMRI methods often require training separate deep neural network (DNN) for each organ due to anatomical variations, creating a barrier to developing generalized medical image reconstruction systems. To address this, we propose CAPNet (cross-organ all-in-one deep unfolding p-CSMRI network), a unified framework that implements a p-CSMRI iterative algorithm via three specialized modules: auxiliary variable module, prior module, and data consistency module. Recognizing that p-CSMRI systems often employ varying sampling ratios for different organs, resulting in organ-specific artifact patterns, we introduce an artifact generation submodule, which extracts and integrates artifact features into the data consistency module to enhance the discriminative capability of the overall network. For the prior module, we design an organ structure-prompt generation submodule that leverages structural features extracted from the segment anything model (SAM) to create cross-organ prompts. These prompts are strategically incorporated into the prior module through an organ structure-aware Mamba submodule. Comprehensive evaluations on a cross-organ dataset confirm that CAPNet achieves state-of-the-art reconstruction performance across multiple anatomical structures using a single unified model. Our code will be published at https://github.com/shibaoshun/CAPNet.
In compressed sensing (CS) MRI, model-based methods are pivotal to achieving accurate reconstruction. One of the main challenges in model-based methods is finding an effective prior to describe the statistical distribution of the target image. Plug-and-Play (PnP) and REgularization by Denoising (RED) are two general frameworks that use denoisers as the prior. While PnP/RED methods with convolutional neural networks (CNNs) based denoisers outperform classical hand-crafted priors in CS MRI, their convergence theory relies on assumptions that do not hold for practical CNNs. The recently developed gradient-driven denoisers offer a framework that bridges the gap between practical performance and theoretical guarantees. However, the numerical solvers for the associated minimization problem remain slow for CS MRI reconstruction. This paper proposes a complex quasi-Newton proximal method that achieves faster convergence than existing approaches. To address the complex domain in CS MRI, we propose a modified Hessian estimation method that guarantees Hermitian positive definiteness. Furthermore, we provide a rigorous convergence analysis of the proposed method for nonconvex settings. Numerical experiments on both Cartesian and non-Cartesian sampling trajectories demonstrate the effectiveness and efficiency of our approach.
Integrated sensing and communication (ISAC) is envisioned be to one of the paradigms upon which next-generation mobile networks will be built, extending localization and tracking capabilities, as well as giving birth to environment-aware wireless access. A key aspect of sensing integration is parameter estimation, which involves extracting information about the surrounding environment, such as the direction, distance, and velocity of various objects within. This is typically of a high-dimensional nature, which leads to significant computational complexity, if performed jointly across multiple sensing dimensions, such as space, frequency, and time. Additionally, due to the incorporation of sensing on top of the data transmission, the time window available for sensing is likely to be short, resulting in an estimation problem where only a single snapshot is accessible. In this work, we propose PLAIN, a tensor-based estimation architecture that flexibly scales with multiple sensing dimensions and can handle high dimensionality, limited measurement time, and super-resolution requirements. It consists of three stages: a compression stage, where the high dimensional input is converted into lower dimensionality, without sacrificing resolution; a decoupled estimation stage, where the parameters across the different dimensions are estimated in parallel with low complexity; an input-based fusion stage, where the decoupled parameters are fused together to form a paired multidimensional estimate. We investigate the performance of the architecture for different configurations and compare it against practical sequential and joint estimation baselines, as well as theoretical bounds. Our results show that PLAIN, using tools from tensor algebra, subspace-based processing, and compressed sensing, can scale flexibly with dimensionality, while operating with low complexity and maintaining super-resolution.
Recent advances in Latent Video Diffusion Models (LVDMs) have revolutionized video generation by leveraging Video Variational Autoencoders (Video VAEs) to compress intricate video data into a compact latent space. However, as LVDM training scales, the computational overhead of Video VAEs becomes a critical bottleneck, particularly for encoding high-resolution videos. To address this, we propose LeanVAE, a novel and ultra-efficient Video VAE framework that introduces two key innovations: (1) a lightweight architecture based on a Neighborhood-Aware Feedforward (NAF) module and non-overlapping patch operations, drastically reducing computational cost, and (2) the integration of wavelet transforms and compressed sensing techniques to enhance reconstruction quality. Extensive experiments validate LeanVAE's superiority in video reconstruction and generation, particularly in enhancing efficiency over existing Video VAEs. Our model offers up to 50x fewer FLOPs and 44x faster inference speed while maintaining competitive reconstruction quality, providing insights for scalable, efficient video generation. Our models and code are available at https://github.com/westlake-repl/LeanVAE
Magnetic resonance imaging (MRI) is a non-invasive imaging modality and provides comprehensive anatomical and functional insights into the human body. However, its long acquisition times can lead to patient discomfort, motion artifacts, and limiting real-time applications. To address these challenges, strategies such as parallel imaging have been applied, which utilize multiple receiver coils to speed up the data acquisition process. Additionally, compressed sensing (CS) is a method that facilitates image reconstruction from sparse data, significantly reducing image acquisition time by minimizing the amount of data collection needed. Recently, deep learning (DL) has emerged as a powerful tool for improving MRI reconstruction. It has been integrated with parallel imaging and CS principles to achieve faster and more accurate MRI reconstructions. This review comprehensively examines DL-based techniques for MRI reconstruction. We categorize and discuss various DL-based methods, including end-to-end approaches, unrolled optimization, and federated learning, highlighting their potential benefits. Our systematic review highlights significant contributions and underscores the potential of DL in MRI reconstruction. Additionally, we summarize key results and trends in DL-based MRI reconstruction, including quantitative metrics, the dataset, acceleration factors, and the progress of and research interest in DL techniques over time. Finally, we discuss potential future directions and the importance of DL-based MRI reconstruction in advancing medical imaging. To facilitate further research in this area, we provide a GitHub repository that includes up-to-date DL-based MRI reconstruction publications and public datasets-https://github.com/mosaf/Awesome-DL-based-CS-MRI.
Pre-trained large models attract widespread attention in recent years, but they face challenges in applications that require high interpretability or have limited resources, such as physical sensing, medical imaging, and bioinformatics. Compressed Sensing (CS) is a well-proved theory that drives many recent breakthroughs in these applications. However, as a typical under-determined linear system, CS suffers from excessively long sparse reconstruction times when using traditional iterative methods, particularly with large-scale data. Current AI methods like deep unfolding fail to substitute them because pre-trained models exhibit poor generality beyond their training conditions and dataset distributions, or lack interpretability. Instead of following the big model fervor, this paper proposes ultra-small artificial neural models called coefficients learning (CL), enabling training-free and rapid sparse reconstruction while perfectly inheriting the generality and interpretability of traditional iterative methods, bringing new feature of incorporating prior knowledges. In CL, a signal of length $n$ only needs a minimal of $n$ trainable parameters. A case study model called CLOMP is implemented for evaluation. Experiments are conducted on both synthetic and real one-dimensional and two-dimensional signals, demonstrating significant improvements in efficiency and accuracy. Compared to representative iterative methods, CLOMP improves efficiency by 100 to 1000 folds for large-scale data. Test results on eight diverse image datasets indicate that CLOMP improves structural similarity index by 292%, 98%, 45% for sampling rates of 0.1, 0.3, 0.5, respectively. We believe this method can truly usher CS reconstruction into the AI era, benefiting countless under-determined linear systems that rely on sparse solution.
Compressed sensing MRI seeks to accelerate MRI acquisition processes by sampling fewer k-space measurements and then reconstructing the missing data algorithmically. The success of these approaches often relies on strong priors or learned statistical models. While recent diffusion model-based priors have shown great potential, previous methods typically ignore clinically available metadata (e.g. patient demographics, imaging parameters, slice-specific information). In practice, metadata contains meaningful cues about the anatomy and acquisition protocol, suggesting it could further constrain the reconstruction problem. In this work, we propose ContextMRI, a text-conditioned diffusion model for MRI that integrates granular metadata into the reconstruction process. We train a pixel-space diffusion model directly on minimally processed, complex-valued MRI images. During inference, metadata is converted into a structured text prompt and fed to the model via CLIP text embeddings. By conditioning the prior on metadata, we unlock more accurate reconstructions and show consistent gains across multiple datasets, acceleration factors, and undersampling patterns. Our experiments demonstrate that increasing the fidelity of metadata, ranging from slice location and contrast to patient age, sex, and pathology, systematically boosts reconstruction performance. This work highlights the untapped potential of leveraging clinical context for inverse problems and opens a new direction for metadata-driven MRI reconstruction.
Objective: To propose and validate an unsupervised MRI reconstruction method that does not require fully sampled k-space data. Materials and Methods: The proposed method, deep image prior with structured sparsity (DISCUS), extends the deep image prior (DIP) by introducing group sparsity to frame-specific code vectors, enabling the discovery of a low-dimensional manifold for capturing temporal variations. \discus was validated using four studies: (I) simulation of a dynamic Shepp-Logan phantom to demonstrate its manifold discovery capabilities, (II) comparison with compressed sensing and DIP-based methods using simulated single-shot late gadolinium enhancement (LGE) image series from six distinct digital cardiac phantoms in terms of normalized mean square error (NMSE) and structural similarity index measure (SSIM), (III) evaluation on retrospectively undersampled single-shot LGE data from eight patients, and (IV) evaluation on prospectively undersampled single-shot LGE data from eight patients, assessed via blind scoring from two expert readers. Results: DISCUS outperformed competing methods, demonstrating superior reconstruction quality in terms of NMSE and SSIM (Studies I--III) and expert reader scoring (Study IV). Discussion: An unsupervised image reconstruction method is presented and validated on simulated and measured data. These developments can benefit applications where acquiring fully sampled data is challenging.
The growing field of remote sensing faces a challenge: the ever-increasing size and volume of imagery data are exceeding the storage and transmission capabilities of satellite platforms. Efficient compression of remote sensing imagery is a critical solution to alleviate these burdens on satellites. However, existing compression methods are often too computationally expensive for satellites. With the continued advancement of compressed sensing theory, single-pixel imaging emerges as a powerful tool that brings new possibilities for on-orbit image compression. However, it still suffers from prolonged imaging times and the inability to perform high-resolution imaging, hindering its practical application. This paper advances the study of compressed sensing in remote sensing image compression, proposing Block Modulated Imaging (BMI). By requiring only a single exposure, BMI significantly enhances imaging acquisition speeds. Additionally, BMI obviates the need for digital micromirror devices and surpasses limitations in image resolution. Furthermore, we propose a novel decoding network specifically designed to reconstruct images compressed under the BMI framework. Leveraging the gated 3D convolutions and promoting efficient information flow across stages through a Two-Way Cross-Attention module, our decoding network exhibits demonstrably superior reconstruction performance. Extensive experiments conducted on multiple renowned remote sensing datasets unequivocally demonstrate the efficacy of our proposed method. To further validate its practical applicability, we developed and tested a prototype of the BMI-based camera, which has shown promising potential for on-orbit image compression. The code is available at https://github.com/Johnathan218/BMNet.
We aim at the solution of inverse problems in imaging, by combining a penalized sparse representation of image patches with an unconstrained smooth one. This allows for a straightforward interpretation of the reconstruction. We formulate the optimization as a bilevel problem. The inner problem deploys classical algorithms while the outer problem optimizes the dictionary and the regularizer parameters through supervised learning. The process is carried out via implicit differentiation and gradient-based optimization. We evaluate our method for denoising, super-resolution, and compressed-sensing magnetic-resonance imaging. We compare it to other classical models as well as deep-learning-based methods and show that it always outperforms the former and also the latter in some instances.
At the time of environmental concerns about artificial intelligence, in particular its need for greedy storage and computation, sparsity inducing neural networks offer a promising path towards frugality and solution for less waste. Sparse learners compress the inputs (features) by selecting only the ones needed for good generalization. A human scientist can then give an intelligent interpretation to the few selected features. If genes are the inputs and cancer type is the output, then the selected genes give the cancerologist clues on what genes have an effect on certain cancers. LASSO-type regularization leads to good input selection for linear associations, but few attempts have been made for nonlinear associations modeled as an artificial neural network. A stringent but efficient way of testing whether a feature selection method works is to check if a phase transition occurs in the probability of retrieving the relevant features, as observed and mathematically studied for linear models. Our method achieves just so for artificial neural networks, and, on real data, it has the best compromise between number of selected features and generalization performance. Our method is flexible, applying to complex models ranging from shallow to deep artificial neural networks and supporting various cost functions and sparsity-promoting penalties. It does not rely on cross-validation or on a validation set to select its single regularization parameter making it user-friendly. Our approach can be seen as a form of compressed sensing for complex models, allowing to distill high-dimensional data into a compact, interpretable subset of meaningful features, just the opposite of a black box. A python package is available at https://github.com/VcMaxouuu/AnnHarderLasso containing all the simulations and ready-to-use models.
Low-rank regularization-based deep unrolling networks have achieved remarkable success in various inverse imaging problems (IIPs). However, the singular value decomposition (SVD) is non-differentiable when duplicated singular values occur, leading to severe numerical instability during training. In this paper, we propose a differentiable SVD based on the Moore-Penrose pseudoinverse to address this issue. To the best of our knowledge, this is the first work to provide a comprehensive analysis of the differentiability of the trivial SVD. Specifically, we show that the non-differentiability of SVD is essentially due to an underdetermined system of linear equations arising in the derivation process. We utilize the Moore-Penrose pseudoinverse to solve the system, thereby proposing a differentiable SVD. A numerical stability analysis in the context of IIPs is provided. Experimental results in color image compressed sensing and dynamic MRI reconstruction show that our proposed differentiable SVD can effectively address the numerical instability issue while ensuring computational precision. Code is available at https://github.com/yhao-z/SVD-inv.
Recent years have witnessed the success of deep networks in compressed sensing (CS), which allows for a significant reduction in sampling cost and has gained growing attention since its inception. In this paper, we propose a new practical and compact network dubbed PCNet for general image CS. Specifically, in PCNet, a novel collaborative sampling operator is designed, which consists of a deep conditional filtering step and a dual-branch fast sampling step. The former learns an implicit representation of a linear transformation matrix into a few convolutions and first performs adaptive local filtering on the input image, while the latter then uses a discrete cosine transform and a scrambled block-diagonal Gaussian matrix to generate under-sampled measurements. Our PCNet is equipped with an enhanced proximal gradient descent algorithm-unrolled network for reconstruction. It offers flexibility, interpretability, and strong recovery performance for arbitrary sampling rates once trained. Additionally, we provide a deployment-oriented extraction scheme for single-pixel CS imaging systems, which allows for the convenient conversion of any linear sampling operator to its matrix form to be loaded onto hardware like digital micro-mirror devices. Extensive experiments on natural image CS, quantized CS, and self-supervised CS demonstrate the superior reconstruction accuracy and generalization ability of PCNet compared to existing state-of-the-art methods, particularly for high-resolution images. Code is available at https://github.com/Guaishou74851/PCNet.
This article proposes a novel algorithm for solving mismatch problem in compressed sensing. Its core is to transform mismatch problem into matched by constructing a new measurement matrix to match measurement value under unknown measurement matrix. Therefore, we propose mismatch equation and establish two types of algorithm based on it, which are matched solution of unknown measurement matrix and calibration of unknown measurement matrix. Experiments have shown that when under low gaussian noise levels, the constructed measurement matrix can transform the mismatch problem into matched and recover original images. The code is available: https://github.com/yanglebupt/mismatch-solution
Wavefront reconstruction is a critical component in various optical systems, including adaptive optics, interferometry, and phase contrast imaging. Traditional reconstruction methods often employ either the Cartesian (pixel) basis or the Zernike polynomial basis. While the Cartesian basis is adept at capturing high-frequency features, it is susceptible to overfitting and inefficiencies due to the high number of degrees of freedom. The Zernike basis efficiently represents common optical aberrations but struggles with complex or non-standard wavefronts such as optical vortices, Bessel beams, or wavefronts with sharp discontinuities. This paper introduces a novel approach to wavefront reconstruction using an over-complete phase dictionary combined with sparse representation techniques. By constructing a dictionary that includes a diverse set of basis functions - ranging from Zernike polynomials to specialized functions representing optical vortices and other complex modes - we enable a more flexible and efficient representation of complex wavefronts. Furthermore, a trainable affine transform is implemented to account for misalignment. Utilizing principles from compressed sensing and sparse coding, we enforce sparsity in the coefficient space to avoid overfitting and enhance robustness to noise.
We examine the problem of selecting a small set of linear measurements for reconstructing high-dimensional signals. Well-established methods for optimizing such measurements include principal component analysis (PCA), independent component analysis (ICA) and compressed sensing (CS) based on random projections, all of which rely on axis- or subspace-aligned statistical characterization of the signal source. However, many naturally occurring signals, including photographic images, contain richer statistical structure. To exploit such structure, we introduce a general method for obtaining an optimized set of linear measurements for efficient image reconstruction, where the signal statistics are expressed by the prior implicit in a neural network trained to perform denoising (known as a ``diffusion model''). We demonstrate that the optimal measurements derived for two natural image datasets differ from those of PCA, ICA, or CS, and result in substantially lower mean squared reconstruction error. Interestingly, the marginal distributions of the measurement values are asymmetrical (skewed), substantially more so than those of previous methods. We also find that optimizing with respect to perceptual loss, as quantified by structural similarity (SSIM), leads to measurements different from those obtained when optimizing for MSE. Our results highlight the importance of incorporating the specific statistical regularities of natural signals when designing effective linear measurements.
Generative models based on flow matching have attracted significant attention for their simplicity and superior performance in high-resolution image synthesis. By leveraging the instantaneous change-of-variables formula, one can directly compute image likelihoods from a learned flow, making them enticing candidates as priors for downstream tasks such as inverse problems. In particular, a natural approach would be to incorporate such image probabilities in a maximum-a-posteriori (MAP) estimation problem. A major obstacle, however, lies in the slow computation of the log-likelihood, as it requires backpropagating through an ODE solver, which can be prohibitively slow for high-dimensional problems. In this work, we propose an iterative algorithm to approximate the MAP estimator efficiently to solve a variety of linear inverse problems. Our algorithm is mathematically justified by the observation that the MAP objective can be approximated by a sum of $N$ ``local MAP'' objectives, where $N$ is the number of function evaluations. By leveraging Tweedie's formula, we show that we can perform gradient steps to sequentially optimize these objectives. We validate our approach for various linear inverse problems, such as super-resolution, deblurring, inpainting, and compressed sensing, and demonstrate that we can outperform other methods based on flow matching. Code is available at https://github.com/YasminZhang/ICTM.
We study nonconvex zeroth-order optimization (ZOO) in a high-dimensional space $\mathbb R^d$ for functions with approximately $s$-sparse gradients. To reduce the dependence on the dimensionality $d$ in the query complexity, high-dimensional ZOO methods seek to leverage gradient sparsity to design gradient estimators. The previous best method needs $O\big(s\log\frac ds\big)$ queries per step to achieve $O\big(\frac1T\big)$ rate of convergence w.r.t. the number T of steps. In this paper, we propose *Gradient Compressed Sensing* (GraCe), a query-efficient and accurate estimator for sparse gradients that uses only $O\big(s\log\log\frac ds\big)$ queries per step and still achieves $O\big(\frac1T\big)$ rate of convergence. To our best knowledge, we are the first to achieve a *double-logarithmic* dependence on $d$ in the query complexity under weaker assumptions. Our proposed GraCe generalizes the Indyk--Price--Woodruff (IPW) algorithm in compressed sensing from linear measurements to nonlinear functions. Furthermore, since the IPW algorithm is purely theoretical due to its impractically large constant, we improve the IPW algorithm via our *dependent random partition* technique together with our corresponding novel analysis and successfully reduce the constant by a factor of nearly 4300. Our GraCe is not only theoretically query-efficient but also achieves strong empirical performance. We benchmark our GraCe against 12 existing ZOO methods with 10000-dimensional functions and demonstrate that GraCe significantly outperforms existing methods.
Deep neural networks are vulnerable to so-called adversarial examples: inputs which are intentionally constructed to cause the model to make incorrect predictions or classifications. Adversarial examples are often visually indistinguishable from natural data samples, making them hard to detect. As such, they pose significant threats to the reliability of deep learning systems. In this work, we study an adversarial defense based on the robust width property (RWP), which was recently introduced for compressed sensing. We show that a specific input purification scheme based on the RWP gives theoretical robustness guarantees for images that are approximately sparse. The defense is easy to implement and can be applied to any existing model without additional training or finetuning. We empirically validate the defense on ImageNet against $L^\infty$ perturbations at perturbation budgets ranging from $4/255$ to $32/255$. In the black-box setting, our method significantly outperforms the state-of-the-art, especially for large perturbations. In the white-box setting, depending on the choice of base classifier, we closely match the state of the art in robust ImageNet classification while avoiding the need for additional data, larger models or expensive adversarial training routines. Our code is available at https://github.com/peck94/robust-width-defense.
Unrolled deep neural networks have attracted significant attention for their success in various practical applications. In this paper, we explore an application of deep unrolling in the direction of arrival (DoA) estimation problem when coarse quantization is applied to the measurements. We present a compressed sensing formulation for DoA estimation from one-bit data in which estimating target DoAs requires recovering a sparse signal from a limited number of severely quantized linear measurements. In particular, we exploit covariance recovery from one-bit dither samples. To recover the covariance of transmitted signal, the learned iterative shrinkage and thresholding algorithm (LISTA) is employed fed by one-bit data. We demonstrate that the upper bound of estimation performance is governed by the recovery error of the transmitted signal covariance matrix. Through numerical experiments, we demonstrate the proposed LISTA-based algorithm's capability in estimating target locations. The code employed in this study is available online.