Accelerating Convergence of Proximal Methods for Compressed Sensing using Polynomials with Application to MRI

Ranked by how close their title and abstract are to this paper’s. Select some to read them together.

Closest papers

1. Very close Same method, another problem Cited by this paper A method it uses Not relevant

   Polynomial Preconditioning for Accelerated Convergence of Proximal Algorithms including FISTA

   S. Iyer, Frank Ong, K. Setsompop · ISMRM Annual Meeting · cited 1 time · Not summarized yet

   Polynomial Preconditioning applies spectrum-targeting polynomial preconditioners to proximal algorithms across imaging applications, including the MRI convergence problem studied here.

   Abstract

   This work aims to accelerate the convergence of proximal gradient algorithms (like FISTA) by designing a preconditioner using polynomials that targets the eigenvalue spectrum of the forward linear model to enable faster convergence. The preconditioner does not assume any explicit structure and can be applied to various imaging applications. The efficacy of the preconditioner is validated on four varied imaging applications, where it seen to achieve 2-4x faster convergence.

2. Very close Another approach to the problem Cited by this paper Not relevant

   Accelerating compressed sensing in parallel imaging reconstructions using an efficient circulant preconditioner for cartesian trajectories

   K. Koolstra, J. V. Van Gemert, P. Börnert et al. · 2017 · Magnetic Resonance in Medicine · cited 17 times · Not summarized yet

   This paper uses a circulant preconditioner to accelerate Cartesian parallel-imaging compressed-sensing reconstructions, rather than the polynomial preconditioner studied here.

   Abstract

   Design of a preconditioner for fast and efficient parallel imaging (PI) and compressed sensing (CS) reconstructions for Cartesian trajectories.

3. Close Another approach to the problem Cited by this paper Used in depth by this paper A method it uses Not relevant

   Accelerating Non-Cartesian MRI Reconstruction Convergence using k-space Preconditioning

   Frank Ong, M. Uecker, M. Lustig · 2019 · IEEE Transactions on Medical Imaging · cited 47 times · Not summarized yet

   This paper preconditions non-Cartesian MRI reconstruction in k-space using a dual formulation and primal-dual hybrid gradient, rather than polynomial preconditioning.

   Abstract

   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 accele…

4. Close Another approach to the problem Cites this paper Uses this paper in depth Not relevant

   A Complex Quasi-Newton Proximal Method for Image Reconstruction in Compressed Sensing MRI

   Tao Hong, L. Hernandez-Garcia, J. Fessler · 2023 · IEEE Transactions on Computational Imaging · cited 21 times · Not summarized yet

   This paper accelerates compressed-sensing MRI with a complex quasi-Newton proximal method, whereas this paper designs a polynomial preconditioner for proximal methods.

   Abstract

   Model-based methods are widely used for reconstruction in compressed sensing (CS) magnetic resonance imaging (MRI), using regularizers to describe the images of interest. The reconstruction process is equivalent to solving a composite optimization problem. Accelerated proximal methods (APMs) are very popular approaches for such problems. This paper proposes a complex quasi-Newton proximal method (CQNPM) for the wavelet and total variation based CS MRI reconstruction. Compared with APMs, CQNPM requires fewer iterations to converge but needs to compute a more challenging proximal mapping called weighted proximal mapping (WPM). To make CQNPM more practical, we propose efficient methods to solve…

5. Close Same question Cites this paper Not relevant

   Provable Preconditioned Plug-and-Play Approach for Compressed Sensing MRI Reconstruction

   Tao Hong, Xiaojian Xu, Jason Hu et al. · 2024 · IEEE Trans. Computational Imaging · cited 20 times · Not summarized yet

   This paper also seeks faster compressed-sensing MRI reconstruction through preconditioning, applying it to plug-and-play methods.

   Abstract

   Model-based methods play a key role in the reconstruction of compressed sensing (CS) MRI. Finding an effective prior to describe the statistical distribution of the image family of interest is crucial for model-based methods. Plug-and-play (PnP) is a general framework that uses denoising algorithms as the prior or regularizer. Recent work showed that PnP methods with denoisers based on pretrained convolutional neural networks outperform other classical regularizers in CS MRI reconstruction. However, the numerical solvers for PnP can be slow for CS MRI reconstruction. This paper proposes a preconditioned PnP P2nP method to accelerate the convergence speed. Moreover, we provide proofs of the f…

6. Close Same question Cites this paper Not relevant

   Deep Distillation Gradient Preconditioning for Inverse Problems

   Romario Gualdrón-Hurtado, Roman Jacome, Leon Suarez et al. · 2025 · IEEE International Workshop on Computational Advances in Multi-Sensor Adaptive Processing · Not summarized yet

   This paper addresses convergence in inverse problems by preconditioning gradient updates, using a learned method rather than polynomial preconditioning.

   Abstract

   Imaging inverse problems are commonly addressed by minimizing measurement consistency and signal prior terms. While huge attention has been paid to developing highperformance priors, even the most advanced signal prior may lose its effectiveness when paired with an ill-conditioned sensing matrix that hinders convergence and degrades reconstruction quality. In optimization theory, preconditioners allow improving the algorithm’s convergence by transforming the gradient update. Traditional linear preconditioning techniques enhance convergence, but their performance remains limited due to their dependence on the structure of the sensing matrix. Learning-based linear preconditioners have been pro…

7. Close Same question Cited by this paper Not relevant

   Rapid Compressed Sensing Reconstruction of 3D Non-Cartesian MRI

   C. Baron, N. Dwork, J. Pauly et al. · 2017 · Magnetic Resonance in Medicine · cited 80 times · Not summarized yet

   This paper seeks faster compressed-sensing reconstruction for 3D non-Cartesian MRI while preserving accuracy, a reconstruction setting related to this paper’s MRI applications.

   Abstract

   Conventional non‐Cartesian compressed sensing requires multiple nonuniform Fourier transforms every iteration, which is computationally expensive. Accordingly, time‐consuming reconstructions have slowed the adoption of undersampled 3D non‐Cartesian acquisitions into clinical protocols. In this work we investigate several approaches to minimize reconstruction times without sacrificing accuracy.

8. Close* Groundwork for this paper Cited by this paper Not relevant

   Sparse MRI: The application of compressed sensing for rapid MR imaging

   M. Lustig, D. Donoho, John M. Pauly · 2007 · Magnetic Resonance in Medicine · cited 7,699 times · Not summarized yet

   Sparse MRI introduces compressed sensing for rapid MR imaging, the application area in which this paper accelerates reconstruction.

Prior work it builds on

1. Related* Broader context Used in depth by this paper A method it uses Not relevant

   Compressed Sensing MRI

   M. Lustig, D. Donoho, Juan M. Santos et al. · 2008 · IEEE Signal Processing Magazine · cited 2,386 times · Not summarized yet

   Compressed Sensing MRI concerns the same broad reconstruction application, while this paper focuses specifically on accelerating proximal methods.

2. Related* Groundwork for this paper Used in depth by this paper A method it uses Not relevant

   A Mathematical Introduction to Compressive Sensing

   Simon Foucart, Holger Rauhut · 2013 · Applied and Numerical Harmonic Analysis · cited 2,582 times · Not summarized yet

   A Mathematical Introduction to Compressive Sensing provides background on the compressed-sensing framework used for the inverse problems studied here.

3. Related Broader context Used in depth by this paper A method it uses Not relevant

   ESPIRiT — An Eigenvalue Approach to Autocalibrating Parallel MRI: Where SENSE meets GRAPPA

   M. Uecker, P. Lai, M. Murphy et al. · 2014 · Magnetic Resonance in Medicine · cited 1,626 times · Not summarized yet

   ESPIRiT develops an autocalibrating parallel MRI reconstruction algorithm, an MRI application context distinct from this paper’s convergence preconditioning.

   Abstract

   Parallel imaging allows the reconstruction of images from undersampled multicoil data. The two main approaches are: SENSE, which explicitly uses coil sensitivities, and GRAPPA, which makes use of learned correlations in k‐space. The purpose of this work is to clarify their relationship and to develop and evaluate an improved algorithm.

4. Related* Broader context Used in depth by this paper A method it uses Not relevant

   Toeplitz-based iterative image reconstruction for MRI with correction for magnetic field inhomogeneity

   J. Fessler, Sangwoo Lee, Valur Thor Olafsson et al. · 2005 · IEEE Transactions on Signal Processing · cited 171 times · Not summarized yet

   This paper uses a Toeplitz-based approach for MRI reconstruction with field-inhomogeneity correction, a neighboring MRI reconstruction problem.

5. Related Another approach to the problem A method it uses Not relevant

   Fast iteratively reweighted least squares algorithms for analysis‐based sparse reconstruction

   Chen Chen, Lei He, Hongsheng Li et al. · 2018 · Medical Image Anal. · cited 44 times · Not summarized yet

   This paper accelerates analysis-based sparse reconstruction, including total variation, using preconditioning and incomplete LU decomposition rather than polynomial preconditioning.

   Abstract

   HighlightsA generalized form for the analysis‐based sparsity reconstruction, which contains the total variation (TV) regularization.A novel method to accelerate the optimization for different structured sparsity patterns using the proposed preconditioning.An entirely new algorithm is proposed to solve the TV and joint TV based reconstruction, by the proposed preconditioner and incomplete LU decomposition.Extensive comparisons with 14 state‐of‐the‐art algorithms. Graphical abstract Figure. No caption available. ABSTRACT In this paper, we propose a novel algorithm for analysis‐based sparsity reconstruction. It can solve the generalized problem by structured sparsity regularization with an orth…

Papers that cite it

1. Related Same question Not relevant

   A Decay-Modeled Compressed Sensing Reconstruction Approach for non-Cartesian Hyperpolarized 129Xe MRI

   J. Plummer, R. Hussain, A. Bdaiwi et al. · 2024 · Magnetic Resonance in Medicine · cited 9 times · Not summarized yet

   This paper reconstructs undersampled non-Cartesian hyperpolarized xenon MRI with compressed sensing, incorporating magnetization decay in the forward model.

   Abstract

   Hyperpolarized 129Xe MRI benefits from non‐Cartesian acquisitions that sample k‐space efficiently and rapidly. However, their reconstructions are complex and burdened by decay processes unique to hyperpolarized gas. Currently used gridded reconstructions are prone to artifacts caused by magnetization decay and are ill‐suited for undersampling. We present a compressed sensing (CS) reconstruction approach that incorporates magnetization decay in the forward model, thereby producing images with increased sharpness and contrast, even in undersampled data.

2. Related Broader context Not relevant

   Rethinking Model-Based Non-Cartesian Fourier Imaging: A New K-Space Model

   Chin-Cheng Chan, Justin P. Haldar · 2025 · IEEE International Symposium on Biomedical Imaging · cited 1 time · Not summarized yet

   This paper examines modeling limitations in non-Cartesian Fourier image reconstruction, a modeling issue adjacent to this paper’s MRI inverse problems.

   Abstract

   Over the past quarter-century, model-based Fourier image reconstruction methods have typically modeled the continuous image as a linear combination of shifted voxel basis functions. Despite its popularity, this model suffers from long-standing practical issues (e.g., expensive computations and a propensity for artifacts). While substantial effort has been spent to alleviate these well-known problems, we observe in this work that this model also suffers from more fundamental issues that do not appear to be previously known. This includes an implicit periodicity assumption (which can limit modeling accuracy) and a systematic tendency to produce unrealistic cross-like structures in k-space. Imp…

3. Related Same question Not relevant

   Learning Preconditioners in Gates-controlled Deep Unfolding Networks based on Quasi-Newton Methods For Accelerated MRI Reconstruction

   Xiaoyu Qiao, Wei-Sheng Li, Bin Xiao et al. · 2025 · IEEE International Conference on Acoustics, Speech, and Signal Processing · Not summarized yet

   This paper uses preconditioning to improve convergence in MRI reconstruction, combining it with gates-controlled deep unfolding and quasi-Newton optimization.

   Abstract

   Deep unfolding networks (DUNs) have made significant progress in MRI reconstruction, successfully tackling the problem of prolonged imaging time. However, the ill-conditioned nature of MRI reconstruction often causes slow convergence in iterative optimization, potentially compromising the performance of DUNs. In this study we propose a preconditioned and gates-controlled DUN (PGDUN) to address these challenges. Our approach starts with optimizing the step size of proximal gradient descent (PGD) through a preconditioner. To improve flexibility and adaptability, we relax the constrains on quasi-newton-based optimization procedure. We design ConvLSTM-based modules, where the gate units automati…

4. Related Broader context Not relevant

   A New k-Space Model for Non-Cartesian Fourier Imaging

   Chin-Cheng Chan, Justin P. Haldar · 2025 · IEEE Transactions on Computational Imaging · Not summarized yet

   This paper reexamines the k-space model for non-Cartesian Fourier imaging, while this paper targets convergence of proximal reconstruction methods.

   Abstract

   For the past several decades, it has been popular to reconstruct Fourier imaging data using model-based approaches that can easily incorporate physical constraints and advanced regularization/machine learning priors. The most common modeling approach is to represent the continuous image as a linear combination of shifted “voxel” basis functions. Although well-studied and widely-deployed, this voxel-based model is associated with longstanding limitations, including high computational costs, slow convergence, and a propensity for artifacts. In this work, we reexamine this model from a fresh perspective, identifying new issues that may have been previously overlooked (including undesirable appr…

5. Related Broader context Not relevant

   On Optimality in ROVir

   J. Haldar · 2023 · cited 1 time · Not summarized yet

   This paper studies virtual-coil compression and spatial signal suppression in MRI, rather than convergence acceleration for image reconstruction.

   Abstract

   We recently published an approach named ROVir (Region-Optimized Virtual coils) that uses the beamforming capabilities of a multichannel magnetic resonance imaging (MRI) receiver array to achieve coil compression (reducing an original set of receiver channels into a much smaller number of virtual channels for the purposes of dimensionality reduction), while simultaneously preserving the MRI signal from desired spatial regions and suppressing the MRI signal arising from unwanted spatial regions. The original ROVir procedure is computationally-simple to implement (involving just a single small generalized eigendecomposition), and its signal-suppression capabilities have proven useful in an incr…