Sparse Recovery

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Overview

Sparse recovery asks how to identify a small set of nonzero coefficients and estimate their values from incomplete or noisy observations, a problem central to compressed sensing, imaging, and high-dimensional regression. Common approaches include convex ℓ1 regularization, greedy and hard-thresholding algorithms, Bayesian and nonconvex penalties, and learned or unrolled methods that incorporate structure such as groups, blocks, or dictionaries. Theory uses tools such as restricted isometry, mutual coherence, and geometric complexity to establish recovery conditions, while newer work extends guarantees to online, nonlinear, and adversarially corrupted settings. A continuing challenge is balancing statistical accuracy and robustness against computational cost, especially when measurements are highly correlated or the assumed sparse representation is imperfect.

Latest papers

CardsList

77 papers11 papers in the last four weeks, up 38% on the four weeks before. 0.1% of all new papers.

  1. A Constructive Orbit-Based Theory of Learnability

    Oct 30, 2026Yunied PuigSparse RecoveryStatistical Learning Theory

  2. Threshold Compatibility and Support-Selection Diagnostics in Neural Discovery of Partial Differential Equations

    Oct 27, 2026Zeen SongPDE DiscoveryModel Selection

    School of Mathematics, Statistics and Mechanics Beijing University of Technology, Beijing 100124, China

  3. A knowledge-driven nonconvex square-root regularization framework for joint group sparsity and structured smoothness

    Oct 26, 2026Wanling Xie, Hu YangStructured SparsitySparse Recovery

    College of Mathematics and Statistics, Hunan University of Technology and Business, Changsha, Hunan 410205, China · College of Mathematics and Statistics, Chongqing University, Chongqing, 401331, China

  4. Sparse Reconstruction by Direct Measurement-to-Field Generation in Function Space

    Oct 26, 2026Linzheng Wang, Jason Chen, Nicolas Tricard +3Sparse RecoveryInverse Problems

    Department of Mechanical Engineering, Massachusetts Institute of Technology, Cambridge, MA 02139, USA · Department of Civil, Environmental and Geomatic Engineering, University College London, London WC1E 6BT, UK · Department of Engineering, University of Cambridge, Cambridge CB2 1PZ, UK

  5. Can Metadata Fix the Gauge? Calibration Turns Sparse Multi-Source Learning from Sparse PCA into Sparse Mean Recovery

    Oct 19, 2026Yirong Xiang, Yibo ZhouSparse Recovery

    Air Force Medical Center · Beihang University

  6. Distinguishability and Recovery for a Doubly Sparse Spiked Wigner Model

    Oct 16, 2026Ioana Dumitriu, JD Flynn, Zhichao WangSparse RecoveryRandom Matrix Theory

    University of California, San Diego · University of California, Berkeley

  7. LGGS: Longitudinal MRI Reconstruction via Guided Group Sparsity

    Oct 15, 2026Nikola Janjušević, Hersh Chandarana, Yao Wang +1Accelerated MRI ReconstructionLongitudinal Medical Image Analysis

    Radiology Department, New York University Grossman School of Medicine, New York, NY 10016 USA · Electrical and Computer Engineering Department, New York University Tandon School of Engineering, Brooklyn, NY 11201 USA

  8. Multiscale Generalized Sparse Plane Wave Decomposition in the Spherical Harmonic Domain

    Oct 15, 2026Huseyin HacihabibogluSpatial AudioSparse Recovery

    Graduate School of Informatics, METU, Ankara, TR-06800, Türkiye

  9. Readout Scaling Shapes Sparse Feature Recovery

    Oct 13, 2026Brian Xiao, Sarah WilsonSparse AutoencodersSparse Recovery

    University of Waterloo · Columbia University

  10. Learning Incompressible 3D Flows from Sparse Samples: A Set Transformer Approach to Divergence-Free Kernel Fitting

    Oct 12, 2026Ramzi Idoughi, Radouan Boukharfane, Peter WonkaSet TransformerComputational Fluid Dynamics

    King Abdullah University of Science and Technology (KAUST), Thuwal, Saudi Arabia · Mohammed VI Polytechnic University (UM6P), Benguerir, Morocco

  11. A Physics-Informed Hybrid Forward-Inverse Machine Learning Framework for High-Dimensional Sparse Recipe Reconstruction

    Oct 8, 2026Md. Muqtadir Fuad, Md. Istiak Adnan, Ridwan Al AzizInverse DesignSparse Recovery

    Department of Industrial and Production Engineering, Bangladesh University of Engineering and Technology (BUET), Dhaka 1000, Bangladesh

  12. Robust Tensor Completion via Reflective Convolution Nuclear Norm Minimization

    Oct 4, 2026Weiguo Zhou, Feng Zhang, Wenjin Qin +1Tensor CompletionNuclear Norm Minimization

    School of Mathematics and Statistics, Southwest University, Chongqing, 400715, China · College of Artificial Intelligence and Advanced Interdisciplinary Sciences, Chongqing Normal University, Chongqing, 401331, China

  13. Non-Adaptive Learning of Sparse Erdős--Rényi Graphs via Affine Splitting

    Sep 27, 2026Hoang TaGraph Structure LearningSparse Recovery

    Department of Computer Science, Hanoi University of Science and Technology, Vietnam

  14. StarBOA: Real-Time Mamba State-Space Unrolling for Sparse Radar Micro-Doppler in ISAC Networks

    Sep 27, 2026Mustafa Bora Çelik, Ceren Çelik, Orhan GaziSparse RecoveryIntegrated Sensing and Communication

  15. Efficient Support Recovery of Mixtures of Sparse Linear Classifiers with Fewer Measurements

    Sep 26, 2026Xiaxin Li, Arya MazumdarSparse RecoverySample Complexity

    Halıcıoğlu Data Science Institute, University of California, San Diego

  16. Iterative Atom Refinement: A Monotonicity Principle for Dictionary Learning

    Sep 20, 2026Alexander Christie, Miguel Moscoso, Alexei Novikov +2Sparse RecoveryDictionary Learning

    Department of Mathematics, Stanford University, Stanford, CA 94305, USA · Department of Mathematics, Universidad Carlos III de Madrid, Leganés, Madrid 28911, Spain · Department of Mathematics, Pennsylvania State University, University Park, PA 16802, USA +1

  17. Sparse Identification for Automatic Large-Scale Screening: A Constraint-Aware Framework with Ultra Fast Decoding Algorithm

    Sep 18, 2026Jianing Li, Li Chai, Yingcheng LaiSparse RecoveryMedical Diagnosis

    College of Control Science and Engineering, Zhejiang University, Hangzhou 310027, China

  18. Diagonalized Attention for Individualized Regression: Latent-Row Localization and Prediction

    Sep 18, 2026Borui Peng, Liwei Lin, Feifei Wang +1Feature SelectionSparse Attention

    School of Computing & Data Science, University of Hong Kong · School of Statistics, Renmin University of China

  19. High-Magnetization Sampling at Low Temperatures: Ising Models and Bayesian Sparse Linear Regression

    Sep 8, 2026Syamantak Kumar, Purnamrita Sarkar, Kevin Tian +1Sparse RecoveryIsing Model

    University of Texas at Austin

  20. Recovering linear images of sparse signals from indirect observations

    Sep 5, 2026Anatoli Juditsky, Arkadi NemirovskiSparse RecoveryCompressed Sensing

    LJK, Université Grenoble Alpes, 700 Avenue Centrale, 38401 Domaine Universitaire de Saint-Martin-d’Hères, France · Georgia Institute of Technology, Atlanta, Georgia 30332, USA

  21. Restricted Eigenvalues Beyond Gaussian Width: Threshold Occupancy under Heavy Tails

    Sep 3, 2026Shi Fu, Huibo Xu, Qixin Zhang +1Sparse RecoveryHeavy-Tailed Noise

    Generative AI Lab, College of Computing and Data Science, Nanyang Technological University, Singapore

  22. HarmoCore: Functional Latent Diffusion for Sparse Reconstruction of Oscillatory Wave Fields

    Sep 1, 2026Lihao Chen, Xinyu Zhang, Panqi Chen +4Sparse RecoveryLatent Diffusion Models

    College of Information Science and Electronic Engineering, Zhejiang University

  23. Sharp Restricted Isometry Thresholds for Global Minima of Rank-Restricted Matrix LASSO

    Aug 29, 2026Richard Y. ZhangMatrix OptimizationSparse Recovery

    Department of Electrical and Computer Engineering, University of Illinois Urbana–Champaign, Urbana, IL 61801 USA

  24. Towards a mathematical theory of superposition

    Aug 27, 2026Michael I. Ivanitskiy, John Jasper, Emily J. King +1Feature SuperpositionSparse Recovery

    Department of Applied Mathematics and Statistics, Colorado School of Mines, Golden, CO, USA · Department of Mathematics & Statistics, Air Force Institute of Technology, Wright-Patterson AFB, OH, USA · Department of Mathematics, Colorado State University, Fort Collins, CO, USA +2

  25. Physical-Support Confidence Sets for Highly Coherent Dictionaries

    Aug 20, 2026Guan-Ju PengQuery IdentifiabilitySparse Recovery

    Institute of Data Science and Information Computing, National Chung Hsing University, Taichung, Taiwan

  26. GCNO: Gramian Chebyshev Neural Operator for Physics-Based Compression of Wireless Channels

    Aug 19, 2026Rafid Umayer Murshed, Shahab Hamidi-Rad, Elahe Soltanaghai +1Wireless CommunicationsNeural Operators

    Department of Computer Science, University of Illinois Urbana-Champaign · InterDigital AI Lab

  27. Online Generalized Sparse Regression: How Does Overparametrization Help?

    Aug 18, 2026Shuoguang Yang, Qiang SunOverparameterizationSparse Recovery

    HKUST · University of Toronto and MBZUAI

  28. Coded Hankel Polynomial Chaos: Spectral Identification of Dominant Polynomial-Chaos Modes

    Aug 17, 2026Zhiliang Deng, Xiaomei YangUncertainty QuantificationSpectral Methods

    School of Mathematical Science, University of Electronic Science and Technology of China · School of Mathematics, Southwest Jiaotong University

  29. Learning the Mathematical Property for Designing Low Mutual Coherence Binary Sensing Matrices

    Aug 13, 2026Rekha, Santosh Singh, S. K. NeogySparse RecoveryCompressed Sensing

    Department of Mathematics, Shiv Nadar Institution of Eminence, Delhi, India. · Centre for Research on Economics and Data Analysis (CREDA), Indian Statistical Institute, New Delhi, India.

  30. Robust data-driven discovery of fractional differential equations via weak formulations and Pareto-based subset selection

    Aug 13, 2026Pongpisit Thanasutives, Yoshinobu KawaharaSparse RecoveryPDE Discovery

    Center for Advanced Intelligence Project (AIP), RIKEN, Tokyo, Japan. · Graduate School of Information Science and Technology, The University of Osaka, Osaka, Japan.