mlsanityData to 7 Oct 2026

A survey of sparse representation: algorithms and applications

arXiv 1602.07017 ↗First posted 23 Feb 2016cs.CV cs.LGcited by 58

Not on the map. Why?

Abstract (arXiv)

Sparse representation has attracted much attention from researchers in fields of signal processing, image processing, computer vision and pattern recognition. Sparse representation also has a good reputation in both theoretical research and practical applications. Many different algorithms have been proposed for sparse representation. The main purpose of this article is to provide a comprehensive study and an updated review on sparse representation and to supply a guidance for researchers. The taxonomy of sparse representation methods can be studied from various viewpoints. For example, in terms of different norm minimizations used in sparsity constraints, the methods can be roughly categorized into five groups: sparse representation with l0-norm minimization, sparse representation with lp-norm (0<p<1) minimization, sparse representation with l1-norm minimization and sparse representation with l2,1-norm minimization. In this paper, a comprehensive overview of sparse representation is provided. The available sparse representation algorithms can also be empirically categorized into four groups: greedy strategy approximation, constrained optimization, proximity algorithm-based optimization, and homotopy algorithm-based sparse representation. The rationales of different algorithms in each category are analyzed and a wide range of sparse representation applications are summarized, which could sufficiently reveal the potential nature of the sparse representation theory. Specifically, an experimentally comparative study of these sparse representation algorithms was presented. The Matlab code used in this paper can be available at: http://www.yongxu.org/lunwen.html.

Key facts. Cited by 58 papers in the map (data through 7 Oct 2026). First posted on arXiv 23 Feb 2016.

Builds on

No reference list yet.

Built on by

Cited by year (2026 to 7 Oct)

Citing papers per year: 2021: 9; 2022: 9; 2023: 8; 2024: 14; 2025: 11; 2026: 7.

58 papers.

Sort:

By area:

  1. 2022Learning Vector-Quantized Item Representation for Transferable Sequential Recommenderscited by 112
  2. 2023ViTMatte: Boosting Image Matting with Pretrained Plain Vision Transformerscited by 56
  3. 2021Tensor Methods in Computer Vision and Deep Learningcited by 52
  4. 2025Beyond Matryoshka: Revisiting Sparse Coding for Adaptive Representationcited by 25
  5. 2022Robust Structured Declarative Classifiers for 3D Point Clouds: Defending Adversarial Attacks with Implicit Gradientscited by 17
  6. 2022Explainable AI via Learning to Optimizecited by 14
  7. 2025Mirror, Mirror of the Flow: How Does Regularization Shape Implicit Bias?cited by 10
  8. 2021Temporal Graph Signal Decompositioncited by 8
  9. 2022Optimization-Derived Learning with Essential Convergence Analysis of Training and Hyper-trainingcited by 5
  10. 2023Do Not Train It: A Linear Neural Architecture Search of Graph Neural Networkscited by 5
  11. 2024Sparse and Faithful Explanations Without Sparse Modelscited by 5
  12. 2024MaVEn: An Effective Multi-granularity Hybrid Visual Encoding Framework for Multimodal Large Language Modelcited by 5
38 more
  1. 2024Beyond Label Attention: Transparency in Language Models for Automated Medical Coding via Dictionary Learningcited by 5
  2. 2021CSC-Unet: A Novel Convolutional Sparse Coding Strategy Based Neural Network for Semantic Segmentationcited by 3
  3. 2021Sparse Coding with Multi-Layer Decoders using Variance Regularizationcited by 3
  4. 2022Adaptive Cross-Layer Attention for Image Restorationcited by 3
  5. 2023SRATTA : Sample Re-ATTribution Attack of Secure Aggregation in Federated Learningcited by 3
  6. 2023Interactive Generalized Additive Model and Its Applications in Electric Load Forecastingcited by 3
  7. 2024DILA: Dictionary Label Attention for Mechanistic Interpretability in High-dimensional Multi-label Medical Coding Predictioncited by 3
  8. 2024Learning of Patch-Based Smooth-Plus-Sparse Models for Image Reconstructioncited by 3
  9. 2024Sparse Reconstruction of Optical Doppler Tomography with Alternative State Space Model and Attentioncited by 2
  10. 2024WARP-LCA: Efficient Convolutional Sparse Coding with Locally Competitive Algorithmcited by 2
  11. 2025DB-KSVD: Scalable Alternating Optimization for Disentangling High-Dimensional Embedding Spacescited by 2
  12. 2025Visual Exploration of Feature Relationships in Sparse Autoencoders with Curated Conceptscited by 2
  13. 2021Salt and pepper noise removal method based on stationary Framelet transform with non-convex sparsity regularizationcited by 1
  14. 2021Discriminative Dictionary Learning based on Statistical Methodscited by 1
  15. 2023Multi-Dictionary Tensor Decompositioncited by 1
  16. 2024Sparsity via Sparse Group k-max Regularizationcited by 1
  17. 2024Low Rank Multi-Dictionary Selection at Scalecited by 1
  18. 2025Robust Foreground-Background Separation for Severely-Degraded Videos Using Convolutional Sparse Representation Modelingcited by 1
  19. 2025WEEP: A Differentiable Nonconvex Sparse Regularizer via Weakly-Convex Envelopecited by 1
  20. 2026Where Concept Erasure Should Occur: Concept-Layer Alignment in Text-to-Video Diffusion Modelscited by 1
  21. 2021Knowledge Distillation By Sparse Representation Matchingcited by 0
  22. 2021Signal Processing Challenges and Examples for it in-situ Transmission Electron Microscopycited by 0
  23. 2021Cascaded Compressed Sensing Networks: A Reversible Architecture for Layerwise Learningcited by 0
  24. 20222D+3D facial expression recognition via embedded tensor manifold regularizationcited by 0
  25. 2022Multi-scale Sparse Representation-Based Shadow Inpainting for Retinal OCT Imagescited by 0
  26. 2022Cautious Learning of Multiattribute Preferencescited by 0
  27. 2022An adaptive shortest-solution guided decimation approach to sparse high-dimensional linear regressioncited by 0
  28. 20233D wind field profiles from hyperspectral sounders: revisiting optic-flow from a meteorological perspectivecited by 0
  29. 2023Harnessing Scalable Transactional Stream Processing for Managing Large Language Models [Vision]cited by 0
  30. 2023Robust Ordinal Regression for Subsets Comparisons with Interactionscited by 0
  31. 2024Automatic dimensionality reduction of Twin-in-the-Loop Observerscited by 0
  32. 2024In-Flight Estimation of Instrument Spectral Response Functions Using Sparse Representationscited by 0
  33. 2024Semi-adaptive Synergetic Two-way Pseudoinverse Learning Systemcited by 0
  34. 2024Dy-mer: An Explainable DNA Sequence Representation Scheme using Dictionary Learningcited by 0
  35. 2024Pareto Data Framework: Steps Towards Resource-Efficient Decision Making Using Minimum Viable Data (MVD)cited by 0
  36. 2025Kernel Recursive Least Squares Dictionary Learning Algorithmcited by 0
  37. 2025Robust Multi-Manifold Clustering via Simplex Pathscited by 0
  38. 2025Multi-Dictionary Learning for Low Rank Sparse Codingcited by 0

50 most cited of 58 All 58 (JSON)