Research map / Learning theory and algorithms / Matrix and tensor methods
Signal recovery and phase retrieval
Recovers signals from measurements through convex programming and generative or structured priors.
66 accepted papers at ICML, NeurIPS, ICLR, CVPR and AAAI (2016–2026) · an approach in Matrix and tensor methods, keyword cluster “sparse · recovery · pca”
State History Tried Preprints Who Export
Where it stands
Not enough benchmark data Fewer than four papers report the same benchmark, so there is no record to follow.
11 papers in 2023–24 and 9 in 2025–26 (at ICML, NeurIPS, ICLR, CVPR and AAAI); its share of the topic shrank, from 6.4% to 4.8%.
How this is decided
A benchmark is tracked when at least four papers of this approach report their own method on the same dataset and metric in at least two different years. Its record is the best number reported up to 2024 compared with the best reported in 2025–26: still improving means at least 1% better, flat means at most 0.2% better with at least two papers from 2025–26 trying. Numbers on a different scale from the rest (a fraction among percentages) and far outliers are left out. Results come from different papers with different setups, so they are signals, not head-to-head comparisons. The share of papers is counted at ICML, NeurIPS, ICLR, CVPR and AAAI.
How it got here
Most cited paper of each year
- 2016 · PSyCo: Manifold Span Reduction for Super Resolution (CVPR 2016 · 56 citations)
- 2017 · On the Global Geometry of Sphere-Constrained Sparse Blind Deconvolution (CVPR 2017 · 56 citations)
- 2018 · Theoretical Linear Convergence of Unfolded ISTA and Its Practical Weights and Thresholds (NeurIPS 2018 · 151 citations)
- 2019 · Block Coordinate Regularization by Denoising (NeurIPS 2019 · 49 citations)
- 2020 · Polarized Non-Line-of-Sight Imaging (CVPR 2020 · 46 citations)
- 2021 · Recovery Analysis for Plug-and-Play Priors using the Restricted Eigenvalue Condition (NeurIPS 2021 · 5 citations)
- 2022 · Near-Exact Recovery for Tomographic Inverse Problems via Deep Learning (ICML 2022 · 29 citations)
- 2023 · Learning Sparse and Low-Rank Priors for Image Recovery via Iterative Reweighted Least Squares Minimization (ICLR 2023 · 3 citations)
- 2024 · Precise asymptotics of reweighted least-squares algorithms for linear diagonal networks (NeurIPS 2024 · 3 citations)
- 2025 · Efficient $k$-Sparse Band–Limited Interpolation with Improved Approximation Ratio (NeurIPS 2025 · 0 citations)
- 2026 · Dual Quaternion SE(3) Synchronization with Recovery Guarantees (ICML 2026 · 0 citations)
Earliest papers here
- PSyCo: Manifold Span Reduction for Super Resolution (CVPR 2016 · 56 citations)
- Fast recovery from a union of subspaces (NeurIPS 2016 · 12 citations)
- Estimating Sparse Signals With Smooth Support via Convex Programming and Block Sparsity (CVPR 2016 · 5 citations)
What has been tried
54 papers here report 347 measured changes (a component added, removed or swapped, compared with a baseline): helped 64%, no clear effect 15%, hurt 15%, mixed 6%. Papers mostly publish changes that helped, so "helped" is over-represented.
Ablations in recent papers
| What was changed | Measured on | Result | Effect | Paper |
|---|---|---|---|---|
| Initialize SEA with zero rather than an existing algorithm's solution | Spike deconvolution · average support distance | Helped | Straight-Through Meets Sparse Recovery: the Support Exploration Algorithm (ICML 2024 · 0 citations) |
Recent preprints
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Who publishes on it
Institutions on the most papers of this approach since 2023 (of 20 papers; from OpenAlex and the papers' affiliations).
- University of California, Berkeley · 2 papers
Use it
Download BibTeX of 34 key papersOpen the topic in the interactive map
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Related approaches
Same keyword cluster
- Sparse regression with guarantees (94 papers)
- High-dimensional estimation theory (89 papers)
- Sparse and robust PCA (66 papers)
- Nonconvex low-rank and sparse optimization (112 papers)
Elsewhere in the topic
- Low-rank approximation theory (142 papers)
- Matrix completion and factorization (118 papers)
- Randomized sketching for matrices (96 papers)
- Structured low-rank learning (87 papers)
- Geometry of low-rank and SPD structure (71 papers)
- Tensor network decompositions (45 papers)
- Low-rank tensor completion (45 papers)
- Randomized tensor decomposition algorithms (43 papers)
Benchmark numbers, ablations and baseline numbers are extracted by AI from each paper's full text and can be wrong; the paper is the authority. Data: results index of 2026-11-02, citation counts from OpenAlex (2026-10-09).