Matrix

Generic Matrix Sensing

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Standard reconstruction benchmark — forward model perfectly known, no calibration needed. Score = 0.5 × clip((PSNR−15)/30, 0, 1) + 0.5 × SSIM

# Method Score PSNR (dB) SSIM Source
🥇 FlowHSI 0.884 38.58 0.982 ✓ Certified Huang et al., arXiv 2025
🥈 ScoreSCI 0.877 38.22 0.980 ✓ Certified Chen et al., NeurIPS 2024
🥉 DiffusionHSI 0.872 37.95 0.978 ✓ Certified Zhang et al., ICCV 2024
4 PromptSCI 0.860 37.35 0.975 ✓ Certified Bai et al., ICCV 2024
5 CSTrans 0.855 37.12 0.973 ✓ Certified Liu et al., CVPR 2024
6 HiSViT+ 0.850 36.85 0.971 ✓ Certified Tao et al., ECCV 2024
7 CST 0.831 35.92 0.965 ✓ Certified Liu et al., ICCV 2023
8 Restormer 0.826 35.68 0.962 ✓ Certified Zamir et al., CVPR 2022
9 MST-L 0.820 35.4 0.960 ✓ Certified Cai et al., CVPR 2022
10 EfficientSCI 0.795 34.21 0.949 ✓ Certified Wang et al., IEEE TIP 2023
11 PnP-FFDNet 0.670 29.65 0.852 ✓ Certified Zhang et al., 2017
12 TVAL3 0.658 29.15 0.845 ✓ Certified Li et al., 2009
13 FISTA-TV 0.634 28.42 0.821 ✓ Certified Beck & Teboulle, 2009
14 GAP-TV 0.574 26.83 0.754 ✓ Certified Yuan et al., 2016

Dataset: PWM Benchmark (14 algorithms)

Blind Reconstruction Challenge — forward model has unknown mismatch, must calibrate from data. Score = 0.4 × PSNR_norm + 0.4 × SSIM + 0.2 × (1 − ‖y − Ĥx̂‖/‖y‖)

# Method Overall Score Public
PSNR / SSIM
 Dev
PSNR / SSIM
 Hidden
PSNR / SSIM
 Trust Source
🥇 ScoreSCI + gradient 0.769
0.823
35.47 dB / 0.971
0.751
30.77 dB / 0.928
0.732
30.43 dB / 0.923
✓ Certified Chen et al., NeurIPS 2024
🥈 FlowHSI + gradient 0.763
0.851
37.3 dB / 0.979
0.745
30.29 dB / 0.921
0.694
28.56 dB / 0.892
✓ Certified Huang et al., arXiv 2025
🥉 CSTrans + gradient 0.754
0.834
35.89 dB / 0.973
0.744
30.98 dB / 0.931
0.683
26.99 dB / 0.858
✓ Certified Liu et al., CVPR 2024
4 CST + gradient 0.750
0.816
34.3 dB / 0.963
0.742
29.82 dB / 0.914
0.693
27.92 dB / 0.879
✓ Certified Liu et al., ICCV 2023
5 MST-L + gradient 0.746
0.812
34.11 dB / 0.962
0.736
30.72 dB / 0.927
0.689
27.4 dB / 0.868
✓ Certified Cai et al., CVPR 2022
6 PromptSCI + gradient 0.745
0.812
34.64 dB / 0.965
0.731
30.42 dB / 0.923
0.692
28.44 dB / 0.890
✓ Certified Bai et al., ICCV 2024
7 HiSViT+ + gradient 0.738
0.830
35.72 dB / 0.972
0.728
29.12 dB / 0.902
0.657
25.61 dB / 0.821
✓ Certified Tao et al., ECCV 2024
8 Restormer + gradient 0.736
0.792
33.08 dB / 0.953
0.739
30.37 dB / 0.922
0.676
27.57 dB / 0.871
✓ Certified Zamir et al., CVPR 2022
9 DiffusionHSI + gradient 0.724
0.823
35.95 dB / 0.973
0.703
28.57 dB / 0.892
0.646
25.32 dB / 0.812
✓ Certified Zhang et al., ICCV 2024
10 EfficientSCI + gradient 0.709
0.795
32.54 dB / 0.948
0.677
27.21 dB / 0.863
0.655
26.19 dB / 0.837
✓ Certified Wang et al., IEEE TIP 2023
11 TVAL3 + gradient 0.655
0.687
26.78 dB / 0.853
0.656
25.41 dB / 0.815
0.623
24.99 dB / 0.802
✓ Certified Li et al., SIAM J. Sci. Comput. 2009
12 FISTA-TV + gradient 0.635
0.664
25.5 dB / 0.818
0.642
24.67 dB / 0.792
0.600
24.03 dB / 0.770
✓ Certified Beck & Teboulle, SIAM J. Imaging Sci. 2009
13 GAP-TV + gradient 0.619
0.664
25.23 dB / 0.809
0.627
24.47 dB / 0.785
0.567
22.64 dB / 0.717
✓ Certified Yuan et al., IEEE TIP 2016
14 PnP-FFDNet + gradient 0.600
0.692
26.94 dB / 0.857
0.583
22.58 dB / 0.714
0.525
21.18 dB / 0.654
✓ Certified Zhang et al., IEEE TPAMI 2020

Complete score requires all 3 tiers (Public + Dev + Hidden).

Join the competition →
Scoring: 0.4 × PSNR_norm + 0.4 × SSIM + 0.2 × (1 − ‖y − Ĥx̂‖/‖y‖) PSNR 40% · SSIM 40% · Consistency 20%
Public 5 scenes

Full-access development tier with all data visible.

What you get & how to use

What you get: Measurements (y), ideal forward operator (H), spec ranges, ground truth (x_true), and true mismatch spec.

How to use: Load HDF5 → compare reconstruction vs x_true → check consistency → iterate.

What to submit: Reconstructed signals (x_hat) and corrected spec as HDF5.

Public Leaderboard
# Method Score PSNR SSIM
1 FlowHSI + gradient 0.851 37.3 0.979
2 CSTrans + gradient 0.834 35.89 0.973
3 HiSViT+ + gradient 0.830 35.72 0.972
4 ScoreSCI + gradient 0.823 35.47 0.971
5 DiffusionHSI + gradient 0.823 35.95 0.973
6 CST + gradient 0.816 34.3 0.963
7 MST-L + gradient 0.812 34.11 0.962
8 PromptSCI + gradient 0.812 34.64 0.965
9 EfficientSCI + gradient 0.795 32.54 0.948
10 Restormer + gradient 0.792 33.08 0.953
11 PnP-FFDNet + gradient 0.692 26.94 0.857
12 TVAL3 + gradient 0.687 26.78 0.853
13 FISTA-TV + gradient 0.664 25.5 0.818
14 GAP-TV + gradient 0.664 25.23 0.809
Spec Ranges (3 parameters)
Parameter Min Max Unit
matrix_perturb -0.01 0.02
gain 0.97 1.06
sigma_y -0.02 0.04
View Details →
Dev 5 scenes

Blind evaluation tier — no ground truth available.

What you get & how to use

What you get: Measurements (y), ideal forward operator (H), and spec ranges only.

How to use: Apply your pipeline from the Public tier. Use consistency as self-check.

What to submit: Reconstructed signals and corrected spec. Scored server-side.

Dev Leaderboard
# Method Score PSNR SSIM
1 ScoreSCI + gradient 0.751 30.77 0.928
2 FlowHSI + gradient 0.745 30.29 0.921
3 CSTrans + gradient 0.744 30.98 0.931
4 CST + gradient 0.742 29.82 0.914
5 Restormer + gradient 0.739 30.37 0.922
6 MST-L + gradient 0.736 30.72 0.927
7 PromptSCI + gradient 0.731 30.42 0.923
8 HiSViT+ + gradient 0.728 29.12 0.902
9 DiffusionHSI + gradient 0.703 28.57 0.892
10 EfficientSCI + gradient 0.677 27.21 0.863
11 TVAL3 + gradient 0.656 25.41 0.815
12 FISTA-TV + gradient 0.642 24.67 0.792
13 GAP-TV + gradient 0.627 24.47 0.785
14 PnP-FFDNet + gradient 0.583 22.58 0.714
Spec Ranges (3 parameters)
Parameter Min Max Unit
matrix_perturb -0.012 0.018
gain 0.964 1.054
sigma_y -0.024 0.036
Submit Reconstruction View Details →
Hidden 5 scenes

Fully blind server-side evaluation — no data download.

What you get & how to use

What you get: No data downloadable. Algorithm runs server-side on hidden measurements.

How to use: Package algorithm as Docker container / Python script. Submit via link.

What to submit: Containerized algorithm accepting y + H, outputting x_hat + corrected spec.

Hidden Leaderboard
# Method Score PSNR SSIM
1 ScoreSCI + gradient 0.732 30.43 0.923
2 FlowHSI + gradient 0.694 28.56 0.892
3 CST + gradient 0.693 27.92 0.879
4 PromptSCI + gradient 0.692 28.44 0.89
5 MST-L + gradient 0.689 27.4 0.868
6 CSTrans + gradient 0.683 26.99 0.858
7 Restormer + gradient 0.676 27.57 0.871
8 HiSViT+ + gradient 0.657 25.61 0.821
9 EfficientSCI + gradient 0.655 26.19 0.837
10 DiffusionHSI + gradient 0.646 25.32 0.812
11 TVAL3 + gradient 0.623 24.99 0.802
12 FISTA-TV + gradient 0.600 24.03 0.77
13 GAP-TV + gradient 0.567 22.64 0.717
14 PnP-FFDNet + gradient 0.525 21.18 0.654
Spec Ranges (3 parameters)
Parameter Min Max Unit
matrix_perturb -0.007 0.023
gain 0.979 1.069
sigma_y -0.014 0.046
Submit Algorithm View Details →

Blind Reconstruction Challenge

Challenge

Given measurements with unknown mismatch and spec ranges (not exact params), reconstruct the original signal. A method must be evaluated on all three tiers for a complete score. Scored on a composite metric: 0.4 × PSNR_norm + 0.4 × SSIM + 0.2 × (1 − ‖y − Ĥx̂‖/‖y‖).

Input

Measurements y, ideal forward model H, spec ranges

Output

Reconstructed signal x̂

About the Imaging Modality

Generic compressive sensing framework where the measurement process is modelled as y = A*x + n with A being an explicit M x N sensing matrix (M < N). This covers any linear inverse problem including random Gaussian, Bernoulli, or structured sensing matrices. The compressed sensing theory of Candes, Romberg, and Tao guarantees exact recovery when x is sparse and A satisfies the restricted isometry property (RIP). Reconstruction uses standard proximal algorithms (FISTA, ADMM) with sparsity-promoting regularizers (L1, TV, wavelet).

Principle

Generic matrix sensing models the forward process as y = Ax + n, where A is an arbitrary measurement matrix (not necessarily structured like a convolution or Radon transform). This is the most general compressive sensing framework, applicable to random projections, coded apertures, and any linear dimensionality reduction scheme. The key requirement is that A satisfies the Restricted Isometry Property (RIP) for successful sparse recovery.

How to Build the System

Implementation depends on the physical sensing modality. For optical random projections, use a DMD or scattering medium to implement pseudo-random measurement vectors. Calibrate the measurement matrix A by measuring the system response to a complete basis set (e.g., Hadamard patterns). Store A as a dense or structured matrix. Ensure the measurement SNR is adequate for the desired reconstruction quality.

Common Reconstruction Algorithms

  • ISTA / FISTA (Iterative Shrinkage-Thresholding Algorithm)
  • Basis pursuit (L1 minimization via linear programming)
  • AMP (Approximate Message Passing)
  • ADMM with various regularizers (TV, wavelet sparsity, low-rank)
  • Learned ISTA (LISTA) and other deep unfolding networks

Common Mistakes

  • Measurement matrix does not satisfy RIP (too coherent or poorly conditioned)
  • Mismatch between calibrated A and actual system behavior (model error)
  • Not accounting for measurement noise level when setting regularization strength
  • Using an insufficiently sparse signal model for the reconstruction
  • Ignoring quantization effects of the detector in the measurement model

How to Avoid Mistakes

  • Verify the condition number and coherence of A; use random or optimized designs
  • Re-calibrate A periodically to account for system drift
  • Set regularization parameter proportional to noise level (e.g., via cross-validation)
  • Validate sparsity assumption on representative signals before deploying CS
  • Include quantization noise in the forward model or use dithering techniques

Forward-Model Mismatch Cases

  • The widefield fallback applies a Gaussian blur (shape-preserving convolution), but the correct compressed sensing operator applies a random measurement matrix y = Phi*x that projects the image into a lower-dimensional space
  • Gaussian blur preserves spatial locality and image structure, whereas the random measurement matrix scrambles all spatial information — the fallback measurements contain no compressed-sensing-compatible encoding

How to Correct the Mismatch

  • Use the correct compressed sensing operator with the measurement matrix Phi (Gaussian random, partial Fourier, or structured random), producing y = Phi * vec(x)
  • Reconstruct using L1/TV-regularized optimization (ISTA, ADMM) or learned proximal operators designed for the specific measurement matrix structure

Experimental Setup — Signal Chain

Experimental setup diagram for Generic Compressive Matrix Sensing

Experimental Setup

Matrix Size: 256x256
Sampling Ratio: 0.25
Sensing Matrix: Gaussian random / partial Fourier
Rank Assumption: low-rank or sparse
Reconstruction: FISTA-L2 / ADMM / ISTA-Net

Key References

  • Candes et al., 'Robust uncertainty principles: exact signal reconstruction from highly incomplete frequency information', IEEE TIT 52, 489-509 (2006)
  • Donoho, 'Compressed sensing', IEEE TIT 52, 1289-1306 (2006)

Canonical Datasets

  • Set11 / BSD68 (simulation benchmarks)

Spec DAG — Forward Model Pipeline

M(Φ) → D(g, η₁)

M Sensing Matrix (Φ)
D Detector (g, η₁)

Mismatch Parameters

Symbol Parameter Description Nominal Perturbed
ΔΦ matrix_perturb Matrix element perturbation std 0 0.01
g gain Detector gain multiplier 1.0 1.03
σ_y sigma_y Measurement noise std 0 0.02

Credits System

40%
Platform Profit Pool
Revenue allocated to benchmark rewards
30%
Winner Share
Top algorithm receives from pool
$100
Min Withdrawal
Minimum payout threshold
Spec Primitives Reference (11 primitives)
P Propagation

Free-space or medium propagation kernel (Fresnel, Rayleigh-Sommerfeld).

M Mask / Modulation

Spatial or spatio-temporal amplitude modulation (coded aperture, SLM pattern).

Π Projection

Geometric projection operator (Radon transform, fan-beam, cone-beam).

F Fourier Sampling

Sampling in the Fourier / k-space domain (MRI, ptychography).

C Convolution

Shift-invariant convolution with a point-spread function (PSF).

Σ Summation / Integration

Summation along a physical dimension (spectral, temporal, angular).

D Detector

Sensor readout with gain g and noise model η (Gaussian, Poisson, mixed).

S Structured Illumination

Patterned illumination (block, Hadamard, random) applied to the scene.

W Wavelength Dispersion

Spectral dispersion element (prism, grating) with shift α and aperture a.

R Rotation / Motion

Sample or gantry rotation (CT, electron tomography).

Λ Wavelength Selection

Spectral filter or monochromator selecting a wavelength band.