SPC-Kronecker

Single-Pixel Camera (Kronecker 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
🥇 PnP-DRUNet 0.753 27.85 0.837 ✓ Certified InverseNet baseline (oracle cal)
🥈 FISTA-TV (tuned) 0.727 26.71 0.804 ✓ Certified InverseNet baseline (oracle cal)
🥉 HATNet + FISTA-TV 0.720 26.45 0.790 ✓ Certified InverseNet baseline (oracle cal)
4 ISTA-Net 0.710 26.4 0.721 ✓ Certified InverseNet baseline (oracle cal)
5 FISTA-TV (paper) 0.708 25.98 0.776 ✓ Certified InverseNet baseline (oracle cal)
6 PnP-BM3D 0.601 21.1 0.582 ✓ Certified InverseNet baseline (oracle cal)

Dataset: Set11, Kronecker, CR=0.25

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
🥇 PnP-DRUNet + blind cal 0.714
0.720
26.33 dB / 0.814
0.736
27.02 dB / 0.828
0.687
24.75 dB / 0.776
✓ Certified InverseNet Scenario IV
🥈 FISTA-TV (tuned) + blind cal 0.691
0.693
25.34 dB / 0.757
0.710
25.93 dB / 0.781
0.671
24.5 dB / 0.730
✓ Certified InverseNet Scenario IV
🥉 FISTA-TV (paper) + blind cal 0.686
0.690
25.21 dB / 0.751
0.704
25.75 dB / 0.767
0.665
24.24 dB / 0.722
✓ Certified InverseNet Scenario IV
4 HATNet + FISTA-TV + blind cal 0.684
0.686
25.38 dB / 0.746
0.702
25.95 dB / 0.768
0.665
24.53 dB / 0.720
✓ Certified InverseNet Scenario IV
5 ISTA-Net + blind cal 0.608
0.628
24.11 dB / 0.595
0.686
26.05 dB / 0.701
0.509
19.99 dB / 0.385
✓ Certified InverseNet Scenario IV
6 PnP-BM3D + blind cal 0.565
0.565
19.57 dB / 0.527
0.550
18.36 dB / 0.511
0.580
20.53 dB / 0.561
✓ Certified InverseNet Scenario IV

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 20 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 PnP-DRUNet + blind cal 0.720 26.33 0.814
2 FISTA-TV (tuned) + blind cal 0.693 25.34 0.757
3 FISTA-TV (paper) + blind cal 0.690 25.21 0.751
4 HATNet + FISTA-TV + blind cal 0.686 25.38 0.746
5 ISTA-Net + blind cal 0.628 24.11 0.595
6 PnP-BM3D + blind cal 0.565 19.57 0.527
Spec Ranges (2 parameters)
Parameter Min Max Unit
gain_decay_alpha 0.0005 0.0095 1/measurement
noise_sigma 0.01 0.05
View Details →
Dev 20 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 PnP-DRUNet + blind cal 0.736 27.02 0.828
2 FISTA-TV (tuned) + blind cal 0.710 25.93 0.781
3 FISTA-TV (paper) + blind cal 0.704 25.75 0.767
4 HATNet + FISTA-TV + blind cal 0.702 25.95 0.768
5 ISTA-Net + blind cal 0.686 26.05 0.701
6 PnP-BM3D + blind cal 0.550 18.36 0.511
Spec Ranges (2 parameters)
Parameter Min Max Unit
gain_decay_alpha -0.0015 0.0075 1/measurement
noise_sigma 0.0 0.04
Submit Reconstruction View Details →
Hidden 20 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 PnP-DRUNet + blind cal 0.687 24.75 0.776
2 FISTA-TV (tuned) + blind cal 0.671 24.5 0.73
3 FISTA-TV (paper) + blind cal 0.665 24.24 0.722
4 HATNet + FISTA-TV + blind cal 0.665 24.53 0.72
5 PnP-BM3D + blind cal 0.580 20.53 0.561
6 ISTA-Net + blind cal 0.509 19.99 0.385
Spec Ranges (2 parameters)
Parameter Min Max Unit
gain_decay_alpha 0.0035 0.0125 1/measurement
noise_sigma 0.02 0.06
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

The single-pixel camera reconstructs a 2D image from scalar intensity measurements acquired by a photodiode after spatially modulating the scene with known patterns on a DMD. Each measurement y_i is the inner product of the scene with a pattern, giving y = Phi*x + n. Compressed sensing theory guarantees recovery from M << N measurements if the scene is sparse. The single detector can operate at wavelengths where array detectors are unavailable (SWIR, THz). Reconstruction uses FISTA with L1/TV penalties or Plug-and-Play methods.

Principle

A single-pixel camera uses a spatial light modulator (DMD) to project a sequence of binary or grayscale patterns onto the scene. Each pattern multiplies the scene, and a single bucket detector (photodiode or PMT) measures the total light for each pattern, producing one scalar measurement per pattern. Compressive sensing recovers the image from far fewer measurements than Nyquist by exploiting sparsity in a transform domain.

How to Build the System

Place a DMD (e.g., Texas Instruments DLP LightCrafter) at the image plane of a relay lens. Focus the scene onto the DMD. After the DMD, collect all reflected light onto a single photodetector (avalanche photodiode for low light, or silicon photodiode for visible). Display Hadamard, random, or optimized patterns at 10-22 kHz DMD rate. Synchronize pattern display with detector readout.

Common Reconstruction Algorithms

  • Basis pursuit / L1 minimization (LASSO)
  • Orthogonal matching pursuit (OMP)
  • Total-variation minimization (TV-CS)
  • TVAL3 (TV with augmented Lagrangian and alternating direction)
  • Deep compressive sensing networks (ReconNet, CSNet)

Common Mistakes

  • Pattern-detector timing mismatch causing wrong measurement-to-pattern association
  • DMD diffraction effects not accounted for at oblique illumination angles
  • Insufficient measurements for the scene complexity (under-sampling ratio too aggressive)
  • Analog-to-digital converter resolution too low for the dynamic range of measurements
  • Not calibrating detector linearity and dark current drift during long acquisitions

How to Avoid Mistakes

  • Hardware-trigger the detector acquisition from the DMD synchronization signal
  • Calibrate the effective pattern at the sample plane (not just the DMD command pattern)
  • Start with 25-50 % measurement ratio for natural scenes; reduce only if sparsity allows
  • Use 16-bit or higher ADC; verify linearity with a calibrated light source
  • Measure dark frames periodically and subtract; maintain stable detector temperature

Forward-Model Mismatch Cases

  • The widefield fallback produces a 2D (64,64) image, but single-pixel camera acquires a 1D vector of M scalar measurements (M << N pixels) via structured illumination patterns and a single photodetector — output shape (M,) vs (64,64)
  • Each SPC measurement is an inner product of the scene with a known pattern (y_i = <phi_i, x>), capturing compressed information — the widefield blur produces N^2 pixels with no compression, making compressive reconstruction algorithms incompatible

How to Correct the Mismatch

  • Use the SPC operator that applies the sensing matrix Phi (Hadamard, random, or learned patterns): y = Phi * x, where y has far fewer entries than the image has pixels
  • Reconstruct using compressive sensing algorithms (ISTA-Net, basis pursuit, total variation) that exploit sparsity to recover the N^2-pixel image from M << N^2 measurements

Experimental Setup — Signal Chain

Experimental setup diagram for Single-Pixel Camera

Experimental Setup

Instrument: Rice SPC prototype / custom DMD system
Spatial Modulator: TI DLP7000 DMD (1024x768 micromirrors)
Detector: Thorlabs PDA100A2 Si photodiode
Effective Resolution: 64x64
Sampling Ratio: 0.25
Sensing Matrix: Walsh-Hadamard (partial)
Pattern Rate Hz: 22000
Collection Optics: 50 mm f/1.4 lens

Key References

  • Duarte et al., 'Single-pixel imaging via compressive sampling', IEEE Signal Processing Magazine 25, 83-91 (2008)
  • Edgar et al., 'Principles and prospects for single-pixel imaging', Nature Photonics 13, 13-20 (2019)

Canonical Datasets

  • Set11 (11 standard test images)
  • BSD68 (Martin et al., ICCV 2001)

Spec DAG — Forward Model Pipeline

M(H⊗W) → D(g, η₁)

M Kronecker Sensing (H⊗W)
D Detector (g, η₁)

Mismatch Parameters

Symbol Parameter Description Nominal Perturbed
α gain_alpha Gain drift coefficient 0 0.0015
σ_y sigma_y Measurement noise std 0 0.03

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.