Single-Pixel Camera

spc Compressive Compressive Sensing Ray
View Benchmarks (2)

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.

Forward Model

Structured Illumination Sensing

Noise Model

Gaussian

Default Solver

pnp fista

Sensor

SINGLE_PIXEL_DETECTOR

Forward-Model Signal Chain

Each primitive represents a physical operation in the measurement process. Arrows show signal flow left to right.

S block Block Illumination M Φ Sensing Matrix Sigma Spatial Sum D g, η₁ Detector
Spec Notation

S(block) → M(Φ) → Σ → D(g, η₁)

Benchmark Variants & Leaderboards

SPC-Block

Single-Pixel Camera (Block Sensing)

Full Benchmark Page →
Spec Notation

S(block) → M(Φ) → Σ → D(g, η₁)

Standard Leaderboard (Top 10)

# Method Score PSNR (dB) SSIM Trust Source
🥇 HATNet 0.731 28.85 0.801 ✓ Certified InverseNet baseline (oracle cal)
🥈 ISTA-Net+ 0.710 27.56 0.762 ✓ Certified ISTA-Net+ (CVPR 2018)
🥉 FISTA-TV 0.686 26.1 0.758 ✓ Certified InverseNet baseline (oracle cal)
4 PnP-DRUNet 0.632 23.85 0.665 ✓ Certified InverseNet baseline (oracle cal)
Mismatch Parameters (2) click to expand
Name Symbol Description Nominal Perturbed
gain_alpha α Gain drift coefficient 0 0.0015
sigma_y σ_y Measurement noise std 0 0.03

SPC-Kronecker

Single-Pixel Camera (Kronecker Sensing)

Full Benchmark Page →
Spec Notation

M(H⊗W) → D(g, η₁)

Standard Leaderboard (Top 10)

# Method Score PSNR (dB) SSIM Trust 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)
Mismatch Parameters (2) click to expand
Name Symbol Description Nominal Perturbed
gain_alpha α Gain drift coefficient 0 0.0015
sigma_y σ_y Measurement noise std 0 0.03

Reconstruction Triad Diagnostics

The three diagnostic gates (G1, G2, G3) characterize how reconstruction quality degrades under different error sources. Each bar shows the relative attribution.

G1 — Forward Model Accuracy How well does the mathematical model match reality?

Model: structured illumination sensing — Mismatch modes: pattern misalignment, detector nonlinearity, diffraction at dmd, ambient light leakage

G2 — Noise Characterization Is the noise model correctly specified?

Noise: gaussian — Typical SNR: 15.0–40.0 dB

G3 — Calibration Quality Are instrument parameters accurately measured?

Requires: pattern matrix, detector response, pattern alignment, dark current

Modality Deep Dive

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

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

Signal Chain Diagram

Experimental setup diagram for Single-Pixel Camera

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)