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Information-Driven Design of Imaging Systems
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Estimates mutual information between noisy measurements and noiseless images directly from measurement data (via cross-entropy upper bounds on measurement entropy plus known noise entropy) and uses its gradient to design imaging systems (IDEAL) that match end-to-end optimization.
Problem
Evaluating and designing imaging systems requires a unified performance metric, but existing approaches either overestimate information with unconstrained communication models, need explicit object models, or rely on expensive decoder-based secondary tasks with ground truth.
Approach
Decompose I(X;Y) into H(Y) minus a sum of per-pixel noise entropies; upper-bound H(Y) by cross-entropy of probabilistic models (stationary Gaussian, full Gaussian, PixelCNN) fit to measurements only; then perform gradient ascent on this differentiable information estimate to optimize encoders (IDEAL) without decoders.
Key results
- Information estimates predicted decoder reconstruction quality across four imaging domains (color photography, radio astronomy, lensless imaging, microscopy), with higher MI consistently giving better MSE, PSNR, and SSIM.
- IDEAL-optimized color filter arrays matched the reconstruction error and measurement mutual information of end-to-end optimization.
- Task-specific classification in lensless imaging was weakly predicted by total information, since the task uses only ~1% of the information in measurements.
Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Use IDEAL to optimize color filter arrays instead of random initialization | Color filter design · Color photography reconstruction | reconstruction accuracy | Helped |
| Optimize the encoder with IDEAL rather than jointly optimizing encoders and decoders end-to-end | Color filter design · Color photography reconstruction | reconstruction error | No clear effect |
| Use PixelCNN rather than Gaussian measurement models | Information estimation · Real imaging data | entropy bound | Helped |
| Use a stationary Gaussian model when the data follows a stationary Gaussian process | Information estimation · Simulated stationary Gaussian data with additive noise | convergence speed | Helped |
| Estimate shot-noise entropy using only noisy measurements | Information estimation · Shot noise across photon counts | entropy estimation accuracy | Mixed |
| Use fewer than approximately 20 photons per pixel | Information estimation · Shot-noise entropy estimation | entropy estimation accuracy | Hurt |
| Use total information estimates to rank designs for a specialized classification task | Lensless imaging · CIFAR classification | classification accuracy | Mixed |
| Use single-LED illumination rather than differential phase contrast | LED array microscopy · Protein prediction | prediction accuracy | Hurt |
| Use larger patches rather than smaller patches | Probabilistic measurement models · Information estimation | spatial relationships captured | Helped |
Surprising findings
- Single-LED microscopy showed inflated information estimates due to optical imperfections, yielding worse protein prediction than differential phase contrast despite higher estimates.
- Designs with similar total information achieved different classification accuracies in lensless imaging, so total information is a weaker predictor for specialized tasks.
Limitations
- Assumes deterministic encoders; stochastic encoders are left to future work.
- Upper-bound estimates overestimate information when measurement models mismatch the data (e.g., Gaussian models miss bimodal statistics).
- Less accurate for task-specific tasks such as classification that rely on specific features.
Experimental setup
Datasets: natural images MNIST CIFAR
Benchmarks: reconstruction MSE/PSNR/SSIM for color demosaicing black hole image reconstruction error lensless reconstruction accuracy CIFAR classification (lensless) protein expression prediction (microscopy)
Metrics: mutual information estimate MSE PSNR SSIM classification accuracy
Baselines: end-to-end optimization communication-system information bound Bayer filter array neural network demosaicing Wiener deconvolution
Builds on: end-to-end optimization PixelCNN deterministic information transfer
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