Image Reconstruction from Cone Excitations using the Implicit Prior in a Denoiser

Abstract

We re-examine the problem of reconstructing a high-dimensional signal from a small set of linear measurements, in combination with image prior from a diffusion probabilistic model. Well-established methods for optimizing such measurements include principal component analysis (PCA), independent component analysis (ICA) and compressed sensing (CS), all of which rely on axis-or subspace-aligned statistical characterization. But many naturally occurring signals, including photographic images, contain richer statistical structure. To exploit such structure, we introduce a general method for obtaining an optimized set of linear measurements, assuming a Bayesian inverse solution that leverages the prior implicit in a neural network trained to perform denoising. We demonstrate that these measurements are distinct from those of PCA and CS, with significant improvements in minimizing squared reconstruction error. In addition, we show that optimizing the measurements for the SSIM perceptual loss leads to perceptually improved reconstruction. Our results highlight the importance of incorporating the specific statistical regularities of natural signals when designing effective linear measurements.

Enhancing Molecular Energy Predictions with Physically Constrained Modifications to the Neural Network Potential

“…In addition to ensuring the correct prediction of physical properties, bias is considered to be the culprit of the overfitting problem, when facing with configuration outside of the training range. 30 Removing all additive constants allows the model to obtain a stronger generalization. To compensate for the reduction in fitting ability resulting from the removal of the bias, we incorporate a wider linear layer in our NNPs.…”