Learning Generative Prior with Latent Space Sparsity Constraints

TL;DR

This paper introduces SDLSS, a sparsity-driven latent space sampling framework with a proximal meta-learning algorithm, improving compressed sensing with deep generative priors, especially under high compression and nonlinear sensing.

Contribution

It proposes SDLSS and PML to enforce latent space sparsity, enabling better union-of-submanifolds modeling and improved sample efficiency in compressed sensing.

Findings

SDLSS outperforms state-of-the-art methods at higher compression levels.

Nonlinear sensing with learned neural networks surpasses linear sensing.

Performance validated using PSNR, SSIM, and RE metrics.

Abstract

We address the problem of compressed sensing using a deep generative prior model and consider both linear and learned nonlinear sensing mechanisms, where the nonlinear one involves either a fully connected neural network or a convolutional neural network. Recently, it has been argued that the distribution of natural images do not lie in a single manifold but rather lie in a union of several submanifolds. We propose a sparsity-driven latent space sampling (SDLSS) framework and develop a proximal meta-learning (PML) algorithm to enforce sparsity in the latent space. SDLSS allows the range-space of the generator to be considered as a union-of-submanifolds. We also derive the sample complexity bounds within the SDLSS framework for the linear measurement model. The results demonstrate that for a higher degree of compression, the SDLSS method is more efficient than the state-of-the-art method. We first consider a comparison between linear and nonlinear sensing mechanisms on Fashion-MNIST dataset and show that the learned nonlinear version is superior to the linear one. Subsequent comparisons with the deep compressive sensing (DCS) framework proposed in the literature are reported. We also consider the effect of the dimension of the latent space and the sparsity factor in validating the SDLSS framework. Performance quantification is carried out by employing three objective metrics: peak signal-to-noise ratio (PSNR), structural similarity index metric (SSIM), and reconstruction error (RE).