Sparsity Driven Latent Space Sampling for Generative Prior Based Compressive Sensing

Abstract

We address the problem of recovering signals from compressed measurements based on generative priors. Recently, generative-model based compressive sensing (GMCS) methods have shown superior performance over traditional compressive sensing (CS) techniques in recovering signals from fewer measurements. However, it is possible to further improve the performance of GMCS by introducing controlled sparsity in the latent-space. We propose a proximal metalearning (PML) algorithm to enforce sparsity in the latentspace while training the generator. Enforcing sparsity naturally leads to a union-of-submanifolds model in the solution space. The overall framework is named as sparsity driven latent space sampling (SDLSS). In addition, we derive the sample complexity bounds for the proposed model. Furthermore, we demonstrate the efficacy of the proposed framework over the state-of-the-art techniques with application to CS on standard datasets such as MNIST and CIFAR-10. In particular, we evaluate the performance of the proposed method as a function of the number of measurements and sparsity factor in the latent space using standard objective measures. Our findings show that the sparsity driven latent space sampling approach improves the accuracy and aids in faster recovery of the signal in GMCS.

Robust multitask compressive sampling via deep generative models for crack detection in structural health monitoring

“…For example, Dhar et al 43 proposed a framework to allow for a sparse deviation from the range set of the generator. Killedar et al 44 proposed to induce sparsity of the latent space when training the generator. In our case, the sparse latent representation of cracks in an image is automatically achieved in the existing generators taken from the literatures.…”

Quantized Generative Models for Solving Inverse Problems

“…The sparsity constraint in the latent representation z results in the range-space of the generator network G θ Q to be composed of a union-of-manifolds [15,16]. The optimization of z involves minimizing L G while satisfying the feasibility condition z 0 ≤ s. This approach is referred to as sparsity-driven latent-space sampling (SDLSS).…”

“…Generative models for solving inverse problems: Generative models have been used to solve inverse problems [2,4,6,[12][13][14][15][16]33] and are shown to outperform the traditional optimization methods using a small number of measurements. Bora et al enforced the constraint that the signal x lies in the range-space of the pre-trained generator network G θ [4].…”

“…Yan et al introduced meta-learning in the context of compressed sensing to jointly optimize the generator weights and latent space [33]. Killedar et al enforced sparsity in the latent space to obtain superior performance over the state-of-the-art methods [14][15][16]. In a survey paper, Zhao et al discusses the use of generative models for solving inverse problems [36] ranging from Xray computed tomography to synthetic aperture radar.…”