Sparsity Driven Latent Space Sampling for Generative Prior Based Compressive Sensing

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 meta-learning (PML) algorithm to enforce sparsity in the latent-space 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.