Recursive Recovery From Compressive Measurements With Generative Models

Compressed sensing aims to recover a high-dimensional vector from an underdetermined system. In this letter, we present a novel approach for compressed sensing of sequential signal by leveraging generative models. Unlike traditional sparse priors, a pre-trained generator can be utilized to estimate vectors from their compressive measurements by searching within the generator's range. The proposed method utilizes estimates from previous time steps to enhance the accuracy of current estimates, ensuring that the latent space of the generative model remains consistent with previous states. We provide a theoretical analysis on the reconstruction of current time slot based on the previous results, and show that the bound can be improved if the signals change slowly with time. Moreover, empirical results demonstrate the effectiveness of our approach as compared to other existing methods.