Dynamic sparse coding with smoothing proximal gradient method

In this work we focus on the problem of estimating time-varying sparse signals from a sequence of under-sampled observations. We formulate this problem as estimating hidden states in a dynamic model and exploit the underlying temporal structure to find a more accurate solution, particularly when the information in the observations is at scarce. We propose an optimization procedure based on smoothing proximal gradient method to estimate these hidden states. We show that the proposed model is efficient and more robust to the noise in the system.