Penalized L1 minimization for reconstruction of time-varying sparse signals

In this paper, we propose a penalized ℓ1 minimization algorithm for reconstructing a time-varying signal based on compressive sensing (CS) principles. The time-varying signal can be seen as a sequence of slow-changing frames. In the proposed algorithm, all frames of the sequence are sampled at an equal rate, which makes the encoder simpler than frame-categorized methods. We introduce a specialized Fréchet mean of the target frame and several adjacent frames as the penalty vector to make the algorithm close to ℓ0 minimization. We prove that the specialized Fréchet mean is a good approximation of the target frame for a sequence of slow time-varying signals. Experimental results demonstrates the superior reconstruction quality of the proposed algorithm.