Penalized L1 minimization for reconstruction of time-varying sparse signals

In this paper, we propose a penalized ℓ
1
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 ℓ
0
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.