SRL1: Structured reweighted ℓ1 minimization for compressive sampling of videos

In this paper, we study compressive sampling of difference frames in videos and introduce a novel reconstruction method that exploits the structural characteristic, i.e., clustered sparsity in difference frames. Our method, referred to as structured reweighted ℓ₁ minimization (SRL1), estimates the signal support and adjusts the weights associated with the signal coefficients in a weighted ℓ₁ minimization in an iterative fashion. For the signal support estimation we propose local exploration and global purification steps to promote the clustered sparsity in difference frames. It is shown that by exploiting the clustered sparsity, isolated non-zero noise could be eliminated, and undiscovered signal coefficients could be retrieved. It should be noted that these steps are done based on the clustered sparsity, rather than the exact signal support distribution. This makes our method robust and distinct from many state-of-the-art algorithms. Experimental results show the effectiveness of our method.