2D signal compression via parallel compressed sensing with permutations

In this paper, we propose a new scheme to compress 2D signals using parallel compressed sensing. According to this scheme, the reconstruction at the decoder can be performed in parallel. By performing certain permutation on a 2D signal, all columns are insured to have approximately the same density level and can be sampled using the same measurement matrix. In this way, vectorization of a 2D signal can be avoided, and thus the size of the measurement matrix can be dramatically reduced. We prove that with a good permutation, we can have a tighter upper bound on reconstruction mean square error. To illustrate this scheme, we apply it to video compression and use two kinds of permutations for different frames: the zigzag-scan-based permutation for reference frames and the block-test-based permutation for non-reference frames. Simulation results show that under the same compression ratio, the peak signal-to-noise ratio can be improved by approximately 3-7 dB compared to the case without permutation.