Block compressed sensing (CS) with optimal permutation is a promising method to improve sampling efficiency in CS-based image compression. However, the existing optimal permutation scheme brings a large amount of extra data to encode the permutation information because it needs to know the permutation information to accomplish signal reconstruction. When the extra data is taken into consideration, the improvement in sampling efficiency of this method is limited. In order to solve this problem, a new optimal permutation strategy for block CS (BCS) is proposed. Based on the proposed permutation strategy, an improved optimal permutation based BCS method called BCS-NOP (BCS with new optimal permutation) is proposed in this paper. Simulation results show that the proposed approach reduces the amount of extra data to encode the permutation information significantly and thereby improves the sampling efficiency compared with the existing optimal permutation based BCS approach.
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