Small-block sensing and larger-block recovery in block-based compressive sensing of images

In the block-based compressive sensing (CS) of images, a small block is more practical due to its low-cost sensing in terms of the required memory and the computational complexity. A large block, however, is more effective in CS recovery because of the high probability of a smaller mutual coherence and a more-compressible representation of the images. This paper proposes a block-based CS scheme that is applicable to images with a small-block sensing and larger-block recovery (SBS-LBR), whereby a block-diagonal sensing matrix is used to arbitrarily set a recovery-block size that is multiple-times larger than the sensing block size; subsequently, a more compressible transform signal is generated with large-sized sparsifying basis. The proposed SBS-LBR not only facilitates a low sampling cost, but also improves the recovered images from the larger recovery-block size. Our experiment results confirm a theoretical analysis of the scheme, and have shown the improvement from the proposed SBS-LBR with the suggested proper choices regarding the sensing- and recovery-block sizes.