Overlapping blocks in reconstruction of sparse images

Abstract

Images are commonly analysed by the discrete cosine transform (DCT) on a number of blocks of smaller size. The blocks are then combined back to the original size image. Since the DCT of blocks have a few nonzero coefficients, the images can be considered as sparse in this transformation domain. The theory of compressive sensing states that some corrupted pixels within blocks can be reconstructed by minimising the blocks sparsity in the DCT domain. Block edges can affect the quality of the reconstruction. In some blocks, a few pixels from an object which mostly belongs to the neighbouring blocks may appear at the edges. Compressive sensing reconstruction algorithm can recognise these pixels as disturbance and perform their false reconstruction in order to minimise the sparsity of the considered block. To overcome this problem, a method with overlapping blocks is proposed. Images are analysed with partially overlapping blocks and then reconstructed using their non-overlapped parts. We have demonstrated the improvements of overlapping blocks on images corrupted with combined noise. A comparison between the reconstructions with non-overlapping and overlapping blocks is presented using the structural similarity index.