Compressive image sampling with side information

Compressive sampling is a novel framework that exploits sparsity of a signal in a transform domain to perform sampling below the Nyquist rate. In this paper, we apply compressive sampling to reduce the sampling rate of images/video. The key idea is to exploit the intra- and inter-frame correlation to improve signal recovery algorithms. The image is split into non-overlapping blocks of fixed size, which are independently compressively sampled exploiting sparsity of natural scenes in the Discrete Cosine Transform (DCT) domain. At the decoder, each block is recovered using useful information extracted from the recovery of a neighboring block. In the case of video, a previous frame is used to help recovery of consecutive frames. The iterative algorithm for signal recovery with side information that extends the standard orthogonal matching pursuit (OMP) algorithm is employed. Simulation results are given for Magnetic Resonance Imaging (MRI) and video sequences to illustrate advantages of the proposed solution compared to the case when side information is not used.