Image compressive sensing using overlapped block projection and reconstruction

Compressive sensing allows a signal to be sampled at sub-Nyquist rate and still get recovered exactly, if the signal is sparse in some domain. Block compressive sensing (BCS) is advocated for practical image compressive sensing, since it processes image at block level and significantly reduces the memory requirement for storing projection matrix. However, existing BCS methods process blocks separately, which breaks the continuity between blocks and usually produces blocking artifacts. This paper proposes a new image compressive sensing scheme using overlapped-block projection and reconstruction (OBPR), in which the sampling is performed on overlapped blocks. During reconstruction, the sparsity constraint in transform domain is also enforced on the overlapped blocks. An augmented Lagrangian method is used to solve the optimization problem efficiently. Experimental results show that the proposed OBPR scheme achieves significantly better results than the existing BCS schemes in reconstruction quality.