A Novel Memory-Efficient Fast Algorithm for 2-DCompressed Sensing

摘要

The basic theories of compressed sensing (CS) turn around the sampling and reconstruction of 1-D signals. To deal with 2-1) signals (images), the conventional treatment is to convert them intol-D vectors. This has drawbacks, including huge memory demands and difficulties in the design and calibration of the optical imaging systems. As a result, in 2009 some researchers proposed the concept of compressed imaging (C1) with separable sensing operators. However, their work is only focused on the sampling phase. In this paper, we propose a scheme for 2-D CS that is memory- and computation-efficient in both sampling and reconstruction. This is achieved by decomposing the 2-D CS problem into two stages With the help of an intermediate image. The intermediate image is then solved by direct orthogonal linear transform and the original image is reconstructed by solving a set of 1-1) l1-norm minimization sub-problems. The experimental results confirm the feasibility of the proposed scheme.