Separate-combine recovery for compressed sensing of large images

Compressed sensing (CS) based image processing is a important branch of CS based signal processing. However, the high complexity involved in CS based large-size image processing is a challenging issue. In this paper, an orthogonal matching pursuit enabled two-stage CS recovery scheme with low complexity yet high performance, termed separate-combine recovery method is proposed for separable image sensing operators. Specifically, at the separate stage, both compressed row and column data is estimated as intermediates. Based on these estimates, two sparse representations of the original image, called row-first-recovery result and column-first-recovery result, are respectively obtained. At the combine stage, the final result is achieved by weighted aggregating these two sparse representations. The complexity and performance of the proposed method are evaluated through extensive numerical results, showing that the presented scheme outperforms existing methods in terms of recovery speed and computational complexity.