An enhanced block-based Compressed Sensing technique using orthogonal matching pursuit

Abstract

The theory of compressed sensing asserts that one can recover signals in $\mathbb {R}^n$ from far fewer samples or measurements, if the signal has a sparse representation in some orthonormal basis; from non-adaptive linear measurements by solving a $\mathbb {L}_1$ norm minimisation problem. The non-adaptive measurements have the character of random linear combinations of the basis or frame elements. However, for large-scale 2D image signals, the randomized sensing matrix consumes enormous computational resources that makes it impractical. The problem has been addressed in the paper as a block compressed sensing (BCS) with sparsity normalization in the transformed domain in the preprocessing stage. The blocks obtained are converted to non-adaptive measurements using identically independent weighted Gaussian random matrices. The feasibility of reconstruction is verified using orthogonal matching pursuit. Simulation results show that better reconstruction performance can be achieved by the proposed technique in comparison with the existing BCS approaches.