Image compressed sensing reconstruction with 3D transform domain collaborative filtering

Compressed Sensing (CS) has drawn quite an amount of attention as novel digital signal sampling theory in recent years when the signal is sparse in some domain. However, signal reconstruction from undersampled data has always been challenging due to its implicit ill-posed nature. This paper proposes an image compressed sensing reconstruction algorithm for image CS application, which consists of iteratively collaborative filtering of non local similar image patches in 3D transform domain and solving the least squares problems. In addition, the linearization technique is exploited to reduce the computation complexity. The results of various experiments on natural images and MRI images consistently demonstrate that the proposed algorithm can efficiently reconstruct images and gain more 2dB as compared to the current leading CS image reconstruction algorithm.