An adaptive reconstruction algorithm for image block Compressed Sensing under low sampling rate

Block Compressed Sensing (CS) adapts to compressed sensing for an image. As the famous BCS with Smoothed Projected Landweber algorithm (BCS-SPL) shows bad performance when the sampling rate is in a low condition, we propose a novel algorithm called Total Variation based Sampling Adaptive Block Compressed Sensing with OMP (Orthogonal Matching Pursuit) (TVSA-BCS-OMP) to solve the following problem of BCS-SPL. TVSA-BCS-OMP blocks the whole image in an overlapping way to eliminate blocking effect. It assigns sampling rate depending on texture complexity of each block, which is measured by the block´s Total Variation (TV) so that the blocks with big TV can attain higher sampling rate. Then only limited nonzero coefficients in each block are retained according to the adaptively assigned sampling rate. At last, we sample the blocks and conducts OMP reconstruction respectively. The experimental results show that under the condition of low initial sampling rate (lower than 0.2), TVSA-BCS-OMP shows better reconstruction precision, especially can attain better reconstruction performance in the texture blocks than BCS-SPL. In addition, the new algorithm costs shorter reconstruction time than BCS-SPL algorithm.