Research On Reconstruction Algorithm In Block Compressive Sensing

Compressed Sensing (CS) theory has brought a great breakthrough for signalprocessing, as it can sample and compress signals simultaneously. When CS isapplied in2D image, it suffers the problems of high computing complexity ofreconstruction algorithm and excessive memory of sensing matrix. In blockcompressed sensing (BCS), the whole image is divided into blocks of the same size,and each block is measured through the same sensing matrix and reconstructedindependently, which has the advantage of low storage and fast reconstruction as well.Under the BCS framework, several image sparse representation and reconstructionalgorithms are proposed in this paper, and the main work is as follows:The tranditional iterative thresholding algorithms has the advantage of simpleprocessing and better performance, meanwhile it has slower convergence speed. Westudies the semi-iterative hard threshold algorithm (SIHT) based on semi-iterativeacceleration technology in this paper. SIHT has fast convergence speed, but itacheivse good reconstructed signal only with orthogonal measurement matrix, whichlimits its application scope. Inspired by the method in OMP algorithm improved byMP, we improved the SIHT algorithm and put forward orthogonal semi-iterative hardthreshold algorithm (OSIHT). Experimental results show that OSIHT algorithm notonly improves the dependent manner of measurement matrix in SIHT algorithm, butalso improve the performance in the reconstruction quality and running time.In order to exploit the signal sparsity, reduce the coding complexity and apply tothe blocked image easily, it introduces the new, non-orthogonal all phase biorthogonaltransform (APBT) method in this paper. Compared with the DCT, APBT makes theenergy gather to the low-frequency in the image, and reveals the sparsity of the image.APBT overcomes the defects of multiscale transform such as wavelet transform withhigh computational complexity and the feature of not being applicable to the blockedimage. Therefore, combined with semi-iterative technology, accelerated smoothprojected Landweber (ASPL) algorithm in APBT domain is proposed. Experimentalresults show that this improved algorithm has better performance than the standardSPL algorithm, not only in the reconstructed image, but also in the number ofiterations and running time.