Compresseive Sensing Reconstruction Algorithms Based On Edge Detection

Compressive sensing (CS) has become a newly emerged branch generated from sparsesignal representation and processing, and attracts a lot of attention. The theory of compressivesensing combines the sampling and compressing of signals which are sparse or compressibletogether. It firstly employs non-adaptive linear projections that nearly preserve all the infor-mation of the signals, and then reconstructs them by an optimization process. At present, thereare still have many questions to be worth studying, and the design of efcient reconstructionalgorithms is became one of the key issues in the application of CS.This thesis introduces the theoretical framework of compressive sensing, and mainly con-centrates on the optimization of reconstruction algorithms in CS. We have analyzed the RecPFalgorithm which based the TVL1-L2model and given the algorithm description, convergenceconditions, performance analysis and simulation results. Based on this algorithm, this thesisproposed the edge guided compressive sensing reconstruction that takes fully use of the imageedge information.It alternatively performs CS reconstruction and edge detection in a way thateach benefits from the latest solution of the other. Meanwhile, we also presented the theo-retical proof of the new algorithm based on the iterative support detection. To overcome theproblem that the reconstruction of images is time-consuming, we proposed an improvementscheme for our algorithm. In the improved algorithm, the original fixed cost parameter valueincreases as the iteration enlarges, i.e. in the next iteration, the parameter values will be somecertain times as the former one.Numerical experiments have been carried out on MATLAB plat-form to compare the per-formance between our algorithm and some current fast reconstruction algorithmS on relativeerror and convergence rate. The simulation results have shown that the reconstruction perfor-mance attained by the algorithm which based on edge information detection is much betterthan the others. In particular, the improved edge guided compressive sensing reconstructionalgorithm achieves much higher performance in terms of both convergence speed and qualitythan the unimproved. It is also shown that our algorithm has better robustness of the measure-ment noise. On the other aspect, our algorithm has optimized the edge detection algorithm during iteration. Thus it is not only a new reconstruction algorithm, but also taking use ofcompressive sensing into image processing, and then enlarge the future application prospect.