Compressive Sensing Reconstruction Based On Ridgelet Redundant Dictionary And Genetic Evolution

This paper firstly describes the theoretical framework of compressed sensing, which focus on the study and application of compressed sensing theory and compressed sensing reconstruction algorithm based on redundant dictionary. As its nature is l0norm’s problem, this article will involve both the Ridgelet redundant dictionary which shows good performance to line and edge, and the evolution genetic algorithm into the framework of compressed sensing, it puts forward the method of compressed sensing reconstruction and executed simulation experiments on the basis of Ridgelet redundant dictionary and genetic evolution. Namely, to start with, establish a novel compressed sensing reconstruction framework on the basis of blocked Ridgelet redundant dictionary; secondly, according to the actual situation for the problem, the article designs the coding and decoding methods of genetic algorithm, adaptive fitness function, genetic operation in detail; finally, the paper proposes three different forms of genetic evolutionary compressed sensing reconstruction method which are respectively genetic evolution for a single measurement, common genetic evolution for similarity measurements and combination of both former compressed sensing reconstruction methods.Compressed sensing reconstruction based on genetic evolution for a single measurement is simply fusing genetic evolution algorithm into reconstruction method. The simulation experiment proved that genetic evolution algorithm indeed could handle such issue, even it can surpass the reconstruction result by means of Orthogonal Matching Pursuit method when it evolutes to certain generation. Compressed sensing reconstruction based on common genetic evolution for similarity measurements is inspired by the self similarity feature existing in non-local parts of image, it can be referred from experiment data that such similarity feature occurred to vectors going through Gaussian Random Matrices, therefore Affinity Propagation algorithm is adopted to obtain groups of similarity measurements, then further define adaptive fitness function. The experimental showed that in contrast to the former algorithm, this solution takes full advantage of constraint among similar sub-blocks, effectively curbs sub-block error, so reduces the number of evolution generation, while improvs the reconstruction results.Comprehensive analysis and comparison is made to the data and reconstruction results of foregoing two reconstruction methods, combined with the highlighted common feature in common genetic evolution for similarity measurements and creative feature in genetic evolution for a single measurement, this paper bring about the reconstruction method combining the former two methods based on measurement common and independent genetic evolution, and make full use of interim output image information after each generation’s evolution, meanwhile filter operation and projection on convex sets operation are newly added to further enhance the quality of the reconstructed image itself, then Orthogonal Matching Pursuit with various sparsity are applied to adaptively optimize the sparsity of sub-block, moreover, the gene group of next generation is updated, finally, comparing the experimental results, it shows that this method is feasible and effective in reconstruction.