Non-Convex Compressed Sensing Reconstruction With PCA Dictionary And Two Stage Optimization

In recent years, in the field of signal processing, a new data sampling theory namedcompressed sensing(CS) has been put forward. CS is a new theory breaking throughthe traditional Nyquist sampling theorem, the signal can be acquired that it can becompressed at the same time. The theory makes a revolutionary change for dataacquisition technology, so that the theory has the wide application prospect in thefields of compressed imaging system, military cryptography, wireless sensors.There are two key points in the image reconstruction algorithm of compressedsensing:(1)The construction of dictionary for sparse representation.(2)The design ofreconstruction algorithm. The reconstruction algorithm of compressed sensing isnon-convex Optimization problem by solving thel0norm, it is NP-hard problem.Genetic evolution and clonal selection algorithm are the representative method forsolving combinatorial optimization problems. Therefore this paper proposes anon-convex compressed sensing reconstruction with PCA dictionary and the two stageoptimization, the method is based on the framework of the block compressed sensing,by constructing a PCA overcomplete dictionary. Then genetic algorithm and clonalselection algorithm get better atomic composition from the global. The innovation ofthis work are as follows:1. The paper proposes the compressed sensing reconstruction method based onPCA direction bases and local structure prior. The method uses the thought thatGuoshen Yu and other scholars[54]propose to get PCA direction bases dictionary fromthe black and white image blocks. We obtain the composition of bases atoms of mostoptimal PCA direction through the reconstructed image block into local structure prior,then we use the sparse coefficients formula of literature [54] to obtain coefficients ofthese PCA direction bases atoms, finally, we get the reconstruction result of imageblock. The simulation results show that this method has better effect for the imageblock reconstruction with single direction.2.PCA base dictionary mentioned above is composed of the base atoms with largereigenvalues of each direction, the base atoms with small eigenvalues are discarded. Inthe sparse representation of image patches, PCA base atoms with large eigenvalueshave the larger contributions, but PCA base atoms with small eigenvalues also havecertain effect. Therefore, this paper constructs a PCA overcomplete dictionary, thedictionary is made up of the base atoms with all eigenvalues of all the PCA directions. Based on the dictionary, this paper proposes a non-convex compressed sensingreconstruction method based on two stage optimization. In the reconstruction of imageblock, firstly, we use genetic algorithm to solve the optimal atoms combination indirection from PCA overcomplete dictionary, secondly, we use clonal selectionalgorithm to get the better atomes combination in the small dictionary composed ofthese atoms in the optimal direction, thirdly, we use the sparse coefficients formula ofliterature[54] to obtain coefficients of these PCA direction base atoms, finally, we getthe reconstruction result of image block. The experimental results show thatreconstruction results of the method are better than the OMP and the third chapter inthe visual effect and the reconstruction error.