Non-convex Compressed Sensing Image Reconstruction Based On Block Constraint And Particle Swarm Optimization

Compressed Sensing(Compressed Sensing, CS) theory is a new theory in the field of signal processing. CS theory mainly includes the following three aspects: the sparse representation of signal, the design of the measurement matrix and the signal reconstruction. However, signal reconstruction is the key of CS. As well known, the compressed sensing reconstruction algorithms based on evolution, such as genetic algorithm and immune clone two-stage algorithm was proposed to obtain better reconstruction effect, with high time cost and bad real-time implementations. In this paper,we introduce a new fast evolutionary algorithm, particle swarm optimization(PSO)algorithm, to deal with the non-convex compressed sensing image reconstruction problem.Therefore, several search strategy and related operators designed, and several corresponding reconstruction method is proposed. In this paper, the main innovation work as follows:Under the framework of non-convex compression based on the strategy of over complete dictionary and image block strategy, the reconstruction model to estimate the image block from the compression observations of image block structure is used to construct the redundant child dictionaries. For smooth blocks, the sub dictionaries of the first five scales in each direction form the Ridgelet complete dictionary are taken as a redundant child dictionary. For single direction block, the sub dictionaries whose directions are the single direction block's direction and the four directions around it are chosen as its redundant child dictionary. For multiple direction blocks, the whole Ridgelet complete dictionary is taken as its complete dictionary.In this paper, the particle swarm optimization reconstruction method based on the Ridgelet redundant dictionary and crosse is proposed, a new initialization of particle swarm optimization is designed, and for smooth blocks and single direction blocks, the particle swarm based on the grouping strategy is designed. For smooth blocks, each group of particles in a population represents a scale. Also, for single direction blocks, each group of particles represents one direction on its complete dictionary, and the direction of each particle is random, but ensure that the particle contains at least 15 direction. And for multiple directions blocks, each particle represents two directions, one of the direction is same as the particle number, and one from the rest of the directions is selected as the other direction. For smooth blocks, with the fact that the scale parameter is more sensitive than others, the method of particle swarm optimization is proposed to mainly search its optimal combination of atoms on scale. For single and multiple direction blocks, the crossover operation introduced in order to search the optimal combination of atoms on direction. The simulation results verify the feasibility of the proposed method, and the reconstruction time is short.This paper also puts forward the particle swarm optimization method based on cross and atomic direction constrained. The particle swarm initialization is the same as above. And for single and multiple direction blocks, the operator based on the atoms direction constraint is designed to search the optimal combination of atoms on direction and scale at the same time. Several other methods including two phase optimization method are compared to our method in the simulation experiment, the experimental results show that the algorithm not only feasible,but also effective, and the reconstruction time is shorter, the reconstruction visual effect is good, PSNR and SSIM values are higher than other methods.Finally, some key parameters in the experiment are analyzed.