The Study On Compressed Sensing Based On Wavelet Tree Structure And Wavelet Fuzzy Feature

Standard Compressed sensing (CS) can reconstruct the original signal and image from fewer projections by using the sparse priors that the signal and image can be represented sparsly. Model-based CS combines the statistic dependency structure of wavelet coefficients with the theory of CS, and present greedy tree structure and optimal tree structure. This method is able to reduce searching space and computation, as well as achieving fast reconstruction. This paper performs researches on the statistic dependency structure of wavelet coefficient based on existing CS reconstruction algorithms.First of all, import greedy pursuit algorithm for GPR imaging of discrete point targets and compare imaging performance with different algorithms. For the imaging of block target, combine the idea of block sparsity, a new GPR imaging based on block sparsity and CS is proposed. Experimental results show that the proposed methods can perform well in GPR imaging, whether there has noise or not.Sencondly, Based on the existing wavelet tree structure in Model-based CS and a number of probability statistic and theory explanation, a new reasonable tree structure of coefficients which using the relationship between neighbor coefficients, parents coefficients and children coefficients is proposed in this paper. What's more, through the reasonable tree structure, the existing compressed sensing reconstruction algorithm that include iterative hard threshold algorithm and model-based CS algorithm are improved. Compare with the two existing reconstruction algorithm, the proposed algorithm can achieve higher image reconstruction performance.Finally, import fuzzy logic for reconstruction algorithm of CS for describing the intra-scale statistic dependency of neighbour Dual-Tree Complex wavelet coefficient effectively. Simulate the statistic dependency of neighbour coefficients within a scale and coefficients with different directions by fuzzy feature. In addition, make use of fuzzy member function for iterative threshold. The image reconstruction algorithm based on Dual-Tree Complex Wavelet's fuzzy feature and fuzzy iterative threshold is propsed. The experiment shows that the proposed algorithm can achieve higher performance, especially for texture reconstruction.