Research On Image Reconstruction Algorithms Based On Compressed Sensing

The traditional Nyquist sampling theorem shows that when the sampling frequency is greater than or equal to twice the highest frequency of the original signal,the sampled signal can restore the original signal of the complete information.In 2006 Donoho and Candès proposed Compression Sensing(CS)theory.The Compression Sensing theory breaks the bounds of the Nyquist sampling theorem to the sampling frequency,especially in the digital image processing,and the original image signal can be accurately recovered by a small amount of signal.Based on the application of compression perception theory in image reconstruction,this paper focuses on gradient projection algorithm and greedy algorithm,and proposes an improved fast two-step iterative mixed norm algorithm to realize image reconstruction.The main work of the paper is as follows:1.The core theory of Compression Sensing is studied,including the sparsity of the signal,the measurement matrix and the signal reconstruction algorithm.The mathematical model of the Compression Sensing theory is established.The sparseness of the image is studied,and the dual-tree complex wavelet transform is selected as the transformation base.The Hadamma matrix is the best,with the comparison of of the various measurement matrices,such as the Bernoulli stochastic matrix,the local Hadamard matrix,the Gaussian random matrix.So the local Hadamard matrix is chosen as the observation matrix.2.The image reconstruction algorithm is researched in this paper.The gradient projection algorithm and the improved gradient projection algorithm(GP)algorithm in the convex optimization algorithm with minimal l1 norm are analyzed.The results show that the algorithm has good convergence speed,good image denoising ang deblurring effect,image reconstruction high quality.At the same time,the greedy algorithm of minimum l0 norm is studied emphatically,including orthogonal matching tracing algorithm,regular orthogonal matching tracing algorithm,sparse adaptive matching tracing algorithm,compression sampling matching tracking algorithm and other image reconstruction algorithms.Research shows that the greedy algorithm is with high efficiency,simple calculation.3.Based on the IST algorithm,an improved fast two-step iterative mixed norm algorithm is proposed,and the objective function is based on the mixed norm model.The two-step iterative mixed norm algorithm is proposed based on the double-tree complex wavelet base as the sparse base and the local Hadamard matrix as the observation matrix.The two-step iteration accelerates the optimization of the objective function,and the two-step iterative mixed norm algorithm converges to the minimum value of the mixed objective function.The improved algorithm is 2.5 times faster than the IST algorithm,and the mean square error of the image is reduced by more than 50%.And the peak signal-to-noise ratio of the improved algorithm is about 1dB compared with the compression-aware reconstruction system with DCT as sparse base and Gaussian matrix as observation matrix and fast two-step iterative mixed norm algorithm.It shows that the improved algorithm has better image reconstruction quality and reconstruction speed.