Study On Image Recontrution Of Compressed Sensing Based On The Dual Tree Complex Wavelet

The traditional sampling of signal must obey the Shannon sampling theorem, that is, the frequency of sampling signal must be at least twice of original signal to avoid losing the information of signal. However, further improving the Nyquist frequency will increase the complexity for data capturing, and be too difficult to achieve for hardware. Compressed sensing theory presents a new method to capture and compress the data, which can reconstruct the original signal from much fewer measurements using the prior knowledge that the signal has the sparse representation.For now, compressed sensing reconstruction algorithms are mostly for 1D signal. This paper performs the researches on image reconstruction based on compressed sensing after learning compressed sensing theory and the existent reconstruction algorithms, mainly including following three aspects.(1)Perform the image compressed sensing reconstruction based on the dual tree complex wavelet and iterative shrinkage. Aiming to overcome the shortcomings of lacking of diretion selectivity and translation variance of the orthogonal wavelet, we propose the algorithm that one can reconstruct the image by iterative shrinkage using the sparse prior in the dual tree complex wavelet domain. The experiment results show the validity of the algorithm.(2)Reconstruct the image based on the two step iterative shrinkage. Because of the slow convergence rate of iterative shrinkage, we introduce the two step iterative shrinkage used in image restiration into compressed sensing, and combine the dual tree complex wavelet with it to reconstruct the image. The results of experiments show that, the reconstructed image has better vision quality, and the convergence rate is faster than iterative shrinkage.(3)Reconstruct the image based on morkov prior model in wavelet domain. A new reconstruction algorithm is proposed by exploiting the neighborhood characteristic of the transform coefficients in some scale. We project the coefficients onto the initial mask firstly, optimize the mask by Bayesian theory and the knowleage of markov random field to update the coefficients, and reconstruct the image after numbers of iterations finally. The results of experiments show the validity of the algorithm.