Image Reconstruction Based On Compressive Sensing Technolgy

Nyquist sampling theorem provides that, in order to avoid the distortion of the sampling signal and the original signal, sampling frequency must be2times greater than or equal to the maximum frequency. In recent years, the communication field is developing continuouly. With the amplification of information processing, strengthening the ability of signal processing hardware has been required. However,upgrading hardware is not a valid way after all。In2006, a new theory, compressed sensing theory, which is proposed by Dr. Candes and Donoho Academy of Sciences in Stanford University, gives a new idea to the researchers engaged in communication research. Compressed sensing theory combines sampling and compression, and besides, subverts the traditional Nyquist sampling theorem. So this theory directly solves the growing hardware requirements in communication field, and besides, effectively extracted the key information of the signal and ensure its accuracy in a series of transmission and reconstruction processing.The following work are mainly completed:1. The paper researches the basic theory of the compressed sensing, analyzes the concrete steps of image reconstruction, places emphasis on the measurement matrix and reconstruction of the principle and algorithm. It compares and evaluates the results from subjective and objective sides that the wavelet transform, DCT transform, multiwavelet transform and dual-tree complex wavelet transform are taken respectively as a sparse prior of compressed sensing image reconstruction.2. This paper proposes a image reconstruction method based on multi wavelet transform and the orthogonal matching pursuit algorithm by using wavelet transform for image sparse representation, choosing Gauss random matrix and Bernoulli random matrix as the measurement matrix in the original image linear projection measurement process and using orthogonal matching pursuit algorithm. The experimental results show the effectiveness of the method.3. This paper puts forward a image reconstruction method based on dual-tree complex wavelet transform and iterative thresholding algorithm, which uses dual-tree complex wavelet as the image sparse representation, chooses Gauss random matrix as the measurement matrix in the original image linear projection measurement process and adopts orthogonal matching pursuit algorithm. Besides, the paper transform soluting optimal sparse representation of the problem in constraint conditions into finding optimization problem in iteration under constraint conditions by using transformation principle in the reconstructed signal process. The experimental results show the effectiveness of the method.