Research Of Image Reconstruction And Restoration Based On Compressed Sensing Theory

With the development of information technology, the demand for information is increasing dramatically. The conventional Nyquist sampling theory requires that sampling rate can't be lower than two times the maximum frequency of singal, which causes the difficulties in the acquisition, transmission, storage and processing of digital images, video and so on. Recently Donoho and Candes have proposed compressed sensing(CS) theory, which indicates that the sparsity prior of the signals or images can accurately reconstruct original signals or images from a small quantity of measurements, the sampling rate based on CS is lower than that based on Nyquist. At present CS theory has become the hotspot of research in digital signal processing, medical imaging, pattern recognition, optical radar imaging, etc.When original data are incomplete, when images are degraded, it is important for images to reconstruct and restorate. How can we find an efficient way to reconstruct and restore images, and at the same time it can decrease observation data, storage space and calculation quantity? Therefore compressed sensing provides us with a feasible method. The paper mainly researches on image reconstruction and restoration.Owing to the advantages of dual tree complex wavelet(DTCWT), such as shift invariance, directional selectivity and a lower computational complexity. The paper proposes an algorithm that one can reconstruct images based on CS and single layer DTCWT transform, which use the sparse prior in the dual tree complex wavelet domain. The experiment results show the validity of the algorithm.Split Bregman algorithm applies split strategy to Bregman iteration, so as to accelerating convergence. We finish image reconstruction based on Split Bregman algorithm and a comb-ination of DCT and wavelet coefficients as sparsity constraints under the frame of CS theory. Experiments show good performances and faster reconstruction speed.In the framework of CS,a novel wavelet-domain image restoration algorithm is proposed. We can reconstruct images based on the two-step iterative shrinkage/thresholding (TwIST) algorithm. Under blur and noise models, the proposed algorithm can effectively improve the qualities of the degraded images, not only in objective but also in subjective aspects of images. Compared with other typical restoration algorithms, it takes less observation data, storage space and calculation quantity, when the restorated outputs are similar.