Image Reconstruction Of Compressed Sensing In Shearlet Domain And It’s Apllication

The traditional Nyquist sampling theorem states that a signal can be reconstructed perfectly from its samples, only if it was sampled at a rate at least twice the highest frequency of the signal. But with the advent of the information age, the bandwidth of the data required to be processed is more and more high, and data quantity is more and more big, all of these give the hardware costs a great deal of pressure. Recently, an emerging theory of signal processing named Compressive Sensing proposed by Candes and Donoho theory suggests that:if the signal is sparse or can be compressed in a transform domain, it can be reconstructed from a smaller number of random linear measurements than Nyquist sampling, with the prior knowledge of sparsity of the signal. The Compressive Sensing theory makes full use of signal sparse characteristics, combines data acquisition with data compression to break the limit of sampling frequency of the traditional Nyquist sampling theorem, as a result, the storage space and bandwidth are cut down on. With the appearance of Compressive Sensing theory, arousing wide concern of experts and scholars of different research fields at home and abroad. It has been widely used in compression imaging, magnetic resonance imaging, geological exploration, Synthetic aperture radar imaging, channel estimation, analog-to-digital conversion, etc.This paper applied the compressive sensing theory to image reconstruction as following three aspects:Firstly, In the compressive sensing image reconstruction, with the sparse prior knowledge we can accurately reconstruct compressible signals from relatively few linear measurements via solving nonsmooth convex optimization problems. In the process, the image representation plays an important role and effects the quality of image reconstruction. Contraposing the direction selective of wavelet transform is poor, and the wavelet transform is not translation invariant, this paper propose image compressed sensing reconstruction based on shearlet sparse representations and compound regularizers, it uses an alternating minimization scheme in which the main computation involves shrinkage and fast Fourier transforms.Secondly, we take advantage of structure characteristics of partial Fourier matrix, use a part of the Fourier coefficients to compressive sensing image reconstruct. Comparison and analysis of the difference between the random Gaussian matrix and partial Fourier matrix.Last, because the measure matrix of the compressive sensing is similar with degenerate matrix of image restoration, applying compressive sensing image reconstruction model of compound regularizers to image restoration. The experimental results indicate that the algorithm obtains better performance in image restoration.