The Research For Image Restoration Based On The Shearlet

With the deeper recession of the informationization in the current society, theway we touch with the world is increasingly diversified, wherein the way based onthe images is playing a much more material status in the recession on account of itsparticular direct-observation and visualization. Nevertheless, the resistless factor likethe physical limitations or the complex imaging environment, altogether with themanageable factor such as the relative motion between the imaging device and thetarget or the defocusing of the imaging device itself would both introduce someblurring into the picture, even bring some smooth distortion, thus prohibit us fromutilizing the picture further. Then, we can figure the image deblurring a significantissue.The Shearlet transform based on a multiresolution analysis which is built in thediscrete framework provides efficient multiscale directional representations andyields approximately optimal representation properties. Thereupon, we employ theShearlet as means of image representation, thus extracting the texture and details atthe extreme, and reducing the possibility of missing the helpful information in thepicture, which has important and direct significance for the image deblurring. Then,the whole paper is organized as follows:First, we discuss the theory of the Shearlet and the corresponding discretizationalgorithm, then present the fast discretization algorithm of the Shearlet based on thefrequency field, subsequently, on the two key steps for the fast algorithm mentionedabove, the multiscale decomposition based on the Laplacian Pyramid algorithm andthe localization of orientation based on the Polar Grid, we do the simulation andanalysis, pointing out that the some-degree decomposition is equivalent to thecorresponding cut-off frequency of the low-pass filtering, that the cut-off becomelower and lower with the number of the multiscale decomposition increasing, lead tothe corresponding energy become less and less from the point of the low-frequencyimage, to the opposite, the energy utilizing in the processing of the localizedorientation is getting abundant and ample which is beneficial for the extraction of the texture and details in the image. In the end of the chapter, we also do the analysis andinstruction on the complexity and redundancy for the Shearlet, furthermore, wefinally verify its sparse characterization through the simulation.Then, we describe the extrude and troublesome ill-posed problem in the imagedeblurring recession, and propose a hybrid image deblurring method based on theTikhonov regularization in the frequency domain together with the self-adaptivethreshold principle generalized-cross validation (GCV) in the Shearlet domain. In theimplementation of the algorithm, we do the self-adaptive evaluation to the unknownparameter. Then from the simulation results, we get satisfied deblurring effect on thewhole. Compared with the Fourier-Wavelet deblurring method, we can judge thedifference visual sense in the texture and details, even the numerical data could helpto strengthen the advantage of our algorithm. Besides, we also do more simulation onvarious blurring operators, and the results show the general performance of thealgorithm.We employ the Laplacian distribution model to describe the coefficients in theShearlet domain, thus get the corresponding priori probability density function, thenwe project the image onto the Shearlet domain, under the Bayesian Theory, ashearlet-based deblurring problem is equivalent to an optimization problem.Experimental results show the effectiveness of the proximal iteration algorithmcorresponding to the optimization model and also show that the proposed deblurringmethod outperforms significantly than the existing traditional methods especially thanthe Wavelet-deconvolution algorithm in the perspective of both subjective vision andobjective criteria such as PSNR or so.