Color Image Restoration Based On Quaternion Representation

Color image restoration is to restore the original image with some prior in the degradation process.During the digitization and transmission process,color images are often corrected by the interference of imaging equipment and external environmental noise,which will produce certain noise and blur on the color image.Noise and blurring will degrade color images and even cover image features,which brings difficulties to subsequent analysis and processing.As an important pre-processing step for many related computer vision tasks,color image denoising has attracted considerable attention in image processing.Unlike grayscale image,each color image has three channels in the RGB color space.Due to the inner-relationship within the three channels,color image restoration is usually much more difficult than its grayscale counterpart.Indeed,new problems such as color artifacts could emerge when the grayscale image processing methods are extended to color images directly.However,traditional methods often regard the red,green,and blue channels of color images independently without considering the correlations among the three channels.In order to overcome this deficiency,this thesis proposes several color image restoration methods based on quaternion representation.The main innovations are as follows:(1)In handling the color image denoising task,this thesis proposes a novel dictionary method for color image denoising based on pure quaternion representation,which efficiently deals with both single-channel and cross-channel information.The pure quaternion constraint is firstly used to force the sparse representations of color images to contain only red,green,and blue color information.Moreover,a total variation regularization is proposed in the quaternion domain and embedded into the pure quaternion-based representation model,which is effective to recover the sharp edges of color images.To solve the proposed model,a new numerical scheme is also developed based on the alternating minimization method(AMM).Experimental results demonstrate that the proposed model has better denoising results in terms of PSNR,SSIM,and visual quality.(2)In handling the color image deblurring and denoising tasks,this thesis proposes a novel quaternion-based color image recovery method.This model combines the advantages of dictionary learning and the total variation method for color image restoration.The new strategy used in the proposed model manages to handle the color image restoration problem in the quaternion space.Moreover,the new proposed model can be easily solved by the classical alternating direction method of multipliers(ADMM)algorithm.Numerical results demonstrate clearly that the performance of our proposed dictionary learning method is better than some state-of-the-art color image dictionary learning and total variation methods in terms of some criteria and visual quality.(3)In handling the color image restoration task,we propose a quaternion-based color image restoration model.Note that one of the most effective gray image restoration methods is the weighted nuclear norm minimization(WNNM)approach.However,when applied to color images,the results of WNNM are usually not as promising as that of grayscale images.In order to solve this problem,in this thesis,we propose to restore color images with the quaternion-based WNNM method(QWNNM)since the structure of color channels can be well preserved with quaternion representation.The proposed model can be solved efficiently by the alternating direction method of multipliers(ADMM).The theoretical analysis of the optimal solution is also presented.Numerical experiments are carefully conducted with different kinds of blurring kernel degradation to illustrate the superior performance of our proposed QWNNM over the state-of-the-art methods in both visual quality and numerical results.