A Smooth Regularization L₀ Algorithm For Image Deconvolution

Image deconvolution is a very important branch of image processing.The task of image deconvolution is to remove or mitigate the image quality degradation that occurs during the acquisition of a digital image,which tends to restore the ideal image without noise.In this paper,two improved image deconvolution algorithms are proposed based on the characteristics of Lo nonn and wavelet framework.In solving the minimization problem,the improved model is transformed into two sub-optimization models,and the minimum value of the objective function is obtained by alternating direction iteration.Preliminary experiments show the effectiveness of the proposed algorithm.In the process of image acquisition,transmission and reception,some property or human factors will make the image quality decline.The image will inevitably be mixed with noise.The image deconvolution has important theoretical significance and practical value.Because of the ill-posedness of deconvolution,regularization is usually used to deal with the problem of image noise pollution.In the image deconvolution algorithm,the application of wavelet analysis is more and more extensive.Wavelet analysis is a time-frequency analysis method with variable resolution.Its main characteristic is that it has good localized characteristic in time-frequency domain,so it is called "mathematical microscope".Previous studies have showed that the Lo norm is able to better reflect the overall structure of the image,so this paper introduces the norm of the wavelet coefficients as a regular tenn.By the definition we can see that the L₀ norm of X is the number of nonzero.L₀ norm does not exist derivative.In our improved algorithm,we use the smooth continuous Gaussian function and the grinding kernel function respectively to construct the smooth approximation of the L₀ norm of the wavelet frame coefficients,so that the smooth approximation norm can be derived.Combining the L₀ norm and the advantage of wavelet framework in image processing,the algorithm proposed in this paper is reasonable and feasible.In this paper,the basic idea of solving the objective function is to convert an optimization problem into two sub-optimization problems.For this reason,we introduce two auxiliary variables and then solve them respectively.For the two auxiliary variables introduced,this paper uses the alternating direction iteration method to solve the minimization problem,and we use the steepest descent method for the minimum value of the smoothing norm,and the optimal solution of the model can be obtained quickly.