An Adaptive Parameter Choosing Approach for Regularization Model

Abstract

The choice of regularization parameters is a troublesome issue for most regularization methods, e.g. Tikhonov regularization method, total variation (TV) method, etc. An appropriate parameter for a certain regularization approach can obtain fascinating results. However, general methods of choosing parameters, e.g. Generalized Cross Validation (GCV), cannot get more precise results in practical applications. In this paper, we consider exploiting the more appropriate regularization parameter within a possible range, and apply the estimated parameter to Tikhonov model. In the meanwhile, we obtain the optimal regularization parameter by the designed criterions and evaluate the recovered solution. Moreover, referred parameter intervals and designed criterions of this method are also presented in the paper. Numerical experiments demonstrate that our method outperforms GCV method evidently for image deblurring application. Especially, the parameter estimation algorithm can also be applied to many regularization models related to pattern recognition, artificial intelligence, computer vision, etc.

A Robust Functional Minimization Technique to Protect Image Details from Disturbances

“…However, the image smoothing problems significantly come into the notice are reported in many research articles including local filtering-based image smoothing [1,2], nonlocal-based methods [3][4][5][6] are also noted in literature. Nonlocal wavelet-based method [7,8], nonlocal-based sparse coding strategy [9], nonlocal lowrank [10], the sparse representation techniques [11], shearlet-based model [12], curvelet-based method [13], dictionary-based approaches [14,15], soft-thresholding method [16], image deblurring technique using regularization [17], the radial basis function (RBF)-based method [18] and image retrieval with color and angle representation [19] are also remarkable in applications. However, many other methods based on variation and partial differential equation (PDE) have been proposed widely since variational calculus come out recently as a powerful tool for image-smoothing and model solutions.…”