Image Restoration Method Based On Geometric Prior

Due to the limitation of imaging equipment and the interference of external factors,image data is inevitably affected by noise,blur,low resolution,and even some missing information during the process of acquisition and transmission,resulting in image distortion.Therefore,it is necessary to develop effective image restoration techniques to recover the latent clear images from degraded images.In recent years,variational methods have received extensive attention since they can provide high-quality recovery results in image restoration.However,the current variational methods still suffer from the difficulties in retaining geometric features,high computational complexity and efficient numerical solution.To overcome these defects,this paper mainly studies the variational image restoration problem based on geometric prior and designs effective numerical solution algorithms,to preserve the important geometric features of restored image and improve the computational efficiency.The specific research work and innovations are detailed as follows:Based on the differential geometry theory,we proposes the Weingarten map regularized restoration model,and then proves the Weingarten map regularization,similar to mean curvature and Gaussian curvature regularization,can preserve image contrast,edges and corners.Since the Weingarten map variational model is non-convex and highly nonlinear,the numerical algorithm converges slowly.In order to reduce the computational complexity,a spatially adaptive first and second order variational model is derived from the Weingarten map regularization,and which is solved by an efficient alternating direction method of multipliers.Numerical experiments verifies the superiority of the modified model in terms of restoration results and computational efficiency.Moreover,we designs effective numerical algorithm for estimating mean curvature,Gaussian curvature and total curvature on the image surface using the first fundamental form and second fundamental form in differential geometry,then establishes the curvature-based regularization models and efficient ADMM numerical algorithms.In image restoration,it not only avoids the defects of solving high-order nonlinear partial differential equations,and improves the computational efficiency,but also maintains the advantages of curvature-based regularization in preserving important geometric features of images.Aiming at the high nonlinearity and computational complexity of Beltrami regularization on differential manifold,we constructs a simplified Beltrami regularization model for solving color image denoising problem,and proposes a fast operator splitting numerical method.Compared with the existing augmented Lagrangian method,the proposed operator splitting method is not only easy to be implemented,but also generates fast convergence and satisfactory restoration.The effectiveness,robustness and superiority of the proposed geometric regularization method are qualitatively and quantitatively verified by a series of comparative experiments in image restoration.