Research On Regularization Algorithms For Image Restoration And Fusion

Image processing technology is to analyze and process the digital images by a computer for satisfying the needs of the practical application.The image processing problem includes image restoration,inpainting,fusion,registration,etc.Image restoration is an important branch in image processing.We aim at restoring a satisfactory image by using the prior of the degraded image.But image fusion is an emerging field.The fused image containing much characteristic information is obtained by integrating the redundant information from the source images.In this paper,we study the image restoration and fusion problems.By combining with the regularization methods,we establish the mathematical model and apply the efficient numerical algorithms to solve the proposed variational models.The main contributions are listed in the following contents:For overcoming the staircase effect caused by the total variation regularization,a convex variational model based on the high order total variation is proposed to remove the blur and impulse noise.We use the primal-dual algorithm to solve the proposed model and analyze the convergence property.Furthermore,the proposed model is extended to the RGB image restoration problem.By the comparison of numerical experiments,the proposed model effectively improves the quality of the restored images.Cauchy noise is a kind of non-Gaussian noise which is often found in engineering applications.In order to eliminate Cauchy noise,we apply the Maximum a Posteriori estimation to derive the non-convex variational model.Then the alternating direction method of multiplier is applied to solve the proposed non-convex model.Numerical results show that the proposed method effectively eliminates Cauchy noise and obtains the high-quality restored images.The peak signal-to-noise ratio is obviously improved.For removing the speckle noise in ultrasonic images,we combine with the total generalized variation and propose a new convex variational model.The proposed model effectively suppresses the staircase effect and preserves the fine details.Furthermore,the alternating direction method of multiplier is used to solve the proposed model.By comparing the visual effects and quantization measures,the proposed model is obviously better than other models.For the mixed additive and multiplicative noise removal problem in synthetic aperture radar images,we apply the total variation with overlapping group sparsity to present two new variational models.Then the alternating direction method of multiplier is used to solve the proposed models.Numerical experiments show that the proposed methods effectively eliminate the mixed additive and multiplicative noise as well as improve the quality of images.For the image fusion and denoising problems,we utilize the feature selection criteria to integrate the fractional-order gradient information of the noisy source images and obtain the target fractional-order feature.Assume that the target fractional-order feature makes fit with the fractional-order gradient of the unknown fused image.In order to further improve the quality of the fusion images,assume that the unknown fused image is approximatively equal to a preprocessed image.For removing Gaussian noise,we combine the total variation regularization to build a new variational model,then apply the alternating direction method of multiplier to solve the proposed model.By the comparison,the proposed model obtains the better numerical results and the high-quality images.