Algorithms For The Multichannel Image Restoration Based On The LLT Model

With deep research on digital image processing, the essence of the imageprocessing attracts more and more profound attention. Researchers tried to classifyand improve the existing image processing algorithms by the strict mathematicaltheory. Image restoration is one of the most important and basic research topics inthe feld of image processing, which has important theoretical value and practicalsignifcance. ROF model is regarded as a classic model for image restoration.However, for images with non-piecewise constant intensities and smooth features,the model will bring in “staircase”efect. In order to overcome this disadvantage,some researchers have been looking for suitable solutions. Since the higher orderpartial diferential equations have some good properties, Lysaker et al. proposedthe fourth-order LLT model.At present, ROF model for recovering the gray image has been widely re-searched However, less research has been done on the corresponding model for themultichannel image restoration. For multichannel images restoration, the methodsused in most articles are to deal with every channel independently. We call suchmethods the single channel methods or the channel by channel methods. Obvi-ously, these methods separate the connection between the channels. If channels ofimages have a closer connection, the results may make some diference. In orderto get a better image restoration efect, we consider the multichannel couplingmethods.Two important research directions in image processing are to seek the ap-propriate functional models and to establish fast and efective algorithms. Thispaper attempts to combine the higher order anisotropy LLT model with the aug-mented Lagrangian algorithm, and considers the case of multichannel coupling formultichannel image restoration. This dissertation is organized as follows:In the frst chapter, we introduce the basic knowledge of digital image process-ing technology, as well as the development and application of image restoration,especially the ROF model and the LLT model. Finally, the main work and contentin this dissertation are presented.The second chapter is devoted to introducing the required preliminary knowl-edge of this dissertation in detail, for instance, theories of image processing andmultichannel image restoration models as well as the theories associated with thisdissertation, including convex analysis, optimization and functional analysis etc. The basic knowledge about image processing and analysis based on the variationalmethods and PDEs is also introduced. At the same time, in order to measurethe models and algorithms well, the evaluation criteria for the quality of imagerestoration are given.In the third chapter, at frst, we review the application of ROF model formultichannel images, and then propose three models by improving the anisotropicLLT model: the channel-by-channel LLT model, the multichannel-coupling LLT-C1、LLT-C2model.In the fourth chapter, for multichannel images, the augmented Lagrangianmethod for the ROF model is reviewed. Then, the corresponding algorithms toseveral models proposed in the third chapter are given, also sub-problem solvingmethods and iterative schemes are introduced in detail.In the ffth chapter, numerical experiments and analysis will be presented.Finally, we analyze the feasibility and efectiveness of our methods, and point outsome problems that need further improvement.