Based On The Original Dual Variational And Wavelet Hybrid Model Recovery Method

Images are inevitably affected by many factors in equipment, environment and scenario in the process of collection, conversion, transmission and display, leading to degradation in quality of the images. It also will affect the subsequent processing and the application of the image. In order to improve image quality and get more reliable information, the degraded image must be restored or improved so as to better satisfy specific applications.Image processing technology is an important approach to help human better recognize the world. It has been widely used in aerospace, biomedical engineering, target identification, geographical surveying and mapping, and other important fields.Image restoration is a basic and important technology, this paper mainly completes do some researches on image techniques based on convex optimization method. The main contents in this dissertation include:(1) A basic convex optimization theory needed in this dissertation is introduced from the point of view of engineering. A general optimization model and some of its applications in image processing and image restoration are given. Finally we have introduced several solving algorithm of the model.(2) The total variation model is introduced and analyzed.One of its advantages in image restoration is its good effect for the edge and block structure. However the non-smoothness leads to difficulty for solving the answers by general optimization methods, so we will solve the problem by approximate alternative or iterative threshold method.(3) An image restoration model based on sparse operator is introduced. The typical sparse operator is Wavelet, Curvelet, etc. By denoising experiments, the advantages and disadvantages of curvelet and wavelet are compared.One of the advantages of curvelet in the image restoration is that it can preserve the image texture information better.(4) We have studied the dual programming method which can be very flexible to solve the total variation problem. At the same time it can also be applied to the problem of sparse regularization. On this basis, we put forward the curvelet operator and the variation operator mixed regularization model, using the original dual method as a mathematical tool to solve the model. The new model is applied to image restoration and denoising. Through experiments it is found that the new model has got much more improvement comparing with the beforehand original dual variation. Finally experimental results are given to verify the validity and the feasibility of the algorithms.