Solving a variational image restoration model which involves L∞ constraints
نویسندگان
چکیده
In this paper, we seek a solution to linear inverse problems arising in image restoration in terms of a recently posed optimization problem which combines total variation minimization and wavelet-thresholding ideas. The resulting nonlinear programming task is solved via a dual Uzawa method in its general form, leading to an efficient and general algorithm which allows for very good structure-preserving reconstructions. Along with a theoretical study of the algorithm, the paper details some aspects of the implementation, discusses the numerical convergence and eventually displays a few images obtained for some difficult restoration tasks.
منابع مشابه
Image Restoration: A General Wavelet Frame Based Model and Its Asymptotic Analysis
Image restoration is one of the most important areas in imaging science. Mathematical tools have been widely used in image restoration, where wavelet frame based approach is one of the successful examples. In this paper, we introduce a generic wavelet frame based image restoration model, called the “general model”, which includes most of the existing wavelet frame based models as special cases....
متن کاملVariational method for joint optical flow estimation and edge-aware image restoration
The most popular optical flow algorithms rely on optimizing the energy function that integrates a data term and a smoothness term. In contrast to this traditional framework, we derive a new objective function that couples optical flow estimation and image restoration. Our method is inspired by the recent successes of edge-aware constraints (EAC) in preserving edges in general gradient domain im...
متن کاملAn Efficient Primal-Dual Hybrid Gradient Algorithm For Total Variation Image Restoration
We propose a simple yet efficient algorithm for total variation (TV) minimizations with applications in the image processing realm. This descent-type algorithm alternates between the primal and dual formulations and exploit the information from both the primal and dual variables. It converges significantly faster than some popular existing methods as demonstrated in our experiments. This approa...
متن کاملA Total Fractional-Order Variation Model for Image Restoration with Nonhomogeneous Boundary Conditions and Its Numerical Solution
To overcome the weakness of a total variation based model for image restoration, various high order (typically second order) regularization models have been proposed and studied recently. In this paper we analyze and test a fractional-order derivative based total α-order variation model, which can outperform the currently popular high order regularization models. There exist several previous wo...
متن کاملEpigraphical splitting for solving constrained convex optimization problems with proximal tools – extended version
We propose a proximal approach to deal with a class of convex variational problems involving nonlinear constraints. A large family of constraints, proven to be effective in the solution of inverse problems, can be expressed as the lower level set of a sum of convex functions evaluated over different blocks of the linearly-transformed signal. For such constraints, the associated projection opera...
متن کامل