A Fast Fixed Point Algorithm for Total Variation Deblurring and Segmentation

Abstract

In this paper, we propose a fast fixed point algorithm and apply it to total variation (TV) deblurring and segmentation. The TV-based models can be written in the form of a general minimization problem. The novel method is derived from the idea of establishing the relation between solutions of the general minimization problem and new variables, which can be obtained by a fixed point algorithm efficiently. Under gentle conditions it provides a platform to develop efficient numerical algorithms for various image processing tasks. We then specialize this fixed point methodology to the TV-based image deblurring and segmentation models, and the resulting algorithms are compared with the split Bregman method, which is a strong contender for the state-of-the-art algorithms. Numerical experiments demonstrate that the algorithm proposed here performs favorably.

Fixed point algorithm based on adapted metric method for convex minimization problem with application to image deblurring

“…Similarly to the literatures [32,33], we find that κ = 0 achieves the best convergence speed compared with other κ ∈ (0, 1), and hence we choose κ = 0 for both algorithms.…”

“…FP 2 O algorithm supplies a simple and efficient method of solving (1.1) with the special case of f 2 (u) = 1 2 u − x 2 2 in the classical framework of fixed-point iteration. In [32], this algorithm has been extended to the more general case that ∇ f 2 (u) is bijective and the inverse can be computed easily. In particular, choose f 2 (u) = 1 2 u T Qu − x T u, where Q is a positive definite N × N matrix.…”

Superiorization vs. accelerated convex optimization: The superiorized / regularized least-squares case

“…We point out that problems of the form (1.4) have been extensively studied from the viewpoint of convex programming; see, e.g., [54,12,35,30]. For example, FISTA [11] is well-known to be particularly efficient for convex problems with sparsity-enforcing 1 or TV regularizers, like R in (1.3), because proximal maps with respect to these regularizers, when iterated, can be carried out efficiently by shrinkage and TV-based denoising, respectively [35,12].…”

A Sobel-TV based Hybrid Model for De-noising Remote Sensing Image with Gaussian and Salt-pepper Noise

“…Choose Sobel operator to detect the edges in the image under consideration (8) STEP2. Using (9) remove image noise according to the image edge information.…”

“…Although the traditional Gaussian and median filter algorithm is simple and easy to implement, but it is hard to meet the requirements of these two aspects. In recent years, image denoising algorithms based on what is called the Total Variation (TV) model which attracts much many research's attention [3][4][5][6][7][8][9]. TV denoising is an approach for noise reduction developed so as to preserve sharp edges in the image.…”