A Novel Variational Model with Strict Convexity for Multiplicative Noise Removal

Abstract

In this paper, a novel variational model with strict convexity for removing multiplicative noise from images is proposed and studied. Firstly, by applying maximum likelihood estimation method and the Bayesian formulation, the variational model is derived. Then, we use an alternating minimization algorithm to find out the minimizer of the objective function, and prove the existence of the minimizer for the underlying variational problem in theory. Finally, Our experimental results show that the quality of images denoised by the proposed method is quite good, and the proposed model is superior to the existing key models in preventing the images from stair-casing, and in restoring more texture details of the denoised image.

An novel image de-noising model based on gradient and adaptive curvature features and its application

“…Salt and Pepper [14][15][16][17][18] noise, also known as Impulse noise, is generated during image transmission. Gamma noise [19][20][21][22] and Exponential noise are less considered in precision electronic defect detection.…”

A Variational Model for Removing Multiple Multiplicative Noises

“…Aiming at solving the problem of the fidelity term sick, a series of variation models have taken logarithmic transformation log z u = [8] [9], and then get a new fidelity term written as ( ) Numerical results show that noise removal ability of HNW is better than AA, but it produces "staircase effect". Alternative iterative algorithm ensures that the solution of the model is unique, and the iterative sequence also converges to optimal solution of it.…”

“…When we get a model, and then must need a good algorithm to solve it. Numerical algorithm of variation model, today, includes ADMM [14] [15], ALM [16] [17], Newton iterative method [8] [9] [18] [19] and dual algorithm [20]- [22] and so on. HNW model has used adaptive alternating iterative algorithm.…”

A Novel Model for Removing the Mixture Noise and Blur of the Image

“…However, the model for retaining image texture features is not perfect, which causes some virtual edges in the smooth area of image, brings the piecewise constant solution and the "stair-case" phenomenon. Later, a lot of improved models for this problem have been put forward [6][7][8][9][10][11] and these models are used to remove the multiplicative noise. In addition, great deals of denoising approaches were proposed to remove the impulse noise [12,13] and Poisson noise [8,14].…”

“…Numerical results have shown that this model can provide the denoised images with better visual qualities. From then on, many fast and efficient algorithms and models were presented to solve above problem [9][10][11]16,17]. In fact, a lot of methods focus on the improvement of the fidelity term [16,17].…”