Abstract
Even though more than 30 years have passed since the seminal Rudin--Osher--Fatemi (ROF) paper on total variation (TV) denoising, it remains relevant due to its simplicity, robustness and interpretability. However, it is known to suffer from artifacts such as the staircasing effect. Many variants of the model have been proposed with the aim of countering this. Recently, against the backdrop of immense research output on double-phase problems in the mathematical analysis community, a double-phase type integral functional, comprising of TV and a weighted term of quadratic growth, was suggested as a regularizer for image restoration. Here, we propose an adaptive variant of the ROF denoising model based on that regularizer. Variable growth of the double-phase functional allows for qualitatively different behavior at image contours, which are captured by an initial ROF reconstruction step. The model is designed to reduce staircasing with respect to the classical ROF model, while preserving the edges of the image in a similar fashion. We derive a closed-form resolvent formula and adapt the primal-dual Chambolle--Pock scheme for the numerical solution of the model. We also propose a practical noise-dependent parameter prescription and evaluate its performance on synthetic and natural images over a range of noise levels. Compared to established models with similar interpretability, we observe an improved or similar performance in terms of similarity metrics SSIM, PSNR, and LPIPS, while the staircasing effect is visibly reduced.
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Oct 3, 2024cs.CV
The total variation (TV) method is an image denoising technique that aims to reduce noise by minimizing the total variation of the image, which measures the variation in pixel intensities. The TV method has been widely applied in image processing and computer vision for its ability to preserve edges and enhance image quality. In this paper, we propose a Mixed-norm TV (MixTV) model for image denoising and the associated numerical algorithm to carry out the procedure, which is particularly effective in removing several types of noise and their combinations. Our MixTV admits a unique solution and the associated numerical algorithm guarantees convergence. Numerical experiments are demonstrated to show improved effectiveness and denoising quality compared to other TV models. Such encouraging results further enhance the utility of the TV method in image processing. Our project page is available at https://jing-en-huang.github.io/MixTV.
Jing-En Huang, Jia-Wei Liao, Ku-Te Lin +2
Jan 10, 2024cs.CV
In this paper, we propose a novel locally statistical variational active contour model based on I-divergence-TV denoising model, which hybrides geodesic active contour (GAC) model with active contours without edges (ACWE) model, and can be used to segment images corrupted by multiplicative gamma noise. By adding a diffusion term into the level set evolution (LSE) equation of the proposed model, we construct a reaction-diffusion (RD) equation, which can gradually regularize the level set function (LSF) to be piecewise constant in each segment domain and gain the stable solution. We further transform the proposed model into a general ROF model by adding a proximity term ,and it can be solved by a fast denoising algorithm proposed by Jia-Zhao or soved by BM3D and NLM denoising algorithm, which also provide a unified solution framework for formally generalized-ROF-like subproblems arising in multivariate splitting algorithms.
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Dec 8, 2023cs.CV
In this paper, we propose a novel locally statistical active contour model (LACM) based on Aubert-Aujol (AA) denoising model and variational level set method, which can be used for SAR images segmentation with intensity inhomogeneity. Then we transform the proposed model into a global optimization model by using convex relaxation technique. Firstly, we apply the Split Bregman technique to transform the global optimization model into two alternating optimization processes of Shrink operator and Laplace operator, which is called SB_LACM model. Moreover, we propose two fast models to solve the global optimization model , which are more efficient than the SB_LACM model. The first model is: we add the proximal function to transform the global optimization model to a general ROF model[29], which can be solved by a fast denoising algorithm proposed by R.-Q.Jia, and H.Zhao; [29] was submitted on 29-Aug-2013, and our early edition was ever submitted to TGRS on 12-Jun-2012, Venkatakrishnan et al. [30] proposed their PnP algorithm on 29-May-2013, so Venkatakrishnan and we proposed the PnP algorithm almost simultaneously. Thus we obtain a fast segmentation algorithm with global optimization solver that does not involve partial differential equations or difference equation, and only need simple difference computation. The second model is: we use a different splitting approach than one model to transform the global optimization model into a differentiable term and a general ROF model term, which can be solved by the same technique as the first model.
Guangming Liu