Related papers: Adaptive double-phase Rudin--Osher--Fatemi denoisi…
This article studies the denoising performance of total variation (TV) image regularization. More precisely, we study geometrical properties of the solution to the so-called Rudin-Osher-Fatemi total variation denoising method. The first…
Over the last 30 years a plethora of variational regularisation models for image reconstruction has been proposed and thoroughly inspected by the applied mathematics community. Among them, the pioneering prototype often taught and learned…
We give a comprehensive survey on a class of higher order variational problems which are motivated by applications in mathematical imaging. The overall aim of this note is to investigate if and in which manner results from the first…
We propose a set of iterative regularization algorithms for the TV-Stokes model to restore images from noisy images with Gaussian noise. These are some extensions of the iterative regularization algorithm proposed for the classical…
We consider one-dimensional variants of the classical first order total variation denoising model introduced by Rudin, Osher and Fatemi. This study is based on our previous work on various denoising and inpainting problems in image…
The problem of restoration of digital images from their degraded measurements plays a central role in a multitude of practically important applications. A particularly challenging instance of this problem occurs in the case when the…
Image restoration is one of the most fundamental issues in imaging science. Total variation (TV) regularization is widely used in image restoration problems for its capability to preserve edges. In the literature, however, it is also well…
The total variation (TV) regularization method is an effective method for image deblurring in preserving edges. However, the TV based solutions usually have some staircase effects. In this paper, in order to alleviate the staircase effect,…
The piecewise constant Mumford-Shah (PCMS) model and the Rudin-Osher-Fatemi (ROF) model are two important variational models in image segmentation and image restoration, respectively. In this paper, we explore a linkage between these…
Recovering high quality surfaces from noisy triangulated surfaces is a fundamental important problem in geometry processing. Sharp features including edges and corners can not be well preserved in most existing denoising methods except the…
In many image and signal processing applications, as interferometric synthetic aperture radar (SAR), electroencephalogram (EEG) data analysis or color image restoration in HSV or LCh spaces the data has its range on the one-dimensional…
In this paper we study a variant to Chan-Vese image segmentation model with rectilinear anisotropy. We show existence of minimizers in the $2$-phases case and how they are related to the (anisotropic) Rudin-Osher-Fatemi denoising model…
This paper considers the constrained total variation (TV) denoising problem for complex-valued images. We extend the definition of TV seminorms for real-valued images to dealing with complex-valued ones. In particular, we introduce two…
In this paper, we propose a regularization technique for noisy-image super-resolution and image denoising. Total variation (TV) regularization is adopted in many image processing applications to preserve the local smoothness. However, TV…
Total variation (TV) regularization is a classical tool for image denoising, but its convex $\ell_1$ formulation often leads to staircase artifacts and loss of contrast. To address these issues, we introduce the Transformed $\ell_1$ (TL1)…
Second order total variation (SOTV) models have advantages for image reconstruction over their first order counterparts including their ability to remove the staircase artefact in the reconstructed image, but they tend to blur the…
Image restoration requires a careful balance between noise suppression and structure preservation. While first-order total variation (TV) regularization effectively preserves edges, it often introduces staircase artifacts, whereas…
Sparsity promoting functions (SPFs) are commonly used in optimization problems to find solutions which are assumed or desired to be sparse in some basis. For example, the l1-regularized variation model and the Rudin-Osher-Fatemi total…
Total Variation (TV) based regularization has been widely applied in restoration problems due to its simple derivative filters based formulation and robust performance. While first order TV suffers from staircase effect, second order TV…
The total variation (TV) regularization has phenomenally boosted various variational models for image processing tasks. We propose to combine the backward diffusion process in the earlier literature of image enhancement with the TV…