Related papers: Color Bregman TV
We consider the task of image reconstruction while simultaneously decomposing the reconstructed image into components with different features. A commonly used tool for this is a variational approach with an infimal convolution of…
Joint reconstruction has recently attracted a lot of attention, especially in the field of medical multi-modality imaging such as PET-MRI. Most of the developed methods rely on the comparison of image gradients, or more precisely their…
All imaging modalities such as computed tomography (CT), emission tomography and magnetic resonance imaging (MRI) require a reconstruction approach to produce an image. A common image processing task for applications that utilise those…
The aim of this paper is to introduce and study a two-step debiasing method for variational regularization. After solving the standard variational problem, the key idea is to add a consecutive debiasing step minimizing the data fidelity on…
We define the space of functions of bounded variation ($BV$) on the graph. Using the notion of divergence of flows on graphs, we show that the unit ball of the dual space to $BV$ in the graph setting can be described as the image of the…
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…
High radiation dose in CT scans increases a lifetime risk of cancer and has become a major clinical concern. Recently, iterative reconstruction algorithms with Total Variation (TV) regularization have been developed to reconstruct CT images…
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…
We propose an extension of a special form of gradient descent -- in the literature known as linearised Bregman iteration -- to a larger class of non-convex functions. We replace the classical (squared) two norm metric in the gradient…
Bregman iterations are known to yield excellent results for denoising, deblurring and compressed sensing tasks, but so far this technique has rarely been used for other image processing problems. In this paper we give a thorough description…
In this paper, a new regularization term is proposed to solve mathematical image problems. By using difference operators in the four directions; horizontal, vertical and two diagonal directions, an estimation of derivative amplitude is…
Total variation (TV) regularization is a popular reconstruction method for ill-posed imaging problems, and particularly useful for applications with piecewise constant targets. However, using TV for medical cone-beam computed X-ray…
Color image denoising is frequently encountered in various image processing and computer vision tasks. One traditional strategy is to convert the RGB image to a less correlated color space and denoise each channel of the new space…
We consider the image denoising problem using total variation (TV) regularization. This problem can be computationally challenging to solve due to the non-differentiability and non-linearity of the regularization term. We propose an…
In dynamic imaging, a key challenge is to reconstruct image sequences with high temporal resolution from strong undersampling projections due to a relatively slow data acquisition speed. In this paper, we propose a variational model using…
Owing to the edge preserving ability and low computational cost of the total variation (TV), variational models with the TV regularization have been widely investigated in the field of multiplicative noise removal. The key points of the…
Even after over two decades, the total variation (TV) remains one of the most popular regularizations for image processing problems and has sparked a tremendous amount of research, particularly to move from scalar to vector-valued…
In biomedical imaging reliable segmentation of objects (e.g. from small cells up to large organs) is of fundamental importance for automated medical diagnosis. New approaches for multi-scale segmentation can considerably improve performance…
Total variation (TV) regularization has proven effective for a range of computer vision tasks through its preferential weighting of sharp image edges. Existing TV-based methods, however, often suffer from the over-smoothing issue and…
This paper addresses the structurally-constrained sparse decomposition of multi-dimensional signals onto overcomplete families of vectors, called dictionaries. The contribution of the paper is threefold. Firstly, a generic spatio-temporal…