Related papers: Directional Total Generalized Variation Regulariza…
Total variation (TV) is a widely used regularizer for stabilizing the solution of ill-posed inverse problems. In this paper, we propose a novel proximal-gradient algorithm for minimizing TV regularized least-squares cost functional. Our…
In this work, we propose Regularization-by-Equivariance (REV), a novel structure-adaptive regularization scheme for solving imaging inverse problems under incomplete measurements. This regularization scheme utilizes the equivariant…
Restore lost images due to noise and blurred is a burgeoning subject in image processing and despite the different algorithms on this subject, but the effort to improve is always considered. The definition of fractional derivatives in…
While medical imaging typically provides massive amounts of data, the extraction of relevant information for predictive diagnosis remains a difficult challenge. Functional MRI (fMRI) data, that provide an indirect measure of task-related or…
Magnetic resonance imaging (MRI) is a versatile imaging technique that allows different contrasts depending on the acquisition parameters. Many clinical imaging studies acquire MRI data for more than one of these contrasts---such as for…
This work proposes the variable exponent Lebesgue modular as a replacement for the 1-norm in total variation (TV) regularization. It allows the exponent to vary with spatial location and thus enables users to locally select whether to…
The Bayesian inference is widely used in many scientific and engineering problems, especially in the linear inverse problems in infinite-dimensional setting where the unknowns are functions. In such problems, choosing an appropriate prior…
Investigation of image reconstruction from data collected over a limited angular range in X-ray CT remains a topic of active research because it may yield insight into the development of imaging workflow of practical significance. This…
Capturing complex high-order interactions among data is an important task in many scenarios. A common way to model high-order interactions is to use hypergraphs whose topology can be mathematically represented by tensors. Existing methods…
In this work we present a novel approach for single depth map super-resolution. Modern consumer depth sensors, especially Time-of-Flight sensors, produce dense depth measurements, but are affected by noise and have a low lateral resolution.…
The aim of this paper is to discuss and evaluate total variation based regularization methods for motion estimation, with particular focus on optical flow models. In addition to standard $L^2$ and $L^1$ data fidelities we give an overview…
In the present paper we propose two new algorithms of tensor completion for three-order tensors. The proposed methods consist in minimizing the average rank of the underlying tensor using its approximate function namely the tensor nuclear…
In this paper, we propose a new framework to remove parts of the systematic errors affecting popular restoration algorithms, with a special focus for image processing tasks. Generalizing ideas that emerged for $\ell_1$ regularization, we…
The total generalized variation extends the total variation by incorporating higher-order smoothness. Thus, it can also suffer from similar discretization issues related to isotropy. Inspired by the success of novel discretization schemes…
Total Variation (TV) is a popular regularization strategy that promotes piece-wise constant signals by constraining the $\ell_1$-norm of the first order derivative of the estimated signal. The resulting optimization problem is usually…
The concept of deep learning is employed for the inversion of NMR signals and it is shown that NMR signal inversion can be considered as an image-to-image regression problem, which can be treated with a convolutional neural net. It is…
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…
Dynamic inverse problems are challenging to solve due to the need to identify and incorporate appropriate regularization in both space and time. Moreover, the very large scale nature of such problems in practice presents an enormous…
Designing appropriate variational regularization schemes is a crucial part of solving inverse problems, making them better-posed and guaranteeing that the solution of the associated optimization problem satisfies desirable properties.…
We study variational regularisation methods for inverse problems with imperfect forward operators whose errors can be modelled by order intervals in a partial order of a Banach lattice. We carry out analysis with respect to existence and…