Related papers: Multigrid methods for total variation
It is known that the solution of a conservative steady-state two-sided fractional diffusion problem can exhibit singularities near the boundaries. As consequence of this, and due to the conservative nature of the problem, we adopt a finite…
This paper proposes a mode multigrid (MMG) method, and applies it to accelerate the convergence of the steady state flow on unstructured grids. The dynamic mode decomposition (DMD) technique is used to analyze the convergence process of…
This work addresses a central topic in Magnetic Resonance Imaging (MRI) which is the motion-correction problem in a joint reconstruction and registration framework. From a set of multiple MR acquisitions corrupted by motion, we aim at -…
We consider the problem of coarse-graining in the context of finite-volume fluid models. If a variable is defined on a high-resolution grid it may be coarse-grained so that it is defined on a grid of lower resolution. In general this will…
We aim at the solution of inverse problems in imaging, by combining a penalized sparse representation of image patches with an unconstrained smooth one. This allows for a straightforward interpretation of the reconstruction. We formulate…
We consider geometric multigrid methods for the solution of linear systems arising from isogeometric discretizations of elliptic partial differential equations. For classical finite elements, such methods are well known to be fast solvers…
We mainly analyze and solve the overfitting problem of deep image prior (DIP). Deep image prior can solve inverse problems such as super-resolution, inpainting and denoising. The main advantage of DIP over other deep learning approaches is…
We propose a variable metric forward-backward splitting algorithm and prove its convergence in real Hilbert spaces. We then use this framework to derive primal-dual splitting algorithms for solving various classes of monotone inclusions in…
Recent diffusion models provide a promising zero-shot solution to noisy linear inverse problems without retraining for specific inverse problems. In this paper, we reveal that recent methods can be uniformly interpreted as employing a…
We derive a variant of the nonsmooth maximum principle for problems with pure state constraints. The interest of our result resides on the nonsmoothness itself since, when applied to smooth problems, it coincides with known results.…
In this paper we construct and analyse a level-dependent coarsegrid correction scheme for indefinite Helmholtz problems. This adapted multigrid method is capable of solving the Helmholtz equation on the finest grid using a series of…
Method for a mosaic image representation (MIR) is proposed for a selective treatment of image fragments of different transition frequency. MIR method is based on piecewise-constant image approximation on a non-uniform orthogonal grid…
Grids are a general representation for capturing regularly-spaced information, but since they are uniform in space, they cannot dynamically allocate resolution to regions with varying levels of detail. There has been some exploration of…
This paper addresses the solution of inverse problems in imaging given an additional reference image. We combine a modification of the discrete geodesic path model for image metamorphosis with a variational model,actually the $L^2$-$TV$…
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…
We consider inverse problems with large null spaces, which arise in important applications such as in inverse ECG and EEG procedures. Standard regularization methods typically produce solutions in or near the orthogonal complement of the…
Variational regularization of ill-posed inverse problems is based on minimizing the sum of a data fidelity term and a regularization term. The balance between them is tuned using a positive regularization parameter, whose automatic choice…
Parallel-in-time methods for partial differential equations (PDEs) have been the subject of intense development over recent decades, particularly for diffusion-dominated problems. It has been widely reported in the literature, however, that…
Multigrid is one of the most efficient methods for solving large-scale linear systems that arise from discretized partial differential equations. As a foundation for multigrid analysis, two-grid theory plays an important role in motivating…
Machine learning has achieved impressive performance in tomographic reconstruction, but supervised training requires paired measurements and ground-truth images that are often unavailable. This has motivated self-supervised approaches,…