相关论文: Convergence of level sets in fractional Laplacian …

We investigate a level-set type method for solving ill-posed problems, with the assumption that the solutions are piecewise, but not necessarily constant functions with unknown level sets and unknown level values. In order to get stable…

We consider the problem of learning a sparse graph under the Laplacian constrained Gaussian graphical models. This problem can be formulated as a penalized maximum likelihood estimation of the Laplacian constrained precision matrix. Like in…

The inherent ill-posed nature of image reconstruction problems, due to limitations in the physical acquisition process, is typically addressed by introducing a regularisation term that incorporates prior knowledge about the underlying…

The advancement of imaging devices and countless images generated everyday pose an increasingly high demand on image denoising, which still remains a challenging task in terms of both effectiveness and efficiency. To improve denoising…

In this paper, we propose two algorithms for solving linear inverse problems when the observations are corrupted by noise. A proper data fidelity term (log-likelihood) is introduced to reflect the statistics of the noise (e.g. Gaussian,…

Inverse problems are inherently ill-posed and therefore require regularization techniques to achieve a stable solution. While traditional variational methods have well-established theoretical foundations, recent advances in machine learning…

Plug-and-Play Priors (PnP) and Regularisation by Denoising (RED) have established that image denoisers can effectively replace traditional regularisers in linear inverse problem solvers for tasks like super-resolution, demosaicing, and…

Jacobian and Hessian regularization aim to reduce the magnitude of the first and second-order partial derivatives with respect to neural network inputs, and they are predominantly used to ensure the adversarial robustness of image…

During a surface acquisition process using 3D scanners, noise is inevitable and an important step in geometry processing is to remove these noise components from these surfaces (given as points-set or triangulated mesh). The noise-removal…

Data dependent regularization is known to benefit a wide variety of problems in machine learning. Often, these regularizers cannot be easily decomposed into a sum over a finite number of terms, e.g., a sum over individual example-wise…

We prove a higher regularity result for the free boundary in the obstacle problem for the fractional Laplacian via a higher order boundary Harnack inequality.

Unpaired image denoising has achieved promising development over the last few years. Regardless of the performance, methods tend to heavily rely on underlying noise properties or any assumption which is not always practical. Alternatively,…

This paper is concerned with the numerical solution of a class of variational inequalities of the second kind, involving the $p$-Laplacian operator. This kind of problems arise, for instance, in the mathematical modelling of non-Newtonian…

We generalize many recent uniqueness results on the fractional Calder\'on problem to cover the cases of all domains with nonempty exterior. The highlight of our work is the characterization of uniqueness and nonuniqueness of partial data…

Phase retrieval is the nonlinear inverse problem of recovering a true signal from its Fourier magnitude measurements. It arises in many applications such as astronomical imaging, X-Ray crystallography, microscopy, and more. The problem is…

We discuss the optimal regularity and nondegeneracy of a free boundary problem related to the fractional Laplacian. This work is related to, but addresses a different problem from, recent work of Caffarelli, Roquejoffre, and Sire. A variant…

Beamforming in ultrasound imaging has significant impact on the quality of the final image, controlling its resolution and contrast. Despite its low spatial resolution and contrast, delay-and-sum is still extensively used nowadays in…

Many challenging image processing tasks can be described by an ill-posed linear inverse problem: deblurring, deconvolution, inpainting, compressed sensing, and superresolution all lie in this framework. Traditional inverse problem solvers…

Inverse scattering is a fundamental challenge in many imaging applications, ranging from microscopy to remote sensing. Solving this problem often requires jointly estimating two unknowns -- the image and the scattering field inside the…

Solving l1 regularized optimization problems is common in the fields of computational biology, signal processing and machine learning. Such l1 regularization is utilized to find sparse minimizers of convex functions. A well-known example is…