Related papers: Double phase image restoration
This work considers the reconstruction of a space-dependent potential from boundary observations in subdiffusion by a stable and robust recovery method. Specifically, we develop an algorithm to minimize the Kohn-Vogelius cost function,…
Dynamical properties of image restoration and hyper-parameter estimation are investigated by means of statistical mechanics. We introduce an exactly solvable model for image restoration and derive differential equations with respect to…
The versatility of quantum gas experiments greatly benefits from the ability to apply variable potentials. Here we describe a method which allows the preparation of potential structures for microcavity photons via spatially selective…
We propose a functional view of matrix decomposition problems on graphs such as geometric matrix completion and graph regularized dimensionality reduction. Our unifying framework is based on the key idea that using a reduced basis to…
We provide the integral representation formula for the relaxation in $BV(\Omega; \mathbb{R}^M)$ with respect to strong convergence in $L^1(\Omega; \mathbb{R}^M)$ of a functional with a boundary contact energy term. This characterization is…
We give necessary and sufficient conditions for minimality of generalized minimizers for linear-growth functionals of the form \[ \mathcal F[u] := \int_\Omega f(x,u(x)) \, \text{d}x, \qquad u:\Omega \subset \mathbb R^N\to \mathbb R^d, \]…
Stochastic approximation techniques have been used in various contexts in data science. We propose a stochastic version of the forward-backward algorithm for minimizing the sum of two convex functions, one of which is not necessarily…
Image restoration is the task of recovering a clean image from a degraded version. In most cases, the degradation is spatially varying, and it requires the restoration network to both localize and restore the affected regions. In this…
Coherent X-ray beams with energies $\geq 50$ keV can potentially enable three-dimensional imaging of atomic lattice distortion fields within individual crystallites in bulk polycrystalline materials through Bragg coherent diffraction…
This paper presents a new method of gray level image enhancement, based on point transforms. In order to define the transform function, it was used a generalization of the homographic function.
In this paper, we develop a dual alternating direction method of multipliers (ADMM) for an image decomposition model. In this model, an image is divided into two meaningful components, i.e., a cartoon part and a texture part. The…
Bilevel programs are optimization problems where some variables are solutions to optimization problems themselves, and they arise in a variety of control applications, including: control of vehicle traffic networks, inverse reinforcement…
We prove a homogenization theorem for a class of quadratic convolution energies with random coefficients. Under suitably stated hypotheses of ergodicity and stationarity we prove that the $\Gamma$-limit of such energy is almost surely a…
The core theme of X-ray crystallography is reconstructing the electron density distribution of crystals under the constraints of observed diffraction data. Nevertheless, the reconstruction of electron density distribution by straightforward…
This paper presents a novel approach for denoising binary images using simulated annealing (SA), a global optimization technique that addresses the inherent challenges of non convex energy functions. Binary images are often corrupted by…
In this paper, we present an inverse problem of identifying the reaction coefficient for time fractional diffusion equations in two dimensional spaces by using boundary Neumann data. It is proved that the forward operator is continuous with…
The minimization of a nonconvex composite function can model a variety of imaging tasks. A popular class of algorithms for solving such problems are majorization-minimization techniques which iteratively approximate the composite nonconvex…
Energy minimization methods are a classical tool in a multitude of computer vision applications. While they are interpretable and well-studied, their regularity assumptions are difficult to design by hand. Deep learning techniques on the…
We propose a first rigorous homogenisation procedure in image-segmentation models by analysing the relative impact of (possibly random) fine-scale oscillations and phase-field regularisations for a family of elliptic functionals of Ambrosio…
Phase retrieval consists in the recovery of a complex-valued signal from intensity-only measurements. As it pervades a broad variety of applications, many researchers have striven to develop phase-retrieval algorithms. Classical approaches…