Related papers: Some comments on the inverse problem of pure point…
We consider a family of holomorphic PDEs whose singular locus is given by the zero set of an analytic map $P$ with $P(0)=0$. Our goal is to establish conditions for the existence and uniqueness of formal power series solutions and to…
Diffraction tomography is a noninvasive technique that estimates the refractive indices of unknown objects and involves an inverse-scattering problem governed by the wave equation. Recent works have shown the benefit of nonlinear models of…
Diffusion models have achieved remarkable success in imaging inverse problems owing to their powerful generative capabilities. However, existing approaches typically rely on models trained for specific degradation types, limiting their…
With the rapid development of diffusion models and flow-based generative models, there has been a surge of interests in solving noisy linear inverse problems, e.g., super-resolution, deblurring, denoising, colorization, etc, with generative…
We propose a method to reconstruct the optical properties of a scattering medium with subwavelength resolution. The method is based on the solution to the inverse scattering problem with photoactivated internal sources. Numerical…
We study inverse problems of reconstructing static and dynamic discrete structures from tomographic data (with a special focus on the `classical' task of reconstructing finite point sets in $\mathbb{R}^d$). The main emphasis is on recent…
The inversion of a diffraction pattern offers aberration-free diffraction-limited 3D images without the resolution and depth-of-field limitations of lens-based tomographic systems, the only limitation being radiation damage. We review our…
METATOYs can change the direction of light in ways that appear to, but do not actually, contravene the laws of wave optics. This direction change applies only to part of the transmitted light beam; the remainder gets re-directed…
We demonstrate new axisymmetric inverse-design techniques that can solve problems radically different from traditional lenses, including \emph{reconfigurable} lenses (that shift a multi-frequency focal spot in response to refractive-index…
We propose a new learning-based approach to solve ill-posed inverse problems in imaging. We address the case where ground truth training samples are rare and the problem is severely ill-posed - both because of the underlying physics and…
The inverse scattering problem from the multi-frequency backscattering data is a long-standing open problem. We advance the theory by proving a local uniqueness result. Moreover, we introduce a direct sampling method for quantitatively…
An example of full solution of the inverse scattering problem on the half line is presented. For this purpose, a simple analytically solvable model system (Morse potential) is used, which is expected to be a reasonable approximation to a…
We establish a result which states that regularizing an inverse problem with the gauge of a convex set $C$ yields solutions which are linear combinations of a few extreme points or elements of the extreme rays of $C$. These can be…
This work is concerned with the inverse source problem of locating multiple multipolar sources from boundary measurements for the Helmholtz equation. We develop simple and effective sampling schemes for location acquisition of the sources…
A new numerical method to solve an inverse source problem for the Helmholtz equation in inhomogenous media is proposed. This method reduces the original inverse problem to a boundary value problem for a coupled system of elliptic PDEs, in…
When considering fractional diffusion equation as model equation in analyzing anomalous diffusion processes, some important parameters in the model, for example, the orders of the fractional derivative or the source term, are often unknown,…
The Differential Fourier Holography (DFH) gives an exact mathematical solution of the inverse problem of diffraction in the Fraunhofer regime. After the first publication [1] the Differential Fourier Holography was successfully applied in…
Describing the solutions of inverse problems arising in signal or image processing is an important issue both for theoretical and numerical purposes. We propose a principle which describes the solutions to convex variational problems…
As a guiding example, the diffraction measure of a random local mixture of the two classic Fibonacci substitutions is determined and reanalysed via self-similar measures of Hutchinson type, defined by a finite family of contractions. Our…
Diffusion models are powerful tools for sampling from high-dimensional distributions by progressively transforming pure noise into structured data through a denoising process. When equipped with a guidance mechanism, these models can also…