Related papers: 2D inverse problem with a Foliation Condition
The inverse problem of amplitude reconstruction on an inclined line based on the values of amplitude or its module as recorded on semi-infinite line orthogonal to the beam propagation direction is considered within the framework of 2D…
High resolution reconstruction of complicated objects from incomplete and noisy data can be achieved by solving modulation equations iteratively under physical constraints. This direct demodulation method is a powerful technique for dealing…
Inverse Problem techniques offer powerful tools which deal naturally with marginal data and asymmetric or strongly smoothing kernels, in cases where parameter-fitting methods may be used only with some caution. Although they are typically…
Reconstructing an object's shape and appearance in terms of a mesh textured by a spatially-varying bidirectional reflectance distribution function (SVBRDF) from a limited set of images captured under collocated light is an ill-posed…
In this work, a novel approach for the solution of the inverse conductivity problem from one and multiple boundary measurements has been developed on the basis of the implication of the framework of BV - functions. The space of the…
Reconstructing the unknown spectrum of a given X-ray source is a common problem in a wide range of X-ray imaging tasks. For high-energy sources, transmission measurements are mostly used to recover the X-ray spectrum, as a solution to an…
In this paper we discuss reconstruction problems for graphs. We develop some new ideas like isomorphic extension of isomorphic graphs, partitioning of vertex sets into sets of equivalent points, subdeck property, etc. and develop an…
We review and extend a technique for recovering a smooth function from its averages over a wide class of curves in a general region of Euclidean space. The method is based on complexification of the underlying vector fields defining the…
Decision trees and systems of decision rules are widely used as classifiers, as a means for knowledge representation, and as algorithms. They are among the most interpretable models for data analysis. The study of the relationships between…
Inverse problems are prevalent in numerous scientific and engineering disciplines, where the objective is to determine unknown parameters within a physical system using indirect measurements or observations. The inherent challenge lies in…
We consider Sturm-Liouville operators on geometrical graphs without cycles (trees) with singular potentials from the class $W_2^{-1}$. We suppose that the potentials are known on a part of the graph, and study the so-called partial inverse…
The paper considers the problem of performing a task defined on a model parameter that is only observed indirectly through noisy data in an ill-posed inverse problem. A key aspect is to formalize the steps of reconstruction and task as…
The so-called inverse problem of dynamics is about constructing a potential for a given family of curves. We observe that there is a more general way of posing the problem by making use of ideas of another inverse problem, namely the…
We present calculations that reconstruct electronic current densities in two stacked layers at known depths, using magnetic field data. Solving this inverse problem requires knowledge of the magnetic field in two planes -- one above both…
The magnetic inverse source problem of reconstructing the positions and currents of very long parallel conductors is considered in a two-dimensional situation, with applications to power line measurements. The input data is the magnetic…
Diffraction tomography aims to recover an object's scattering potential from measured wave fields. In the classical setting, the object is illuminated by plane waves from many directions, and the Fourier diffraction theorem provides a…
Many problems in Computer Vision can be reduced to either working around a known transform, or given a model for the transform computing the inverse problem of the transform itself. We will look at two ways of working with the matrix $A$…
This article handles in a short manner a few Laplace transform pairs and some extensions to the basic equations are developed. They can be applied to a wide variety of functions in order to find the Laplace transform or its inverse when…
We reduce the broken ray transform on some Riemannian manifolds (with corners) to the geodesic ray transform on another manifold, which is obtained from the original one by reflection. We give examples of this idea and present injectivity…
Inspired by the seminal result that a graph and an associated rotation system uniquely determine the topology of a closed manifold, we propose a combinatorial method for reconstruction of surfaces from points. Our method constructs a…