Related papers: Direct Method for Calculating the Inverse Radon Tr…
There is rising interest in differentiable rendering, which allows explicitly modeling geometric priors and constraints in optimization pipelines using first-order methods such as backpropagation. Incorporating such domain knowledge can…
We provide a simple approach for the evaluation of inverse integral transforms that does not require any knowledge of complex analysis. The central idea behind the method is to reduce the inverse transform to the solution of an ordinary…
In this paper we present an algorithmic procedure that transforms, if possible, a given system of ordinary or partial differential equations with radical dependencies in the unknown function and its derivatives into a system with polynomial…
Modeling outdoor scenes for the synthetic 3D environment requires the recovery of reflectance/albedo information from raw images, which is an ill-posed problem due to the complicated unmodeled physics in this process (e.g., indirect…
This manuscript is designed to introduce students in applied mathematics and data science to the concept of regularization for ill-posed inverse problems. Construct a mathematical model that describes how an image gets blurred. Convert a…
The accuracy of reconstruction of a response function from its Lorentz integral transform is studied in an exactly solvable model. An inversion procedure is elaborated in detail and features of the procedure are studied. Unlike results in…
We introduce a new numerical method for the computation of the inverse nonlinear Fourier transform and compare its computational complexity and accuracy to those of other methods available in the literature. For a given accuracy, the…
Image reconstruction in Magnetic Resonance Imaging (MRI) is fundamentally a linear inverse problem, such that the image can be recovered via explicit pseudoinversion of the encoding matrix by solving $\textbf{data} = \textbf{Encode} \times…
In this paper, the photon stationary transport equation has been extended from $\mathbb{R}^3$ to $\mathbb{C}^3$. A solution of the inverse problem is obtained on a hyper-sphere and a hyper-cylinder as X-ray and Radon transform,…
Inverse rendering, the process of inferring scene properties from images, is a challenging inverse problem. The task is ill-posed, as many different scene configurations can give rise to the same image. Most existing solutions incorporate…
Recently, experiments have been reported where researchers were able to perform high dynamic range (HDR) tomography in a heuristic fashion, by fusing multiple tomographic projections. This approach to HDR tomography has been inspired by HDR…
Deep learning models have a large number of free parameters that must be estimated by efficient training of the models on a large number of training data samples to increase their generalization performance. In real-world applications, the…
Computer vision tasks require processing large amounts of data to perform image classification, segmentation, and feature extraction. Optical preprocessors can potentially reduce the number of floating point operations required by computer…
We propose a novel indicator function for reconstructing acoustic sources from multi-frequency near-field measurements. The theoretical basis is established by a formula relating the scattered field to the source function through the Radon…
We derive an original direct imaging method of an object. It is based on topological derivatives, and aims at inverting the amplitude of waves that are retropropagated after laser illuminations.
Hyperplane is a set of non-injectivity of the spherical Radon transform (SRT) in the space of continuous functions in R^d. In this article, for the reconstruction of an unknown function f from C(R^3) (the support can be non-compact), using…
English: This paper concerns the image reconstruction from a few projections in Computed Tomography (CT). The main objective of this paper is to show that the problem is so ill posed that no classical method, such as analytical methods…
Real algebraic geometry adapts the methods and ideas from (complex) algebraic geometry to study the real solutions to systems of polynomial equations and polynomial inequalities. As it is the real solutions to such systems modeling…
We obtain explicit inversion formulas for the Radon-like transform that assigns to a function on the unit sphere the integrals of that function over hemispheres lying in lower dimensional central cross-sections. The results are applied to…
The conical Radon transform is an integral transform that maps a given function $f$ to its integral over a conical surface. In this study, we invesgate the conical Radon transform with a fixed central axis and opening angle, considering the…