Related papers: A Radon-transform-based formula for reconstructing…
Sound propagation in the ocean is considered. We demonstrate a novel algorithm for full wavefield reconstruction using pointwise measurements by means of a vertical array. The algorithm is based on the so-called discrete variable…
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…
We consider the inverse problem of reconstructing the scattering coefficient of a simple radiative transport equation (RTE) used to model light propagation inside a scattering medium. To do so, we extract information from the second term in…
Narrow optical resonances of atoms or molecules have immense significance in various precision measurements, such as testing fundamental physics and the generation of primary frequency standards. In these studies, accurate transition…
Light emitters or scatterers embedded in stratified media may couple energy to both free space modes and guided modes of the stratified structure. For a comprehensive analysis, it is important to evaluate the angular intensity distribution…
We consider an inverse acoustic scattering problem in simultaneously recovering an embedded obstacle and its surrounding inhomogeneous medium by formally determined far-field data. It is shown that the knowledge of the scattering amplitude…
Invertible image representation methods (transforms) are routinely employed as low-level image processing operations based on which feature extraction and recognition algorithms are developed. Most transforms in current use (e.g. Fourier,…
Autonomous robot networks are an effective tool for monitoring large-scale environmental fields. This paper proposes distributed control strategies for localizing the source of a noisy signal, which could represent a physical quantity of…
We are going to study some conditions on which the Radon transform and its dual are invertible. Two function spaces are introduced that the Radon transform on which is bijective linear operator. In this regards, a reconstruction formula is…
The circular Radon transform integrates a function over the set of all spheres with a given set of centers. The problem of injectivity of this transform (as well as inversion formulas, range descriptions, etc.) arises in many fields from…
We study the inversion of the conical Radon which integrates a function in three-dimensional space from integrals over circular cones. The conical Radon recently got significant attention due to its relevance in various imaging applications…
In an ultrasonic array system, increasing the aperture size to achieve a high resolution requires more transmit and receive channels, thus making it essential to have an analysis technique that can reconstruct the shape and physical…
We present an optical wavefront shaping approach that allows tracking and localization of signal hidden inside or behind a scattering medium. The method combines traditional feedback based wavefront shaping together with a switch function,…
In this article we present a review of the Radon transform and the instability of the tomographic reconstruction process. We show some new mathematical results in tomography obtained by a variational formulation of the reconstruction…
We present a strategy for the recovery of a sparse solution of a common problem in acoustic engineering, which is the reconstruction of sound source levels and locations applying microphone array measurements. The considered task bears…
Due to manufacturing defects or wear and tear, industrial components may have uncertainties. In order to evaluate the performance of machined components, it is crucial to quantify the uncertainty of the scattering surface. This brings up an…
We study reconstruction of an unknown function from its $d$-plane Radon transform on the flat $n$-torus when $1 \leq d \leq n-1$. We prove new reconstruction formulas and stability results with respect to weighted Bessel potential norms. We…
Source enumeration, the task of estimating the number of sources from the signal received by the array of antennas, is a critical problem in array signal processing. Numerous methods have been proposed to estimate the number of sources…
The quadratic scalar radar equations are obtained for SuperDARN radars that are suitable for the analysis and interpretation of experimental data. The paper is based on a unified approach to the obtaining radar equations for the monostatic…
The present paper develops recursive algorithms to track shifts in the resonance frequency of linear systems in real time. To date, automatic resonance tracking has been limited to non-model-based approaches, which rely solely on the phase…