Related papers: Single-angle Radon samples based reconstruction of…
Contrary to the traditional pursuit of research on nonuniform sampling of bandlimited signals, the objective of the present paper is not to find sampling conditions that permit perfect reconstruction, but to perform the best possible signal…
In this paper we refer to the reconstruction formulas given in L.-E. Andersson's On the determination of a function from spherical averages, which are often used in applications such as SAR and SONAR. We demonstrate that the first one of…
Data acquisition in array signal processing (ASP) is costly because achieving high angular and range resolutions necessitates large antenna apertures and wide frequency bandwidths, respectively. The data requirements for ASP problems grow…
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…
Moment methods to reconstruct images from their Radon transforms are both natural and useful. They can be used to suppress noise or other spurious effects and can lead to highly efficient reconstructions from relatively few projections. We…
Recovering a function from its integrals over circular cones recently gained significance because of its relevance to novel medical imaging technologies such emission tomography using Compton cameras. In this paper we investigate the case…
Modern imaging and sensing in complex environments, ranging from biomedical diagnostics to wireless communication, relies on accurately measuring and then controlling the wave propagation. Conventional approaches demand large arrays of…
The one dimensional wave equation serves as a basic model for imaging modalities such as seismic which utilize acoustic data reflected back from a layered medium. In 1955 Peterson et al. described a single scattering approximation for the…
Computed Tomography (CT) is an imaging technique where information about an object are collected at different angles (called projections or scans). Then the cross-sectional image showing the internal structure of the slice is produced by…
This work introduces a novel and general class of continuous transforms based on hierarchical Voronoi based refinement schemes. The resulting transform space generalizes classical approaches such as wavelets and Radon transforms by…
The inverse Radon transform allows to obtain partonic double distributions from (extended) generalized parton distributions. We express the extension of generalized parton distributions by their dual parts, generalized distribution…
This paper investigates signle-antenna radar imaging with a reconfigurable intelligent surface (RIS). Configuring phase shifts in a RIS-aided radar system can be thought as synthetic aperture radar (SAR) imaging with a moving virtual…
The two-dimensional Radon transform of the Wigner quasiprobability is introduced in canonical form and the functions playing a role in its inversion are discussed. The transformation properties of this Radon transform with respect to…
In complex-valued coherent inverse problems such as synthetic aperture radar (SAR), one may often have prior information only on the magnitude image which shows the features of interest such as strength of reflectivity. In contrast, there…
The article suggests a new approach what is called a consistency method for the inversion of the spherical Radon transform in 2D with detectors on a line. It is known that there is not an exact inversion formula in 2D. By means of the…
We study a Radon-like transform that takes functions on the Grassmannian of $j$-dimensional affine planes in $\Bbb R ^n$ to functions on a similar manifold of $k$-dimensional planes by integration over the set of all $j$-planes that meet a…
The theory of sampling and the reconstruction of data has a wide range of applications and a rich collection of techniques. For many methods a core problem is the estimation of the number of samples needed in order to secure a stable and…
In this paper, we present new regularized Shannon sampling formulas related to the special affine Fourier transform (SAFT). These sampling formulas use localized sampling with special compactly supported window functions, namely B-spline,…
We consider the inverse problem of the reconstruction of the spatially distributed dielectric constant $\varepsilon_{r}\left(\mathbf{x}\right), \ \mathbf{x}\in \mathbb{R}^{3}$, which is an unknown coefficient in the Maxwell's equations,…
The generalized spherical Radon transform associates the mean values over spherical tori to a function $f$ defined on $\mathbb{S}^3 \subset \mathbb{H}$, where the elements of $\mathbb{S}^3$ are considered as quaternions representing…