Related papers: A series solution and a fast algorithm for the inv…
In this paper the generalized Radon transform over level hypersurfaces of CES-functions of measures supported in positive orthant is studied. A characterization of the generalized Radon transform of nonnegative measures is found. Explicit…
A method of approximating the inverse Radon transform on the plane by integrating against a smooth kernel is investigated. For piecewise smooth integrable functions, convergence theorems are proven and Gibbs phenomena are ruled out.…
We propose a novel direct sampling method (DSM) for the effective and stable inversion of the Radon transform. The DSM is based on a generalization of the important almost orthogonality property in classical DSMs to fractional order Sobolev…
The Radon transform is a linear integral transform that mimics the data formation process in medical imaging modalities like X-ray Computerized Tomography and Positron Emission Tomography. The Hough transform is a pattern recognition…
Geometric moments and moment invariants of image artifacts have many uses in computer vision applications, e.g. shape classification or object position and orientation. Higher order moments are of interest to provide additional feature…
Higher spatial resolution and larger imaging scene are always the goals pursued by advanced space-borne SAR system.High resolution and wide swath SAR imaging can provide more information about the illuminated scene of interest on one…
The article presents an efficient image reconstruction algorithm for single scattering optical tomography (SSOT) in circular geometry of data acquisition. This novel medical imaging modality uses photons of light that scatter once in the…
Expensive computation of the conventional sparse Radon transform limits its use for effective transformation of 3D anisotropic seismic data cubes. We introduce a fast algorithm for azimuthally anisotropic 3D Radon transform with sparsity…
In tomographic reconstruction, the goal is to reconstruct an unknown object from a collection of line integrals. Given a complete sampling of such line integrals for various angles and directions, explicit inverse formulas exist to…
Tomography can be used to reveal internal properties of a 3D object using any penetrating wave. Advanced tomographic imaging techniques, however, are vulnerable to both systematic and random errors associated with the experimental…
Waveform inversion is theoretically a powerful tool to reconstruct subsurface structures, but a usually encountered problem is that accurate sources are very rare, causing the computation unstable and divergent. This challenging problem,…
We develop an algorithm capable of imaging a three-dimensional object given a collection of two-dimensional images of that object that are significantly influenced by the curvature of the Ewald sphere. These two-dimensional images cannot be…
Frequency-domain electromagnetic instruments allow the collection of data in different configurations, that is, varying the intercoil spacing, the frequency, and the height above the ground. Their handy size makes these tools very practical…
We develop a new numerical scheme for solving the radiative transfer equation in a spherically symmetric system. This scheme does not rely on any kind of diffusion approximation and it is accurate for optically thin, thick, and intermediate…
The transform considered in the paper integrates a function supported in the unit disk on the plane over all circles centered at the boundary of this disk. Such circular Radon transform arises in several contemporary imaging techniques, as…
A fast and accurate algorithm is presented for registering scans from an RGB-D camera on a pan-tilt platform. The pan-tilt RGB-D camera rotates and scans the entire scene in an automated fashion. The proposed algorithm exploits the movement…
Here we present a new non-parametric approach to density estimation and classification derived from theory in Radon transforms and image reconstruction. We start by constructing a "forward problem" in which the unknown density is mapped to…
In this paper we deal with the problem of recovering functions from their spherical mean transform $\mathcal{R}$, which integrates functions on circles in the plane, in case where the centers of the circles of integration are located on a…
We consider the imaging problem of the reconstruction of a three-dimensional object via optical diffraction tomography under the assumptions of the Born approximation. Our focus lies in the situation that a rigid object performs an…
A new algorithm for reconstructing a two dimensional object from a set of one dimensional projected views is presented that is both computationally exact and experimentally practical. The algorithm has a computational complexity of O(n log2…