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Modulo imaging enables high dynamic range (HDR) acquisition by cyclically wrapping saturated intensities, but accurate reconstruction remains challenging due to ambiguities between natural image edges and artificial wrap discontinuities.…
We define variable parameter analogues of the affine arclength measure on curves and prove near-optimal $L^p$-improving estimates for associated multilinear generalized Radon transforms. Some of our results are new even in the convolution…
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…
We revisit the spherical Radon transform, also called the Funk-Radon transform, viewing it as an axisymmetric convolution on the sphere. Viewing the spherical Radon transform in this manner leads to a straightforward derivation of its…
Modern tomography involves gathering projection data from multiple directions and feeding them into a software algorithm for tomographic reconstruction. We focus our study on image reconstruction from Radon data in the setting of…
This paper is devoted to the analysis of the angular resolution limit (ARL), an important performance measure in the directions-of-arrival estimation theory. The main fruit of our endeavor takes the form of an explicit, analytical…
The manuscript describes fast and scalable architectures and associated algorithms for computing convolutions and cross-correlations. The basic idea is to map 2D convolutions and cross-correlations to a collection of 1D convolutions and…
We introduce an improved mass formula for the nucleon and delta resonances and show how it emerges from AdS/QCD in a straightforward extension of the 'metric soft wall' gravity dual. The resulting spectrum depends on just one adjustable…
We consider discrete analogues of fractional Radon transforms involving integration over paraboloids defined by positive definite quadratic forms. We prove that such discrete operators extend to bounded operators from $\ell^p$ to $\ell^q$…
Low-dose Computed Tomography is a common issue in reality. Current reduction, sparse sampling and limited-view scanning can all cause it. Between them, limited-view CT is general in the industry due to inevitable mechanical and physical…
The aim of this research is to reconstruct the 3D X-ray refractive index gradient maps by the proposed vector Radon transform and its inverse, assuming that the small-angle deviation condition is met. Theoretical analyses show that the…
We obtain new inversion formulas for the Radon transform and the corresponding dual transform acting on affine Grassmann manifolds of planes in $R^n$. The consideration is performed in full generality on continuous functions and functions…
A common problem that arises in radar imaging systems, especially those mounted on mobile platforms, is antenna position ambiguity. Approaches to resolve this ambiguity and correct position errors are generally known as radar autofocus.…
Multivariate functions are typically governed by anisotropic features such as edges in images or shock fronts in solutions of transport-dominated equations. One major goal both for the purpose of compression as well as for an efficient…
We proposed a novel approach to coherent imaging of dynamic samples. The inter-frame similarity of the sample's local structures is found to be a powerful constraint in phasing a sequence of diffraction patterns. We devised a new image…
Forward modeling of wave scattering and radar imaging mechanisms is the key to information extraction from synthetic aperture radar (SAR) images. Like inverse graphics in optical domain, an inherently-integrated forward-inverse approach…
Deep convolutional networks have attracted great attention in image restoration and enhancement. Generally, restoration quality has been improved by building more and more convolutional block. However, these methods mostly learn a specific…
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…
The AdS/CFT correspondence between string theory in AdS space and conformal field theories in physical space-time leads to an analytic, semi-classical model for strongly-coupled QCD which has scale invariance and dimensional counting at…
A radar system emits probing signals and records the reflections. Estimating the relative angles, delays, and Doppler shifts from the received signals allows to determine the locations and velocities of objects. However, due to practical…