Search results for "Radon transform."
showing 10 items of 23 documents
Monte Carlo evaluation of the Filtered Back Projection method for image reconstruction in proton computed tomography
2011
Abstract In this paper the use of the Filtered Back Projection (FBP) Algorithm, in order to reconstruct tomographic images using the high energy (200–250 MeV) proton beams, is investigated. The algorithm has been studied in detail with a Monte Carlo approach and image quality has been analysed and compared with the total absorbed dose. A proton Computed Tomography (pCT) apparatus, developed by our group, has been fully simulated to exploit the power of the Geant4 Monte Carlo toolkit. From the simulation of the apparatus, a set of tomographic images of a test phantom has been reconstructed using the FBP at different absorbed dose values. The images have been evaluated in terms of homogeneity…
Torus computed tomography
2020
We present a new computed tomography (CT) method for inverting the Radon transform in 2D. The idea relies on the geometry of the flat torus, hence we call the new method Torus CT. We prove new inversion formulas for integrable functions, solve a minimization problem associated to Tikhonov regularization in Sobolev spaces and prove that the solution operator provides an admissible regularization strategy with a quantitative stability estimate. This regularization is a simple post-processing low-pass filter for the Fourier series of a phantom. We also study the adjoint and the normal operator of the X-ray transform on the flat torus. The X-ray transform is unitary on the flat torus. We have i…
Uniform estimates for the X-ray transform restricted to polynomial curves
2012
We establish near-optimal mixed-norm estimates for the X-ray transform restricted to polynomial curves with a weight that is a power of the affine arclength. The bounds that we establish depend only on the spatial dimension and the degree of the polynomial. Some of our results are new even in the well-curved case.
Unique continuation property and Poincar�� inequality for higher order fractional Laplacians with applications in inverse problems
2020
We prove a unique continuation property for the fractional Laplacian $(-\Delta)^s$ when $s \in (-n/2,\infty)\setminus \mathbb{Z}$. In addition, we study Poincar\'e-type inequalities for the operator $(-\Delta)^s$ when $s\geq 0$. We apply the results to show that one can uniquely recover, up to a gauge, electric and magnetic potentials from the Dirichlet-to-Neumann map associated to the higher order fractional magnetic Schr\"odinger equation. We also study the higher order fractional Schr\"odinger equation with singular electric potential. In both cases, we obtain a Runge approximation property for the equation. Furthermore, we prove a uniqueness result for a partial data problem of the $d$-…
A new proof of the support theorem and the range characterization for the Radon transform
1983
The aim of this note is to give a new and elementary proof of the support theorem for the Radon transform, which is based only on the projection theorem and the Paley-Wiener theorem for the Fourier transform. The idea is to solve a certain system of linear equations in order to determine the coefficients of a homogeneous polynomial (interpolation problem). By the same method, we get a short proof of the range characterization for Radon transforms of functions supported in a ball.
Fourier analysis of periodic Radon transforms
2019
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 solve the associated Tikhonov minimization problem on $H^s$ Sobolev spaces using the properties of the adjoint and normal operators. One of the inversion formulas implies that a compactly supported distribution on the plane with zero average is a weighted sum of its X-ray data.
Gaussian surface measures and the radon transform on separable banach spaces
1980
EFFICIENT MACHINE LEARNING FRAMEWORK FOR COMPUTER-AIDED DETECTION OF CEREBRAL MICROBLEEDS USING THE RADON TRANSFORM
2014
International audience; Recent developments of susceptibility weighted MR techniques have improved visualization of venous vasculature and underlying pathologies such as cerebral microbleed (CMB). CMBs are small round hypointense lesions on MRI images that are emerging as a potential biomarker for cerebrovascular disease. CMB manual rating has limited reliability, is time-consuming and is prone to errors as small CMBs can be easily missed or mistaken for venous crosssections. This paper presents a computer-aided detection technique that utilizes a novel cascade of random forest classifiers which are trained on robust Radon-based features with an unbalanced sample distribution. The training …
Microaneurysm detection with radon transform-based classification on retina images.
2012
The creation of an automatic diabetic retinopathy screening system using retina cameras is currently receiving considerable interest in the medical imaging community. The detection of microaneurysms is a key element in this effort. In this work, we propose a new microaneurysms segmentation technique based on a novel application of the radon transform, which is able to identify these lesions without any previous knowledge of the retina morphological features and with minimal image preprocessing. The algorithm has been evaluated on the Retinopathy Online Challenge public dataset, and its performance compares with the best current techniques. The performance is particularly good at low false p…