Related papers: Revisit to the Inverse Exponential Radon Transform
The relation between Radon transform and orthogonal expansions of a function on the unit ball in $\RR^d$ is exploited. A compact formula for the partial sums of the expansion is given in terms of the Radon transform, which leads to…
Generalized Abel equations have been employed in the recent literature to invert Radon transforms which arise in a number of important imaging applications, including Compton Scatter Tomography (CST), Ultrasound Reflection Tomography (URT),…
We study the influence of analytical regularization used in the generalized function (distribution) space to the Tikhonov regularization procedure utilized in the different versions of Moore-Penrose's inversion. By introducing a new…
Compressed sensing allows for the recovery of sparse signals from few measurements, whose number is proportional to the sparsity of the unknown signal, up to logarithmic factors. The classical theory typically considers either random linear…
We give an exact inversion formula for the approximate discrete Radon transform introduced in [Brady, SIAM J. Comput., 27(1), 107--119] that is of cost $O(N \log N)$ for a square 2D image with $N$ pixels and requires only partial data.
For the reconstruction problem, the universal representation of inverse Radon transforms implies the needed complexity of the direct Radon transforms which leads to the additional contributions. In the standard theory of generalized…
The light field reconstruction from the focal stack can be mathematically formulated as an ill-posed integral equation inversion problem. Although the previous research about this problem has made progress both in practice and theory, its…
Electrical Impedance Tomography (EIT) is a powerful imaging modality widely used in medical diagnostics, industrial monitoring, and environmental studies. The EIT inverse problem is about inferring the internal conductivity distribution of…
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…
The approximate discrete Radon transform (ADRT) is a hierarchical multiscale approximation of the Radon transform. In this paper, we factor the ADRT into a product of linear transforms that resemble convolutions and derive an explicit…
The subject of this thesis is in the area of Applied Mathematics known as Inverse Problems. Inverse problems are those where a set of measured data is analysed in order to get as much information as possible on a model which is assumed to…
A method for photoacoustic tomography is presented that uses circular integrals of the acoustic wave for the reconstruction of a three-dimensional image. Image reconstruction is a two-step process: In the first step data from a stack of…
The Lorentz Integral Transform approach allows microscopic calculations of electromagnetic reaction cross sections without explicit knowledge of final state wave functions. The necessary inversion of the transform has to be treated with…
Promoted by the advent of coherent synchrotron light sources, phase contrast tomography allows to resolve three-dimensional variations of an unknown sample's complex refractive index from scattering intensities recorded at different…
In this paper, we deal with the problem of reconstruction from Radon random samples in local shift-invariant signal space. Different from sampling after Radon transform, we consider sampling before Radon transform, where the sample set is…
Electron tomography is becoming an increasingly important tool in materials science for studying the three-dimensional morphologies and chemical compositions of nanostructures. The image quality obtained by many current algorithms is…
The monograph contains a systematic treatment of a circle of problems in analysis and integral geometry related to inversion of the Radon transform on the space of real rectangular matrices. This transform assigns to a function $f$ on the…
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…
Proton radiography is a technique extensively used to resolve magnetic field structures in high energy density plasmas, revealing a whole variety of interesting phenomena such as magnetic reconnection and collisionless shocks found in…
Radon transform is a type of transform which is used in image processing to transfer the image into intercept-slope coordinate. Its diagonal properties made it appropriate for some applications which need processes in different degrees.…