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The computer-aided diagnosis (CAD) system can provide a reference basis for the clinical diagnosis of skin diseases. Convolutional neural networks (CNNs) can not only extract visual elements such as colors and shapes but also semantic…
Compton scatter tomography is an emerging technique with attractive applications in several fields in imaging such as non-destructive testing and medical scanning. In this paper, we introduce a novel modality in three dimensions with a…
In computed tomography (CT), the forward model consists of a linear Radon transform followed by an exponential nonlinearity based on the attenuation of light according to the Beer-Lambert Law. Conventional reconstruction often involves…
In this paper, we investigate the relations between the Radon and weighted divergent beam and cone transforms. Novel inversion formulas are derived for the latter two. The weighted cone transform arises, for instance, in image…
A fast implementation of the OPED algorithm, a reconstruction algorithm for Radon data introduced recently, is proposed and tested. The new implementation uses FFT for discrete sine transform and an interpolation step. The convergence of…
A new multiplication-free transform derived from DHT is introduced: the RHT. Investigations on the properties of the RHT led us to the concept of weak-inversion. Using new constructs, we show that RHT is not involutional like the DHT, but…
Tomography deals with the reconstruction of objects from their projections, acquired along a range of angles. Discrete tomography is concerned with objects that consist of a small number of materials, which makes it possible to compute…
Most existing learning-based methods for solving imaging inverse problems can be roughly divided into two classes: iterative algorithms, such as plug-and-play and diffusion methods leveraging pretrained denoisers, and unrolled architectures…
The limited angle Radon transform is notoriously difficult to invert due to its ill-posedness. In this work, we give a mathematical explanation that data-driven approaches can stably reconstruct more information compared to traditional…
We derive an explicit inversion algorithm for the spherical Radon transform in odd dimensions with partial radial data. We prove that the reconstruction of the unknown function can be reduced to solving ordinary differential equations,…
Deformable image registration is a standard engineering problem used to determine the distortion experienced by a body by comparing two images of it in different states. This study introduces two new DIR methods designed to capture…
We consider the generalized Radon transform (defined in terms of smooth weight functions) on hyperplanes in $\mathbb{R}^n$. We analyze general filtered backprojection type reconstruction methods for limited data with filters given by…
This work is concerned with the recovery of piecewise constant images from noisy linear measurements. We study the noise robustness of a variational reconstruction method, which is based on total (gradient) variation regularization. We show…
Direct reconstruction through filtered back projection engenders metal artifacts in polychromatic computed tomography images, attributed to highly attenuating implants, which further poses great challenges for subsequent image analysis.…
We introduce and study a new Radon-like transform that averages projected differential p-forms in R^n over affine (n-k)-planes. We then prove an explicit inversion formula for our transform on the space of rapidly-decaying smooth p-forms.…
In this article we present a review of the Radon transform and the instability of the tomographic reconstruction process. We show some new mathematical results in tomography obtained by a variational formulation of the reconstruction…
Many interesting tasks in image restoration can be cast as linear inverse problems. A recent family of approaches for solving these problems uses stochastic algorithms that sample from the posterior distribution of natural images given the…
Inversion of Radon transforms is the mathematical foundation of many modern tomographic imaging modalities. In this paper we study a conical Radon transform, which is important for computed tomography taking Compton scattering into account.…
The Discrete Fourier Transform (DFT) underpins the solution to many inverse problems commonly possessing missing or un-measured frequency information. This incomplete coverage of Fourier space always produces systematic artefacts called…
Low dose CT is of great interest in these days. Dose reduction raises noise level in projections and decrease image quality in reconstructions. Model based image reconstruction can combine statistical noise model together with prior…