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Two algorithms are introduced for the computation of discrete integral transforms with a multiscale approach operating in discrete three-dimensional (3D) volumes while considering its real-time implementation. The first algorithm, referred…
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…
Diffuse Optical Tomography (DOT) is an emerging technology in medical imaging which employs light in the NIR spectrum to estimate the distribution of optical coefficients in biological tissues for diagnostic and monitoring purposes. DOT…
Electrical Impedance Tomography (EIT) is a non-invasive imaging technique that reconstructs conductivity distributions within a body from boundary measurements. However, EIT reconstruction is hindered by its ill-posed nonlinear inverse…
Reconstructing an image from its Radon transform is a fundamental computed tomography (CT) task arising in applications such as X-ray scans. In many practical scenarios, a full 180-degree scan is not feasible, or there is a desire to reduce…
We study the interpolation capabilities of implicit neural representations (INRs) of images. In principle, INRs promise a number of advantages, such as continuous derivatives and arbitrary sampling, being freed from the restrictions of a…
Let $\mathcal R$ denote the generalized Radon transform (GRT), which integrates over a family of $N$-dimensional smooth submanifolds $\mathcal S_{\tilde y}\subset\mathcal U$, $1\le N\le n-1$, where an open set $\mathcal U\subset\mathbb R^n$…
Recently, generative diffusion priors have made huge strides as inverse problem solvers, including the ability to be adapted for inference on out-of-distribution data. Concurrently, implicit neural representations (INRs) have emerged as…
The Discrete Periodic Radon Transform (DPRT) has been extensively used in applications that involve image reconstructions from projections. This manuscript introduces a fast and scalable approach for computing the forward and inverse DPRT…
Medical imaging is nowadays a pillar in diagnostics and therapeutic follow-up. Current research tries to integrate established - but ionizing - tomographic techniques with technologies offering reduced radiation exposure. Diffuse Optical…
3D volumetric reconstruction from incomplete or noisy measurements is a fundamental problem in medical imaging and computational tomography. Deep image prior (DIP)-based methods have recently shown strong capability for solving inverse…
Accurately estimating the probability of failure in engineering systems under uncertainty is a fundamental challenge, particularly in high-dimensional settings and for rare events. Conventional reliability analysis methods often become…
Inspired by the multiple-exposure fusion approach in computational photography, recently, several practitioners have explored the idea of high dynamic range (HDR) X-ray imaging and tomography. While establishing promising results, these…
Direct collocation is a widely used method for solving dynamic optimization problems (DOPs), but its implementation simplicity and computational efficiency are limited for challenging problems like those involving singular arcs. In this…
We find a new and simple inversion formula of the Radon transform RT with the only use of the shearlet system and of well-known properties of RT. No intertwining relation of differential operators in Euclidean space and Radon domain is…
Purpose: Neural network image reconstruction directly from measurement data is a relatively new field of research, that until now has been limited to producing small single-slice images (e.g., 1x128x128). This paper proposes a novel and…
Diffuse optical tomography (DOT) has been investigated as an alternative imaging modality for breast cancer detection thanks to its excellent contrast to hemoglobin oxidization level. However, due to the complicated non-linear photon…
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…
In this work, we investigate the diffusive optical tomography (DOT) problem in the case that limited boundary measurements are available. Motivated by the direct sampling method (DSM), we develop a deep direct sampling method (DDSM) to…
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…