Related papers: Fast algorithms and efficient GPU implementations …
The cylindrical Taylor Interpolation through FFT (TI-FFT) algorithm for computation of the near-field and far-field in the quasi-cylindrical geometry has been introduced. The modal expansion coefficient of the vector potentials ${\bf F}$…
W projection is a commonly-used approach to allow interferometric imaging to be accelerated by Fast Fourier Transforms (FFTs), but it can require a huge amount of storage for convolution kernels. The kernels are not separable, but we show…
Sparse-view Computed Tomography (CT) reconstructs images from a limited number of X-ray projections to reduce radiation and scanning time, which makes reconstruction an ill-posed inverse problem. Deep learning methods achieve high-fidelity…
Here we present a new non-parametric approach to density estimation and classification derived from theory in Radon transforms and image reconstruction. We start by constructing a "forward problem" in which the unknown density is mapped to…
Convolutional gridding is a processor-intensive step in interferometric imaging. While it is possible to use graphics processing units (GPUs) to accelerate this operation, existing methods use only a fraction of the available flops. We…
Image moments are weighted sums over pixel values in a given image and are used in object detection and localization. Raw image moments are derived directly from the image and are fundamental in deriving moment invariants quantities. The…
We use Deep Operator Networks (DeepONets) to perform super-resolution reconstruction of the solutions of two types of partial differential equations and compare the model predictions with the results obtained using conventional…
Zernike moments can be used to generate invariant features that are applied in various machine vision applications. They, however, suffer from slow implementation and numerical stability problems. We propose a novel method for computing…
Fast Fourier transform algorithms are an arsenal of effective tools for solving various problems of analysis and high-speed processing of signals of various natures. Almost all of these algorithms are designed to process sequences of…
This paper introduces the `Projectron' as a new neural network architecture that uses Radon projections to both classify and represent medical images. The motivation is to build shallow networks which are more interpretable in the medical…
Since the Radon transform (RT) consists in a line integral function, some modeling assumptions are made on Computed Tomography (CT) system, making image reconstruction analytical methods, such as Filtered Backprojection (FBP), sensitive to…
Winograd-based convolution has quickly gained traction as a preferred approach to implement convolutional neural networks (ConvNet) on various hardware platforms because it requires fewer floating point operations than FFT-based or direct…
Stencil computations are widely used to simulate the change of state of physical systems across a multidimensional grid over multiple timesteps. The state-of-the-art techniques in this area fall into three groups: cache-aware tiled looping…
We investigate efficient algorithmic realisations for robust deconvolution of grey-value images with known space-invariant point-spread function, with emphasis on 1D motion blur scenarios. The goal is to make deconvolution suitable as…
Neutron Computed Tomography (CT) is an increasingly utilised non-destructive analysis tool in material science, palaeontology, and cultural heritage. With the development of new neutron imaging facilities (such as DINGO, ANSTO, Australia)…
This paper presents a novel mathematical framework for understanding pixel-driven approaches for the parallel beam Radon transform as well as for the fanbeam transform, showing that with the correct discretization strategy, convergence -…
We propose a stable and fast reconstruction technique for parallel-beam (PB) tomographic X-ray imaging, relying on the discrete pseudo-polar (PP) Radon transform. Our main contribution is a resampling method, based on modern sampling…
In his article "Powerlist: A Structure for Parallel Recursion" Jayadev Misra wrote: "Many data parallel algorithms - Fast Fourier Transform, Batcher's sorting schemes and prefix sum - exhibit recursive structure. We propose a data…
We propose a programming technology that bridges cross-platform compatibility and hardware acceleration in ray tracing applications. Our methodology enables developers to define algorithms while our translator manages implementation…
In this article, we present an $O(N \log N)$ rapidly convergent algorithm for the numerical approximation of the convolution integral with radially symmetric weakly singular kernels and compactly supported densities. To achieve the reduced…