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Nonuniform Fourier data are routinely collected in applications such as magnetic resonance imaging, synthetic aperture radar, and synthetic imaging in radio astronomy. To acquire a fast reconstruction that does not require an online inverse…
The Fast Fourier Transform (FFT) over a finite field $\mathbb{F}_q$ computes evaluations of a given polynomial of degree less than $n$ at a specifically chosen set of $n$ distinct evaluation points in $\mathbb{F}_q$. If $q$ or $q-1$ is a…
The graph Fourier transform (GFT) is an important tool for graph signal processing, with applications ranging from graph-based image processing to spectral clustering. However, unlike the discrete Fourier transform, the GFT typically does…
Fast convolution algorithms, including Winograd and FFT, can efficiently accelerate convolution operations in deep models. However, these algorithms depend on high-precision arithmetic to maintain inference accuracy, which conflicts with…
In image deconvolution problems, the diagonalization of the underlying operators by means of the FFT usually yields very large speedups. When there are incomplete observations (e.g., in the case of unknown boundaries), standard…
Electronic structure calculation of atoms and molecules, in the past few decades has largely been dominated by density functional methods. This is primarily due to the fact that this can account for electron correlation effects in a…
FPGAs provide a flexible and efficient platform to accelerate rapidly-changing algorithms for computer vision. The majority of existing work focuses on accelerating image classification, while other fundamental vision problems, including…
One of the most efficient ways to produce unconditional simulations is with the kernel convolution using fast Fourier transform (FFT) [1]. However, when data is located on a surface, this approach is not efficient because data needs to be…
Lifting is an efficient technique to scale up graphical models generalized to relational domains by exploiting the underlying symmetries. Concurrently, neural models are continuously expanding from grid-like tensor data into structured…
We introduce a new class of multilevel, adaptive, dual-space methods for computing fast convolutional transforms. These methods can be applied to a broad class of kernels, from the Green's functions for classical partial differential…
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…
Haptic-assisted virtual assembly and prototyping has seen significant attention over the past two decades. However, in spite of the appealing prospects, its adoption has been slower than expected. We identify the main roadblocks as the…
For smooth finite fields $F_q$ (i.e., when $q-1$ factors into small primes) the Fast Fourier Transform (FFT) leads to the fastest known algebraic algorithms for many basic polynomial operations, such as multiplication, division,…
In the analysis of High-Energy Physics data, it is frequently desired to separate resonant signals from a smooth, non-resonant background. This paper introduces a new technique - functional decomposition (FD) - to accomplish this task. It…
We propose a novel framework for fast integral operations by uncovering hidden geometries in the row and column structures of the underlying operators. This is accomplished through the \texttt{Questionnaire} algorithm, an iterative…
The notion of fractional Fourier transform (FrFT) has been used and investigated for many years by various research communities, which finds widespread applications in many diverse fields of research study. The potential applications…
We report on a new algorithm for detection of crystallographic information in 3D, as retained in Atom Probe Tomography (APT), with improved robustness and signal detection performance. The algorithm is underpinned by 1D distribution…
In this paper we consider the fundamental operations dilation and erosion of mathematical morphology. Many powerful image filtering operations are based on their combinations. We establish homomorphism between max-plus semi-ring of integers…
Object orientation provides a flexible framework for the implementation of the convolution of arbitrary distributions of real-valued random variables. We discuss an algorithm which is based on the discrete Fourier transformation (DFT) and…
Standard convolutions are prevalent in image processing and deep learning, but their fixed kernels limits adaptability. Several deformation strategies of the reference kernel grid have been proposed. Yet, they lack a unified theoretical…