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Modern data is customarily of multimodal nature, and analysis tasks typically require separation into the single components. Although a highly ill-posed problem, the morphological difference of these components sometimes allow a very…
The Fast Fourier Transform (FFT), as a core computation in a wide range of scientific applications, is increasingly threatened by reliability issues. In this paper, we introduce TurboFFT, a high-performance FFT implementation equipped with…
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…
Targeting simulations on parallel hardware architectures, this paper presents computational kernels for efficient computations in mortar finite element methods. Mortar methods enable a variationally consistent imposition of coupling…
Understanding how laser light scatters from realistic mirror surfaces is crucial for the design, com- missioning and operation of precision interferometers, such as the current and next generation of gravitational-wave detectors. Numerical…
Gaussian graphical models can capture complex dependency structures among variables. For such models, Bayesian inference is attractive as it provides principled ways to incorporate prior information and to quantify uncertainty through the…
We present the first q-Gaussian smoothed functional (SF) estimator of the Hessian and the first Newton-based stochastic optimization algorithm that estimates both the Hessian and the gradient of the objective function using q-Gaussian…
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,…
Graph Transformers (GTs) have shown advantages in numerous graph structure tasks but their self-attention mechanism ignores the generalization bias of graphs, with existing methods mainly compensating for this bias from aspects like…
Modern processors deliver higher throughput for lower-precision arithmetic than for higher-precision arithmetic. For matrix multiplication, the Ozaki scheme exploits this performance gap by splitting the inputs into lower-precision…
This research work focuses on the design of a high-resolution fast Fourier transform (FFT) /inverse fast Fourier transform (IFFT) processors for constraints analysis purpose. Amongst the major setbacks associated with such high resolution,…
The Radon transform and its adjoint, the back-projection operator, can both be expressed as convolutions in log-polar coordinates. Hence, fast algorithms for the application of the operators can be constructed by using FFT, if data is…
We present a general probabilistic perspective on Gaussian filtering and smoothing. This allows us to show that common approaches to Gaussian filtering/smoothing can be distinguished solely by their methods of computing/approximating the…
Wavefront reconstruction in lateral shearing interferometry typically assumes that the shear amount is an integer multiple of the sampling interval. When the shear is fractional, approximating it with the nearest integer value leads to…
This paper introduces a fast algorithm for simultaneous inversion and determinant computation of small sized matrices in the context of fully Polarimetric Synthetic Aperture Radar (PolSAR) image processing and analysis. The proposed fast…
The inverse of an invertible convolution is an important operation that comes up in Normalizing Flows, Image Deblurring, etc. The naive algorithm for backpropagation of this operation using Gaussian elimination has running time $O(n^3)$…
This paper presents a comprehensive exploration of Fast Fourier Transform (FFT) and linear convolution implementations, integrating both conventional methods and novel approaches leveraging the Bit Slicing Multiplier (BSM) technique. The…
Graph Signal Processing has become a very useful framework for signal operations and representations defined on irregular domains. Exploiting transformations that are defined on graph models can be highly beneficial when the graph encodes…
In the field of graph signal processing (GSP), directed graphs present a particular challenge for the "standard approaches" of GSP to due to their asymmetric nature. The presence of negative- or complex-weight directed edges, a graphical…
Wavelet decompositions of integral operators have proven their efficiency in reducing computing times for many problems, ranging from the simulation of waves or fluids to the resolution of inverse problems in imaging. Unfortunately,…