Related papers: A Unified Framework for Oscillatory Integral Trans…
The one-dimensional (1D) fractional Fourier transform (FRFT) generalizes the Fourier transform, offering significant advantages in the time-frequency analysis of non-stationary signals. While various 2D extensions exist, such as the 2D…
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…
The Fast Fourier Transform (FFT) is the most efficiently known way to compute the Discrete Fourier Transform (DFT) of an arbitrary n-length signal, and has a computational complexity of O(n log n). If the DFT X of the signal x has only k…
Integral Field Spectrographs (IFS) often require non-trivial calibration techniques to process raw data. The OH Suppressing InfraRed Imaging Spectrograph (OSIRIS) at the W. M. Keck Observatory is a lenslet-based IFS that requires precise…
Neutrino oscillations are at the forefront of advances in Physics beyond the Standard Model. Increasing accuracy in measurements of the neutrino mixing matrix is an important challenge in current experiments. It depends on parameters that…
We present a fast algorithm for computing the diffracted field from arbitrary binary (sharp-edged) planar apertures and occulters in the scalar Fresnel approximation, for up to moderately high Fresnel numbers ($\lesssim 10^3$). It uses a…
Matrix factorization is a popular framework for modeling low-rank data matrices. Motivated by manifold learning problems, this paper proposes a quadratic matrix factorization (QMF) framework to learn the curved manifold on which the dataset…
We present an architecture-algorithm co-design study of the Optimistic Quantum Fourier Transform (OQFT) under a surface-code fault-tolerant execution model for reconfigurable neutral-atom hardware. Analyzing the OQFT structure, particularly…
A butterfly-accelerated volume integral equation (VIE) solver is proposed for fast and accurate electromagnetic (EM) analysis of scattering from heterogeneous objects. The proposed solver leverages the hierarchical off-diagonal butterfly…
The Quantum Fourier Transformation (QFT) is a well-known subroutine for algorithms on qubit-based universal quantum computers. In this work, the known QFT circuit is used to derive an efficient circuit for the multidimensional QFT. The…
The achievable data rates of current fiber-optic wavelength-division-multiplexing (WDM) systems are limited by nonlinear interactions between different subchannels. Recently, it was thus proposed to replace the conventional Fourier…
Symmetric nonnegative matrix factorization has found abundant applications in various domains by providing a symmetric low-rank decomposition of nonnegative matrices. In this paper we propose a Frank-Wolfe (FW) solver to optimize the…
With the increasing demand for multi-carrier communication in high-mobility scenarios, it is urgent to design new multi-carrier communication waveforms that can resist large delay-Doppler spreads. Various multi-carrier waveforms in the…
Recent neural networks (NNs) with self-attention exhibit competitiveness across different AI domains, but the essential attention mechanism brings massive computation and memory demands. To this end, various sparsity patterns are introduced…
We present a unified algorithmic framework for quantum simulation of non-unitary dynamics and matrix functions, governed by the principle of spectral aliasing derived from the Poisson Summation Formula (PSF). By reinterpreting…
The fast Fourier transform (FFT) is one of the most successful numerical algorithms of the 20th century and has found numerous applications in many branches of computational science and engineering. The FFT algorithm can be derived from a…
Computing Fourier transforms of k-sparse signals, where only k of N frequencies are non-zero, is fundamental in compressed sensing, radar, and medical imaging. While the Fast Fourier Transform (FFT) evaluates all N frequencies in $O(N \log…
Two-dimensional Fourier transform plays a significant role in a variety of image processing problems, such as medical image processing, digital holography, correlation pattern recognition, hybrid digital optical processing, optical…
The Quantum Fisher Information matrix (QFIM) is a central metric in promising algorithms, such as Quantum Natural Gradient Descent and Variational Quantum Imaginary Time Evolution. Computing the full QFIM for a model with $d$ parameters,…
Many state-of-the-art signal decomposition techniques rely on a low-rank factorization of a time-frequency (t-f) transform. In particular, nonnegative matrix factorization (NMF) of the spectrogram has been considered in many audio…