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Low-light image enhancement is a classical computer vision problem aiming to recover normal-exposure images from low-light images. However, convolutional neural networks commonly used in this field are good at sampling low-frequency local…
A joint frame and carrier frequency synchronization algorithm for coherent optical systems, based on the digital computation of the fractional Fourier transform (FRFT), is proposed. The algorithm utilizes the characteristics of energy…
The algorithm behind the Fast Fourier Transform has a simple yet beautiful geometric interpretation that is often lost in translation in a classroom. This article provides a visual perspective which aims to capture the essence of it.
Fourier transforms are ubiquitous mathematical tools in basic and applied sciences. We here report classical and quantum optical realizations of the discrete fractional Fourier transform, a generalization of the Fourier transform. In the…
Density functional theory (DFT) provides a theoretical framework for efficient and fairly accurate calculations of the electronic structure of molecules and crystals. The main features of density functional theory are described and DFT…
The usage of linear transformations has great relevance for data decorrelation applications, like image and video compression. In that sense, the discrete Tchebichef transform (DTT) possesses useful coding and decorrelation properties. The…
The Quantum Fourier Transform (QFT) is a fundamental component of many quantum computing algorithms. In this paper, we present an alternative method for factoring this transformation. Inspired by this approach, we introduce a new quantum…
Quantum Fourier transform (QFT) is a key function to realize quantum computers. A QFT followed by measurement was demonstrated on a simple circuit based on fiber-optics. The QFT was shown to be robust against imperfections in the rotation…
Optoacoustic imaging technologies require fast and accurate signal pre-processing algorithms to enable widespread deployment in clinical and home-care settings. However, they still rely on the Discrete Fourier Transform (DFT) as the default…
In this paper, we study the impact of computational complexity on the throughput limits of the {\color{black}fast Fourier transform (FFT)} algorithm for {\color{black}orthogonal frequency division multiplexing(OFDM)} waveforms. Based on the…
In this paper we consider the problem of constructing graph Fourier transforms (GFTs) for directed graphs (digraphs), with a focus on developing multiple GFT designs that can capture different types of variation over the digraph…
This tutorial aims to establish connections between polynomial modular multiplication over a ring to circular convolution and discrete Fourier transform (DFT). The main goal is to extend the well-known theory of DFT in signal processing…
Aggregation of multi-stage features has been revealed to play a significant role in semantic segmentation. Unlike previous methods employing point-wise summation or concatenation for feature aggregation, this study proposes the Category…
Image computation is a fundamental tool for performance assessment of astronomical instrumentation, usually implemented by Fourier transform techniques. We review the numerical implementation, evaluating a direct implementation of the…
Approximate methods have been considered as a means to the evaluation of discrete transforms. In this work, we propose and analyze a class of integer transforms for the discrete Fourier, Hartley, and cosine transforms (DFT, DHT, and DCT),…
This paper details the purpose, difficulties, theory, implementation, and results of developing a Fast Fourier Transform (FFT) using the prime factor algorithm on an embedded system. Many applications analyze the frequency content of…
In this research paper, our primary focus revolves around the domain-specific hardware mapping strategy tailored for Quantum Fourier Transformation (QFT) circuits. While previous approaches have heavily relied on SAT solvers or heuristic…
Vision transformers have been successfully applied to image recognition tasks due to their ability to capture long-range dependencies within an image. However, there are still gaps in both performance and computational cost between…
For any finite group $G$, we give an arithmetic algorithm to compute generalized Discrete Fourier Transforms (DFTs) with respect to $G$, using $O(|G|^{\omega/2 + \epsilon})$ operations, for any $\epsilon > 0$. Here, $\omega$ is the exponent…
We first review the convolution fast-Fourier-transform (CFFT) approach for the numerical solution of backward stochastic differential equations (BSDEs) introduced in (Hyndman and Oyono Ngou, 2017). We then propose a method for improving the…