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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…

Improving the generalization ability of Deep Neural Networks (DNNs) is critical for their practical uses, which has been a longstanding challenge. Some theoretical studies have uncovered that DNNs have preferences for some frequency…

Discrete Fourier transform (DFT) is the base of modern signal or information processing. 1-Dimensional fast Fourier transform (1D FFT) and 2D FFT have time complexity O(NlogN) and O(N^2logN) respectively. Quantum 1D and 2D DFT algorithms…

Dispersive Fourier transformation is a powerful technique in which the spectrum of an optical pulse is mapped into a time-domain waveform using chromatic dispersion. It replaces a diffraction grating and detector array with a dispersive…

The fifth generation (5G) wireless standard will support several new use cases and 10 to 100 times the performance of fourth generation (4G) systems. Because of the diverse applications for 5G, flexible solutions which can address…

Wrapping a computation domain with a perfectly matched layer (PML) is one of the most effective methods of imitating/approximating the radiation boundary condition in Maxwell and wave equation solvers. Many PML implementations often use a…

Many experiments, and in particular gravitational wave detectors, produce continuous streams of data whose frequency representations contain discrete, relatively narrowband coherent features at high amplitude. We discuss the application of…

The Discrete Fourier Transform (DFT) is a fundamental computational primitive, and the fastest known algorithm for computing the DFT is the FFT (Fast Fourier Transform) algorithm. One remarkable feature of FFT is the fact that its runtime…

In this paper we consider Sparse Fourier Transform (SFT) algorithms for approximately computing the best $s$-term approximation of the Discrete Fourier Transform (DFT) $\mathbf{\hat{f}} \in \mathbb{C}^N$ of any given input vector…

Although face recognition (FR) has achieved great success in recent years, it is still challenging to accurately recognize faces in low-quality images due to the obscured facial details. Nevertheless, it is often feasible to make…

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…

In this paper, we extend the Generalized Finite Difference Method (GFDM) on unknown compact submanifolds of the Euclidean domain, identified by randomly sampled data that (almost surely) lie on the interior of the manifolds. Theoretically,…

We have designed and constructed a ``dispersed Fourier Transform Spectrometer'' (dFTS), consisting of a conventional FTS followed by a grating spectrometer. By combining these two devices, we negate a substantial fraction of the sensitivity…

Image restoration of biological structures in microscopy poses unique challenges for preserving fine textures and sharp edges. While recent GAN-based image restoration formulations have introduced frequency-domain losses for natural images,…

Dark-Field X-ray Microscopy (DFXM) is a diffraction-based synchrotron imaging techique capable of imaging defects in the bulk of extended crystalline samples. We present numerical simulations of image-formation in such a microscope using…

Federated Learning (FL) offers a powerful strategy for training machine learning models across decentralized datasets while maintaining data privacy, yet domain shifts among clients can degrade performance, particularly in medical imaging…

Various imaging modalities are used in patient diagnosis, each offering unique advantages and valuable insights into anatomy and pathology. Computed Tomography (CT) is crucial in diagnostics, providing high-resolution images for precise…

Graph signal processing (GSP) advances spectral analysis on irregular domains. However, existing two-dimensional graph fractional Fourier transform (2D-GFRFT) employs a single fractional order for both factor graphs, thereby limiting its…

This paper introduces a new algorithm for the fundamental problem of generating a random integer from a discrete probability distribution using a source of independent and unbiased random coin flips. We prove that this algorithm, which we…

This paper introduces a new tool for time-series analysis: the Sliding Window Discrete Fourier Transform (SWDFT). The SWDFT is especially useful for time-series with local- in-time periodic components. We define a 5-parameter model for…