Related papers: 2D Discrete Fourier Transform with Simultaneous Ed…
In this paper, we present two variations of an algorithm for signal reconstruction from one-bit or two-bit noisy observations of the discrete Fourier transform (DFT). The one-bit observations of the DFT correspond to the sign of its real…
Physics-driven artificial intelligence (PD-AI) reconstruction methods have emerged as the state-of-the-art for accelerating MRI scans, enabling higher spatial and temporal resolutions. However, the high resolution of these scans generates…
Image compression is one of the essential methods of image processing. Its most prominent advantage is the significant reduction of image size allowing for more efficient storage and transfer. However, lossy compression is associated with…
The discrete Fourier transform (DFT) is of fundamental interest in photonic quantum information, yet the ability to scale it to high dimensions depends heavily on the physical encoding, with practical recipes lacking in emerging platforms…
We present a new algorithm for the 2D Sliding Window Discrete Fourier Transform (SWDFT). Our algorithm avoids repeating calculations in overlapping windows by storing them in a tree data-structure based on the ideas of the Cooley- Tukey…
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…
Fast Fourier Transforms (FFT) are widely used to reduce memory and computational costs in deep learning. However, existing implementations, including standard FFT and real FFT (rFFT), cannot achieve true in-place computation. In particular,…
We report a computational 3D microscopy technique, termed Fourier ptychographic diffraction tomography (FPDT), that iteratively stitches together numerous variably illuminated, low-resolution images acquired with a low-numerical aperture…
Low-dose computed tomography (LDCT) reduces radiation exposure but suffers from image artifacts and loss of detail due to quantum and electronic noise, potentially impacting diagnostic accuracy. Transformer combined with diffusion models…
Fast Fourier Transform (FFT) is an efficient algorithm to compute the Discrete Fourier Transform (DFT) and its inverse. In this paper, we pay special attention to the description of complex-data FFT. We analyze two common descriptions of…
In this work, we present the \emph{twiddless fast Fourier transform (TFFT)}, a novel algorithm for computing the $N$-point discrete Fourier transform (DFT). The TFFT's divide strategy builds on recent results that decimate an $N$-point…
Diffusion-weighted MRI is nowadays performed routinely due to its prognostic ability, yet the quality of the scans are often unsatisfactory which can subsequently hamper the clinical utility. To overcome the limitations, here we propose a…
The fast Fourier transform, FFT, is a useful and prevalent algorithm in signal processing. It characterizes the spectral components of a signal, or is used in combination with other operations to perform more complex computations such as…
Discrete Fourier transforms~(DFTs) over finite fields have widespread applications in digital communication and storage systems. Hence, reducing the computational complexities of DFTs is of great significance. Recently proposed cyclotomic…
In this article, we develop comprehensive frequency domain methods for estimating and inferring the second-order structure of spatial point processes. The main element here is on utilizing the discrete Fourier transform (DFT) of the point…
This work proposes an extension of the 1-D Hilbert Huang transform for the analysis of images. The proposed method consists in (i) adaptively decomposing an image into oscillating parts called intrinsic mode functions (IMFs) using a mode…
Recent years have witnessed the remarkable performance of diffusion models in various vision tasks. However, for image restoration that aims to recover clear images with sharper details from given degraded observations, diffusion-based…
We present a differentiation framework for plane-wave density-functional theory (DFT) that combines the strengths of forward-mode algorithmic differentiation (AD) and density-functional perturbation theory (DFPT). In the resulting AD-DFPT…
Discrete Fourier transforms~(DFTs) over finite fields have widespread applications in error correction coding. Hence, reducing the computational complexities of DFTs is of great significance, especially for long DFTs as increasingly longer…
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…