Related papers: An efficient PSF construction method
Discrete cosine transform (DCT) and other Fourier-related transforms have broad applications in scientific computing. However, off-the-shelf high-performance multi-dimensional DCT (MD DCT) libraries are not readily available in parallel…
The point-spread function (PSF) of an imaging system describes the response of the system to a point source. Accurately determining the PSF enables one to correct for the combined effects of focussing and scattering within the imaging…
Digital signal processing is a valuable practical skill for the contemporary physicist, yet in physics curricula its central concepts are often introduced either in method courses in a highly abstract and mathematics-oriented manner or in…
In a recent paper, published at arXiv:0910.2381, we started a discussion on the new possibilities arising from the use of fractional differential calculus in image processing. We have seen that the fractional calculation is able to enhance…
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…
The basic principle of astronomical interferometry is to derive the angular distribution of radiation in the sky from the Fourier transform of the electric field on the ground. What is so special about the Fourier transform? Nothing, it…
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.
We demonstrate the use of the Fast Fourier Transform Beam Propagation Method (FFT BPM) to simulate dynamic diffraction effects, including scattering from deformed crystals with arbitrary shapes in Bragg, Laue, and asymmetric geometries. The…
Convolutional neural networks have become an essential element of spatial deep learning systems. In the prevailing architecture, the convolution operation is performed with Fast Fourier Transforms (FFT) electronically in GPUs. The…
We propose a discrete fractional random transform based on a generalization of the discrete fractional Fourier transform with an intrinsic randomness. Such discrete fractional random transform inheres excellent mathematical properties of…
We report experimental implementation of discrete Fourier transformation(DFT) on a nuclear magnetic resonance(NMR) quantum computer. Experimental results agree with theoretical results. Using the pulse sequences we introduced, DFT can be…
This work presents a highly optimized computational framework for the Discrete Dipole Approximation, a numerical method for calculating the optical properties associated with a target of arbitrary geometry that is widely used in…
One of the most efficient ways to produce unconditional simulations is with the kernel convolution using fast Fourier transform (FFT) [1]. However, when data is located on a surface, this approach is not efficient because data needs to be…
This paper shows that it is possible to improve the computational cost, the memory requirements and the accuracy of Quick Fourier Transform (QFT) algorithm for power-of-two FFT (Fast Fourier Transform) just introducing a slight modification…
The Quantum Fourier transform (QFT) is a key ingredient in most quantum algorithms. We have compared various spin-based quantum computing schemes to implement the QFT from the point of view of their actual time-costs and the accuracy of the…
This paper presents a new effective method for image encryption which employs magnitude and phase manipulation using Differential Evolution (DE) approach. The novelty of this work lies in deploying the concept of keyed discrete Fourier…
We present a general theory of fractal transformations and show how it leads to a new type of method for filtering and transforming digital images. This work substantially generalizes earlier work on fractal tops. The approach involves…
A special algorithm for the Fourier-transform Ghost Imaging (GI) scheme is discussed based on the Compressive Sampling (CS) theory. The CS algorithm could also be used for the Fourier spectrum reconstruction of pure phase object by setting…
Optical spectrum analysis is the cornerstone of spectroscopic sensing, optical network performance monitoring, and hyperspectral imaging. While conventional high-performance spectrometers used to perform such analysis are often large…
Traditional data collection from sensors produce a lot of data, which lead to constant power consumption and require more storage space. This study proposes an algorithm for a data acquisition and processing method based on Fourier…