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Frequency domain analysis using the Fast Fourier transform (FFT) has been a popular method for diagnosing broken rotor bar (BRB) faults in squirrel-cage induction motors (IM). However, FFT analysis is limited by sampling frequency and time…
Phase retrieval consists in the recovery of an unknown signal from phaseless measurements of its usually complex-valued Fourier transform. Without further assumptions, this problem is notorious to be severe ill posed such that the recovery…
Phase retrieval, a long-established challenge for recovering a complex-valued signal from its Fourier intensity measurements, has attracted significant interest because of its far-flung applications in optical imaging. To enhance accuracy,…
Advanced wavefront sensors (WFS) are essential for enabling new science cases for telescopes that utilize adaptive optics (AO) systems. While complex field WFS -- those that estimate the electric field phase and amplitude through…
This paper aims to quantify uncertainty for SVBRDF acquisition in multi-view captures. Under uncontrolled illumination and unstructured viewpoints, there is no guarantee that the observations contain enough information to reconstruct the…
We introduce a dual-wavelength Fourier ptychographic topography (FPT) method that extends the lambda/2 height-range limit of single-wavelength FPT. By reconstructing complex fields at two illumination wavelengths and exploiting their phase…
In many processes, the variations in underlying characteristics can be approximated by noisy multi-periodic patterns. If large-scale patterns are superimposed by a noise with long-range correlations, the detection of multi-periodic patterns…
We experimentally demonstrate how to solve the phase problem of diffraction using multi-wave interference with standard diffraction experimental setups without the need for taking any auxiliary data. In particular, we show that the phases…
This paper is concerned with the inverse source problem of reconstructing an unknown acoustic excitation from phaseless measurements of the radiated fields away at multiple frequencies. It is well known that the non-uniqueness issue is a…
Fourier phase retrieval is a classical problem that deals with the recovery of an image from the amplitude measurements of its Fourier coefficients. Conventional methods solve this problem via iterative (alternating) minimization by…
In this paper, we present an assortment of both standard and advanced Fourier techniques that are useful in the analysis of astrophysical time series of very long duration -- where the observation time is much greater than the time…
Synchrosqueezing transform (SST) is a useful tool for vibration signal analysis due to its high time-frequency (TF) concentration and reconstruction properties. However, existing SST requires much processing time for large-scale data. In…
For a HOM interferometer with two independent incident pulses, the interference pattern can be affected by adding a dispersion medium on one of the incident directions, but there hasn't been a method to reconstruct the phase constant of the…
The conjugate phase retrieval problem concerns the determination of a complex-valued function, up to a unimodular constant and conjugation, from its magnitude observations. It can also be considered as a conjugate phaseless sampling and…
This paper introduces a multi-frequency factorization method for imaging a time-dependent source, specifically to recover its spatial support and the associated excitation instants. Using far-field data from two opposite directions, we…
Fourier representation (FR) is an indispensable mathematical formulation for modeling and analysis of physical phenomenon, engineering systems and signals in numerous applications. In this study, we present the generalized Fourier…
In this paper, we investigate the uniqueness of the phase retrieval problem for the fractional Fourier transform (FrFT) of variable order. This problem occurs naturally in optics and quantum physics. More precisely, we show that if $u$ and…
In this paper a novel data embedding technique in frequency domain has been proposed using Discrete Fourier Transform (DFT) for image authentication and secured message transmission based on hiding a large volume of data into gray images.…
Image subtraction is essential for transient detection in time-domain astronomy. The point spread function (PSF), photometric scaling, and sky background generally vary with time and across the field-of-view for imaging data taken with…
Interferometric methods, renowned for their reliability and precision, play a vital role in phase imaging. Interferometry typically requires high coherence and stability between the measured and the reference beam. The presence of rapid…