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Multiple wavelength phase shifting interferometry is widely used to extend the unambiguous range (UR) beyond that of a single wavelength. Towards this end, many algorithms have been developed to calculate the optical path difference (OPD)…
A phase shift and sum (PSAS) algorithm to image objects in dispersive media is presented. The algorithm compensates the phase shift of the scattered field from the receiver to the source for each frequency component in an ultrawideband…
We consider the classical 1D phase retrieval problem. In order to overcome the difficulties associated with phase retrieval from measurements of the Fourier magnitude, we treat recovery from the magnitude of the short-time Fourier transform…
Traditional phase-shifting interferometry technique cannot be used to measure time-varying phase distributions. But single shot techniques could resolve the problem. Many efforts have been made on the phase retrieval methods from a single…
One of the major challenges of employing a dual-frequency phase-shifting algorithm for phase retrieval is its sensitivity to noise. Yun et. al [H Yun, B Li, S Zhang. 2017] proposed a dual-frequency method based on the Fourier transform…
Phase retrieval problems in antenna measurements arise when a reference phase cannot be provided to all measurement locations. Phase retrieval algorithms require sufficiently many independent measurement samples of the radiated fields to be…
This paper presents a novel algorithm for residual phase estimation in wireless OFDM systems, including the carrier frequency offset (CFO) and the sampling frequency offset (SFO). The subcarriers are partitioned into several regions which…
Quaternionic signal processing provides powerful tools for efficiently managing color signals by preserving the intrinsic correlations among signal dimensions through quaternion algebra. In this paper, we address the quaternionic phase…
Many interesting and fundamentally practical optimization problems, ranging from optics, to signal processing, to radar and acoustics, involve constraints on the Fourier transform of a function. It is well-known that the {\em fast Fourier…
This paper addresses the problem of expressing a signal as a sum of frequency components (sinusoids) wherein each sinusoid may exhibit abrupt changes in its amplitude and/or phase. The Fourier transform of a narrow-band signal, with a…
Purpose: To develop a general phase regularized image reconstruction method, with applications to partial Fourier imaging, water-fat imaging and flow imaging. Theory and Methods: The problem of enforcing phase constraints in reconstruction…
A compressive sensing (CS) reconstruction method for polynomial phase signals is proposed in this paper. It relies on the Polynomial Fourier transform, which is used to establish a relationship between the observation and sparsity domain.…
A unified method for three-dimensional reconstruction of objects from transmission images collected at multiple illumination directions is described. The method may be applicable to experimental conditions relevant to absorption-based,…
Generally, phase retrieval problem can be viewed as the reconstruction of a function/signal from only the magnitude of the linear measurements. These measurements can be, for example, the Fourier transform of the density function.…
A numerical method for processing the data of ground penetrating radars for a piece-wise continuous layered medium is proposed. The method combines the layer stripping technique with numerical continuation of data into the complex…
In many practical applications, spatial data are often collected at areal levels (i.e., block data) and the inferences and predictions about the variable at points or blocks different from those at which it has been observed typically…
If the phase retrieval problem can be solved by a method similar to that of solving a system of linear equations under the context of FFT, the time complexity of computer based phase retrieval algorithm would be reduced. Here I present such…
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,…
The interference of fluorescence signals and noise remains a significant challenge in Raman spectrum analysis, often obscuring subtle spectral features that are critical for accurate analysis. Inspired by variational methods similar to…
When using Laguerre and Hermite spectral methods to numerically solve PDEs in unbounded domains, the number of collocation points assigned inside the region of interest is often insufficient, particularly when the region is expanded or…