Related papers: Octonion Phase Retrieval
In this paper, we propose a new non-convex algorithm for solving the phase retrieval problem, i.e., the reconstruction of a signal $ \vx\in\H^n $ ($\H=\R$ or $\C$) from phaseless samples $ b_j=\abs{\langle \va_j, \vx\rangle } $, $…
A variational approach to reconstruction of phase and amplitude of a complex-valued object from Poissonian intensity observations is developed. The observation model corresponds to the typical optical setups with a phase modulation of…
This review article provides a contemporary overview of phase retrieval in optical imaging, linking the relevant optical physics to the information processing methods and algorithms. Its purpose is to describe the current state of the art…
In many areas of imaging science, it is difficult to measure the phase of linear measurements. As such, one often wishes to reconstruct a signal from intensity measurements, that is, perform phase retrieval. In this paper, we provide a…
The one-dimensional phase retrieval problem consists in the recovery of a complex-valued signal from its Fourier intensity. Due to the well-known ambiguousness of this problem, the determination of the original signal within the extensive…
The paper is devoted to the development of the octonion Fourier transform (OFT) theory initiated in 2011 in articles by Hahn and Snopek. It is also a continuation and generalization of earlier work by Blaszczyk and Snopek, where they proved…
One of the aims of next generation optical interferometric instrumentation is to be able to make use of information contained in the visibility phase to construct high dynamic range images. Radio and optical interferometry are at the two…
We present the first phase retrieval algorithm guaranteed to solve the multidimensional phase retrieval problem in polynomial arithmetic complexity without prior information. The method successfully terminates in O(N log(N)) operations for…
For audio source separation applications, it is common to estimate the magnitude of the short-time Fourier transform (STFT) of each source. In order to further synthesizing time-domain signals, it is necessary to recover the phase of the…
Phase retrieval refers to a classical nonconvex problem of recovering a signal from its Fourier magnitude measurements. Inspired by the compressed sensing technique, signal sparsity is exploited in recent studies of phase retrieval to…
The ill-posed problem of phase retrieval in optics, using one or more intensity measurements, has a multitude of applications using electromagnetic or matter waves. Many phase retrieval algorithms are computed on pixel arrays using discrete…
Opto-mechano-fluidic resonators (OMFRs) are a new platform for high-throughput sensing of the mechanical properties of freely flowing microparticles in arbitrary media. Experimental extraction of OMFR mode shapes, especially the acoustic…
The problem of signal recovery from its Fourier transform magnitude is of paramount importance in various fields of engineering and has been around for over 100 years. Due to the absence of phase information, some form of additional…
Fourier phase retrieval is the problem of reconstructing a signal given only the magnitude of its Fourier transformation. Optimization-based approaches, like the well-established Gerchberg-Saxton or the hybrid input output algorithm,…
We introduce a framework for the reconstruction of the amplitude, phase and polarisation of an optical vector-field using calibration measurements acquired by an imaging device with an unknown linear transformation. By incorporating…
We consider the phase retrieval problem, in which the observer wishes to recover a $n$-dimensional real or complex signal $\mathbf{X}^\star$ from the (possibly noisy) observation of $|\mathbf{\Phi} \mathbf{X}^\star|$, in which…
A new computational imaging method to reconstruct the complex wave-field is reported. Due to the existence of zero frequency component, the measured signal by amplitude modulation of pupil has a spectrum similar to the one of off-axis…
We propose and demonstrate a high-bandwidth optical intensity waveform monitoring technique based on frequency-division phase random optimization (FD-PRO) using an opto-electronic finite impulse response (OE-FIR) filter. In this technology,…
We consider the problem of conjugate phase retrieval in Paley-Wiener space $PW_{\pi}$. The goal of conjugate phase retrieval is to recover a signal $f$ from the magnitudes of linear measurements up to unknown phase factor and unknown…
This paper aims to address the phase retrieval problem from subgaussian measurements with arbitrary noise, with a focus on devising robust and efficient algorithms for solving non-convex problems. To ensure uniqueness of solutions in the…