Related papers: Faster than Fast: Accelerating the Griffin-Lim Alg…
The recovery of a signal from the magnitudes of its transformation, like the Fourier transform, is known as the phase retrieval problem and is of big relevance in various fields of engineering and applied physics. In this paper, we present…
Phase retrieval is a problem encountered not only in speech and audio processing, but in many other fields such as optics. Iterative algorithms based on non-convex set projections are effective and frequently used for retrieving the phase…
We propose a novel iterative phase estimation framework, termed multi-source Griffin-Lim algorithm (MSGLA), for speech enhancement (SE) under additive noise conditions. The core idea is to leverage the ad-hoc consistency constraint of…
A recently proposed convex formulation of the phase retrieval problem estimates the unknown signal by solving a simple linear program. This new scheme, known as PhaseMax, is computationally efficient compared to standard convex relaxation…
This paper presents a novel phase reconstruction method (only from a given amplitude spectrogram) by combining a signal-processing-based approach and a deep neural network (DNN). To retrieve a time-domain signal from its amplitude…
Several recent contributions in the field of iterative STFT phase retrieval have demonstrated that the performance of the classical Griffin-Lim method can be considerably improved upon. By using the same projection operators as Griffin-Lim,…
The ``fast iterative shrinkage-thresholding algorithm'', a.k.a. FISTA, is one of the most widely used algorithms in the literature. However, despite its optimal theoretical $O(1/k^2)$ convergence rate guarantee, oftentimes in practice its…
Phase retrieval deals with the recovery of complex- or real-valued signals from magnitude measurements. As shown recently, the method PhaseMax enables phase retrieval via convex optimization and without lifting the problem to a higher…
We propose a flexible convex relaxation for the phase retrieval problem that operates in the natural domain of the signal. Therefore, we avoid the prohibitive computational cost associated with "lifting" and semidefinite programming (SDP)…
Phase retrieval aims to recover a signal from magnitude or power spectra measurements. It is often addressed by considering a minimization problem involving a quadratic cost function. We propose a different formulation based on Bregman…
The phase retrieval problem is a fundamental problem in many fields, which is appealing for investigation. It is to recover the signal vector $\tilde{x}\in\mathbb{C}^d$ from a set of $N$ measurements $b_n=|f^*_n\tilde{x}|^2,\ n=1,\cdots,…
Phase retrieval consists in the recovery of a complex-valued signal from intensity-only measurements. As it pervades a broad variety of applications, many researchers have striven to develop phase-retrieval algorithms. Classical approaches…
Fast Iterative Shrinking-Threshold Algorithm (FISTA) is a popular fast gradient descent method (FGM) in the field of large scale convex optimization problems. However, it can exhibit undesirable periodic oscillatory behaviour in some…
Reconstructing a signal from squared linear (rank-one quadratic) measurements is a challenging problem with important applications in optics and imaging, where it is known as phase retrieval. This paper proposes two new phase retrieval…
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…
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.…
The problem of phase retrieval is revisited and studied from a fresh perspective. In particular, we establish a connection between the phase retrieval problem and the sensor network localization problem, which allows us to utilize the vast…
In this paper, we propose a new algorithm to speed-up the convergence of accelerated proximal gradient (APG) methods. In order to minimize a convex function $f(\mathbf{x})$, our algorithm introduces a simple line search step after each…
Phase retrieval problems involve solving linear equations, but with missing sign (or phase, for complex numbers) information. More than four decades after it was first proposed, the seminal error reduction algorithm of (Gerchberg and Saxton…
The Square Kilometre Array (SKA) project will be the world largest radio telescope array. With its large number of antennas, the number of signals that need to be processed is dramatic. One important element of the SKA's Central Signal…