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Positive time varying frequency representation for transient signals has been a hearty desire of signal analysts due to its theoretical and practical importance. During approximately the last two decades there has formulated a signal…

Complex Variables · Mathematics 2018-05-17 Tao Qian

This paper is concerned with stable phase retrieval for a family of phase retrieval models we name "locally stable and conditionally connected" (LSCC) measurement schemes. For every signal $f$, we associate a corresponding weighted graph…

Information Theory · Computer Science 2020-06-23 Cheng Cheng , Ingrid Daubechies , Nadav Dym , Jianfeng Lu

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…

Information Theory · Computer Science 2015-07-02 Kishore Jaganathan , Samet Oymak , Babak Hassibi

Ptychography is an imaging technique which involves a sample being illuminated by a coherent, localized probe of illumination. When the probe interacts with the sample, the light is diffracted and a diffraction pattern is detected. Then the…

Numerical Analysis · Mathematics 2023-01-31 Mark Iwen , Michael Perlmutter , Mark Philip Roach

A new method for phase recovery from a single two-beam interferogram is presented. Conventional approaches, relying on trigonometric inversion followed by phase unfolding and unwrapping, are hindered by discontinuities typically addressed…

Optics · Physics 2025-09-24 V. Berejnov , B. Y. Rubinstein

In coherent X-ray diffraction microscopy the diffraction pattern generated by a sample illuminated with coherent x-rays is recorded, and a computer algorithm recovers the unmeasured phases to synthesize an image. By avoiding the use of a…

This study investigates phase reconstruction for deep learning based monaural talker-independent speaker separation in the short-time Fourier transform (STFT) domain. The key observation is that, for a mixture of two sources, with their…

Sound · Computer Science 2018-11-26 Zhong-Qiu Wang , Ke Tan , DeLiang Wang

This paper is concerned with uniqueness, phase retrieval and shape reconstruction methods for inverse elastic scattering problems with phaseless far field data. Systematically, we study two basic models, i.e., inverse scattering of plane…

Analysis of PDEs · Mathematics 2020-01-08 Xia Ji , Xiaodong Liu

Material response of real, passive, linear, time-invariant media to external influences is described by complex analytic functions of frequency that can always be written in terms of Stieltjes functions -- a special class of analytic…

Optimization and Control · Mathematics 2022-03-25 Yury Grabovsky

In this paper, we consider the problem of recovering a compactly supported multivariate function from a collection of pointwise samples of its Fourier transform taken nonuniformly. We do this by using the concept of weighted Fourier frames.…

Numerical Analysis · Mathematics 2015-09-08 Ben Adcock , Milana Gataric , Anders C. Hansen

The identification of sampling sets that enable unique signal recovery is fundamental to many applications in signal processing and remains a central problem in mathematical analysis. Recent studies in the mathematical literature,…

Classical Analysis and ODEs · Mathematics 2025-12-16 Oleg Szehr

In this paper a sublinear time algorithm is presented for the reconstruction of functions that can be represented by just few out of a potentially large candidate set of Fourier basis functions in high spatial dimensions, a so-called…

Numerical Analysis · Mathematics 2020-06-24 Lutz Kämmerer , Felix Krahmer , Toni Volkmer

In many applications sampled data are collected in irregular fashion or are partly lost or unavailable. In these cases it is required to convert irregularly sampled signals to regularly sampled ones or to restore missing data. In this…

Precise characterization of three-dimensional heterogeneous media is indispensable in finding the relationships between structure and macroscopic physical properties (permeability, conductivity, and others). The most widely used…

Materials Science · Physics 2021-09-15 Aleksei Cherkasov , Andrey Ananev , Marina Karsanina , Aleksey Khlyupin , Kirill Gerke

In a variety of fields, in particular those involving imaging and optics, we often measure signals whose phase is missing or has been irremediably distorted. Phase retrieval attempts the recovery of the phase information of a signal from…

Information Theory · Computer Science 2013-09-27 Juri Ranieri , Amina Chebira , Yue M. Lu , Martin Vetterli

We consider quantum and acoustic wave propagation at fixed frequency for compactly supported scatterers in dimension $d\ge 2$. In these framework we give explicit formulas for phase recovering from appropriate phaseless scattering data. As…

Mathematical Physics · Physics 2015-02-17 Roman Novikov

Time-frequency concentration operators restrict the integral analysis-synthesis formula for the short-time Fourier transform to a given compact domain. We estimate how much the corresponding eigenvalue counting function deviates from the…

Spectral Theory · Mathematics 2024-03-14 Felipe Marceca , José Luis Romero

In this paper we study a realistic setup for phase retrieval, where the signal of interest is modulated or masked and then for each modulation or mask a diffraction pattern is collected, producing a coded diffraction pattern (CDP) [CLM13].…

Information Theory · Computer Science 2014-03-25 Youssef Mroueh

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…

This paper considers the model problem of reconstructing an object from incomplete frequency samples. Consider a discrete-time signal $f \in \C^N$ and a randomly chosen set of frequencies $\Omega$ of mean size $\tau N$. Is it possible to…

Numerical Analysis · Mathematics 2007-05-23 Emmanuel Candes , Justin Romberg , Terence Tao