Related papers: Injectivity of Multi-window Gabor Phase Retrieval
The problem of recovering a one-dimensional signal from its Fourier transform magnitude, called Fourier phase retrieval, is ill-posed in most cases. We consider the closely-related problem of recovering a signal from its phaseless…
Compressive phase retrieval refers to the problem of recovering a structured $n$-dimensional complex-valued vector from its phase-less under-determined linear measurements. The non-linearity of measurements makes designing…
We study the phase reconstruction of signals $f$ belonging to complex Gaussian shift-invariant spaces $V^\infty(\varphi)$ from spectrogram measurements $|\mathcal{G} f(X)|$ where $\mathcal{G}$ is the Gabor transform and $X \subseteq…
This paper shows how data-driven deep generative models can be utilized to solve challenging phase retrieval problems, in which one wants to reconstruct a signal from only few intensity measurements. Classical iterative algorithms are known…
In this paper, we study phase retrievable sequences and give a characterization of phase retrievability of a sequence of bounded linear operators on a Hilbert space $H$; in particular, for $H=\ell_2^d(\Bbb{C})$. We also give several…
This work deals with an inverse source problem for the biharmonic wave equation. A two-stage numerical method is proposed to identify the unknown source from the multi-frequency phaseless data. In the first stage, we introduce some…
A fundamental task in phase retrieval is to recover an unknown signal $\vx\in \Rn$ from a set of magnitude-only measurements $y_i=\abs{\nj{\va_i,\vx}}, \; i=1,\ldots,m$. In this paper, we propose two novel perturbed amplitude models (PAMs)…
Suppose that we observe noisy linear measurements of an unknown signal that can be modeled as the sum of two component signals, each of which arises from a nonlinear sub-manifold of a high dimensional ambient space. We introduce SPIN, a…
In the phase retrieval problem, an unknown vector is to be recovered given quadratic measurements. This problem has received considerable attention in recent times. In this paper, we present an algorithm to solve a nonconvex formulation of…
Inverse problems in imaging are typically ill-posed and are usually solved by employing regularized optimization techniques. The usage of appropriate constraints can restrict the solution space, thus making it feasible for a reconstruction…
Given a linear system in a real or complex domain, linear regression aims to recover the model parameters from a set of observations. Recent studies in compressive sensing have successfully shown that under certain conditions, a linear…
We investigate the recovery of vectors from magnitudes of frame coefficients when the frames have a low redundancy, meaning a small number of frame vectors compared to the dimension of the Hilbert space. We first show that for vectors in d…
Phase retrieval approaches based on DL provide a framework to obtain phase information from an intensity hologram or diffraction pattern in a robust manner and in real time. However, current DL architectures applied to the phase problem…
Almost all known image reconstruction algorithms for photoacoustic and thermoacoustic tomography assume that the acoustic waves leave the region of interest after a finite time. This assumption is reasonable if the reflections from the…
Signal models formed as linear combinations of few atoms from an over-complete dictionary or few frame vectors from a redundant frame have become central to many applications in high dimensional signal processing and data analysis. A core…
Advances in compressive sensing provided reconstruction algorithms of sparse signals from linear measurements with optimal sample complexity, but natural extensions of this methodology to nonlinear inverse problems have been met with…
Blind ptychography is a phase retrieval method using multiple coded diffraction patterns from different, overlapping parts of the unknown extended object illuminated with an unknown window function. The window function is also known as the…
One of the challenges in phase measuring deflectometry is to retrieve the wavefront from objects that present discontinuities or non-differentiable gradient fields. Here, we propose the integration of such gradients fields based on an…
This paper considers the problem of recovering a $k$-sparse, $N$-dimensional complex signal from Fourier magnitude measurements. It proposes a Fourier optics setup such that signal recovery up to a global phase factor is possible with very…
This paper explores the problem of generalized phase retrieval, which involves reconstructing a length-$n$ signal $\bm{x}$ from its $m$ phaseless samples $y_k = \left|\langle \bm{a}_k,\bm{x}\rangle\right|^2$, where $k = 1,2,...,m$, and…