相关论文: Conjugate Phase Retrieval on ${\mathbb C}^M$ by re…
X-ray near field holography has proven to be a powerful 2D and 3D imaging technique with applications ranging from biomedical research to material sciences. To reconstruct meaningful and quantitative images from the measurement intensities,…
Zernike's phase contrast microscopy (PCM) is among the most widely used techniques for observing phase objects, but it lacks quantitative nature, as it cannot directly provide phase information. Current methods for computationally…
Characterizing the phase space distribution of particle beams in accelerators is a central part of accelerator understanding and performance optimization. However, conventional reconstruction-based techniques either use simplifying…
We study information theoretic limits of recovering an unknown $n$ dimensional, complex signal vector $\mathbf{x}_\star$ with unit norm from $m$ magnitude-only measurements of the form $y_i = |(\mathbf{A} \mathbf{x}_\star)_i|^2, \; i = 1,2…
The retrieval of phases from intensity measurements is a key process in many fields in science, from optical microscopy to x-ray crystallography. Here we study phase retrieval of a one-dimensional multi-phase object that is illuminated by…
Phase retrieval arises in various fields of science and engineering and it is well studied in a finite-dimensional setting. In this paper, we consider an infinite-dimensional phase retrieval problem to reconstruct real-valued signals living…
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…
Phase-retrieval techniques aim to recover the original signal from just the modulus of its Fourier transform, which is usually much easier to measure than its phase, but the standard iterative techniques tend to fail if only part of the…
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…
We consider the problem of reconstructing two signals from the autocorrelation and cross-correlation measurements. This inverse problem is a fundamental one in signal processing, and arises in many applications, including phase retrieval…
Phase retrieval problem has been studied in various applications. It is an inverse problem without the standard uniqueness guarantee. To make complete theoretical analyses and devise efficient algorithms to recover the signal is…
We consider the problem of reconstructing a function $f\in L^2(\mathbb{R})$ given phase-less samples of its Gabor transform, which is defined by $$\mathcal{G} f(x,\omega) := 2^{\frac14} \int_{\mathbb{R}} f(t) e^{-\pi (t-x)^2} e^{-2\pi i y…
This paper considers the phase retrieval problem in which measurements consist of only the magnitude of several linear measurements of the unknown, e.g., spectral components of a time sequence. We develop low-complexity algorithms with…
Determining the phase of a wave from intensity measurements has many applications in fields such as electron microscopy, visible light optics, and medical imaging. Propagation based phase retrieval, where the phase is obtained from…
In this paper, we introduce two symmetric directed graphs depending on supports of signals and windows, and we show that the connectivity of those graphs provides either necessary and sufficient conditions to phase retrieval of a signal…
I show that the power iteration method applied to the phase retrieval problem converges under special conditions. One is given the relative phases between small non-overlapping groups of pixels of a recorded intensity pattern, but no…
The paper aims to study the performance of the amplitude-based model \newline $\widehat{\mathbf x} \in {\rm argmin}_{{\mathbf x}\in \mathbb{C}^d}\sum_{j=1}^m\left(|\langle {\mathbf a}_j,{\mathbf x}\rangle|-b_j\right)^2$, where…
We introduce and study conjugate reversibility (or $c$-reversibility) in the complex special linear group $\SL(n,\C)$ where an element is conjugate to the inverse of its complex conjugate. We prove that in $\SL(n, \C)$, every $c$-reversible…
This chapter develops a theoretical analysis of the convex programming method for recovering a structured signal from independent random linear measurements. This technique delivers bounds for the sampling complexity that are similar with…
Phase retrieval consists in the recovery of an unknown signal from phaseless measurements of its usually complex-valued Fourier transform. Without further assumptions, this problem is notorious to be severe ill posed such that the recovery…