Related papers: Phase retrieval by random binary questions: Which …
Proximal algorithms have gained popularity in recent years in large-scale and distributed optimization problems. One such problem is the phase retrieval problem, for which proximal operators have been proposed recently. The phase retrieval…
Several strategies in phase retrieval are unified by an iterative "difference map" constructed from a pair of elementary projections and a single real parameter $\beta$. For the standard application in optics, where the two projections…
This work presents a fast and non-convex algorithm for robust subspace recovery. The data sets considered include inliers drawn around a low-dimensional subspace of a higher dimensional ambient space, and a possibly large portion of…
Hilbert space fusion frames are a natural extension of Hilbert space frames, extending the notion from a set of vectors in a Hilbert space to a set of subspaces of a Hilbert space with analogous notions of overcompleteness and boundedness.…
We study the problem of binary classification from the point of view of learning convex polyhedra in Hilbert spaces, to which one can reduce any binary classification problem. The problem of learning convex polyhedra in finite-dimensional…
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…
This paper deals with sparse phase retrieval, i.e., the problem of estimating a vector from quadratic measurements under the assumption that few components are nonzero. In particular, we consider the problem of finding the sparsest vector…
In this note we study the problem of sampling and reconstructing signals which are assumed to lie on or close to one of several subspaces of a Hilbert space. Importantly, we here consider a very general setting in which we allow infinitely…
We introduce a method to reconstruct an element of a Hilbert space in terms of an arbitrary finite collection of linearly independent reconstruction vectors, given a finite number of its samples with respect to any Riesz basis. As we…
The problem of phase retrieval is to determine a signal $f\in \mathcal{H}$, with $\mathcal{H}$ a Hilbert space, from intensity measurements $|F(\omega)|$, where $F(\omega):=\langle f , \varphi_\omega\rangle$ are measurements of $f$ with…
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 consider a phase retrieval problem, where the goal is to reconstruct a $n$-dimensional complex vector from its phaseless scalar products with $m$ sensing vectors, independently sampled from complex normal distributions. We show that,…
Networked sensing, where the goal is to perform complex inference using a large number of inexpensive and decentralized sensors, has become an increasingly attractive research topic due to its applications in wireless sensor networks and…
Phase retrieval seeks to recover a signal x from the amplitude |Ax| of linear measurements. We cast the phase retrieval problem as a non-convex quadratic program over a complex phase vector and formulate a tractable relaxation (called…
This work studies the problem of sequentially recovering a sparse vector $x_t$ and a vector from a low-dimensional subspace $l_t$ from knowledge of their sum $m_t = x_t + l_t$. If the primary goal is to recover the low-dimensional subspace…
Natural images tend to mostly consist of smooth regions with individual pixels having highly correlated spectra. This information can be exploited to recover hyperspectral images of natural scenes from their incomplete and noisy…
The mutual intensity and its equivalent phase-space representations quantify an optical field's state of coherence and are important tools in the study of light propagation and dynamics, but they can only be estimated indirectly from…
We improve a phase retrieval approach that uses correlation-based measurements with compactly supported measurement masks [27]. The improved algorithm admits deterministic measurement constructions together with a robust, fast recovery…
This paper considers phase retrieval from the magnitude of 1D over-sampled Fourier measurements, a classical problem that has challenged researchers in various fields of science and engineering. We show that an optimal vector in a…
Performing inference in Bayesian models requires sampling algorithms to draw samples from the posterior. This becomes prohibitively expensive as the size of data sets increase. Constructing approximations to the posterior which are cheap to…