Related papers: Continuous Approach to Phase (Norm) Retrieval Fram…

We address the problem of signal reconstruction from intensity measurements with respect to a measurement frame. This non-convex inverse problem is known as phase retrieval. The case considered in this paper concerns phaseless measurements…

The problem of phase retrieval, i.e., the problem of recovering a function from the magnitudes of its Fourier transform, naturally arises in various fields of physics, such as astronomy, radar, speech recognition, quantum mechanics and,…

We make a detailed study of norm retrieval. We give several classification theorems for norm retrieval and give a large number of examples to go with the theory. One consequence is a new result about Parseval frames: If a Parseval frame is…

In this present paper we introduce weaving Hilbert space frames in the continuous case, we give new approaches for manufacturing pairs of woven continuous frames and we obtain new properties in continuous weaving frame theory related to…

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…

Phase retrieval has been an attractive but difficult problem rising from physical science, and there has been a gap between state-of-the-art theoretical convergence analyses and the corresponding efficient retrieval methods. Firstly, these…

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…

We consider a popular nonsmooth formulation of the real phase retrieval problem. We show that under standard statistical assumptions, a simple subgradient method converges linearly when initialized within a constant relative distance of an…

In this paper we consider on the notion of continuous frame of subspace and define a new concept of continuous frame, entitled {\it continuous atomic resolution of identity}, for arbitrary Hilbert space $\h$ which has a countable…

The main objective of this paper is to find algorithms accompanied by explicit error bounds for phase retrieval from noisy magnitudes of frame coefficients when the underlying frame has a low redundancy. We achieve these goals with frames…

In the present paper the notion of continuous frames is introduced and some results of these frames are proved. Next, we give the concept of duals of continuous frames in Hilbert C*-modules and investigate some properties of them.

As a generalization of the standard phase retrieval problem, we seek to reconstruct symmetric rank-1 matrices from inner products with subclasses of positive semidefinite matrices. For such subclasses, we introduce random cubatures for…

The problem of reconstructing a function from the magnitudes of its frame coefficients has recently been shown to be never uniformly stable in infinite-dimensional spaces [5]. This result also holds for frames that are possibly continuous…

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…

In this paper, we explore the interplay between topological structures and phase retrieval in the context of projective Hilbert spaces. This work provides not only a deeper understanding and a new classification of the phase retrieval…

Given a frame in a finite dimensional Hilbert space we construct additive perturbations which decrease the condition number of the frame. By iterating this perturbation, we introduce an algorithm that produces a tight frame in a finite…

In this paper, we study the Hilbert$-$Schmidt frame (HS-frame) theory for separable Hilbert spaces. We first present some characterizations of HS-frames and prove that HS-frames share many important properties with frames. Then, we show how…

Finite frames, or spanning sets for finite-dimensional Hilbert spaces, are a ubiquitous tool in signal processing. There has been much recent work on understanding the global structure of collections of finite frames with prescribed…

We consider countable families of vectors in a separable Hilbert space, which are mutually localized with respect to a fixed localized Riesz basis. We prove the equivalence of the frame property and nine conditions that do not involve any…

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…