Related papers: Phase retrieval using alternating minimization in …

We address the problem of recovering signals from samples taken at their rate of innovation. Our only assumption is that the sampling system is such that the parameters defining the signal can be stably determined from the samples, a…

In this work we analyze the problem of phase retrieval from Fourier measurements with random diffraction patterns. To this end, we consider the recently introduced PhaseLift algorithm, which expresses the problem in the language of convex…

The problem of recovering a vector from the absolute values of its inner products against a family of measurement vectors has been well studied in mathematics and engineering. A generalization of this phase retrieval problem also exists in…

We establish theoretical recovery guarantees of a family of Riemannian optimization algorithms for low rank matrix recovery, which is about recovering an $m\times n$ rank $r$ matrix from $p < mn$ number of linear measurements. The…

This work studies the Low Rank Phase Retrieval (LRPR) problem: recover an $n \times q$ rank-$r$ matrix $X^*$ from $y_k = |A_k^\top x^*_k|$, $k=1, 2,..., q$, when each $y_k$ is an m-length vector containing independent phaseless linear…

Let $P=(P_1, P_2, \ldots, P_n)$, $P_i \in \field{R}$ for all $i$, be a signal and let $C$ be a constant. In this work our goal is to find a function $F:[n]\rightarrow \field{R}$ which optimizes the following objective function: $$ \min_{F}…

This paper introduces a novel approach for recovering sparse signals using sorted L1/L2 minimization. The proposed method assigns higher weights to indices with smaller absolute values and lower weights to larger values, effectively…

In phase retrieval, the goal is to recover a complex signal from the magnitude of its linear measurements. While many well-known algorithms guarantee deterministic recovery of the unknown signal using i.i.d. random measurement matrices,…

This paper considers the recovery of continuous time signals from the magnitude of its samples. It uses a combination of structured modulation and oversampling and provides sufficient conditions on the signal and the sampling system such…

In this paper we propose a global optimization-based approach to jointly matching a set of images. The estimated correspondences simultaneously maximize pairwise feature affinities and cycle consistency across multiple images. Unlike…

PhaseLift is a noted convex optimization technique for phase retrieval that can recover a signal exactly from amplitude measurements only, with high probability. Conventional PhaseLift requires a relatively large number of samples that…

As technology grows, higher frequency signals are required to be processed in various applications. In order to digitize such signals, conventional analog to digital convertors are facing implementation challenges due to the higher sampling…

The theory behind compressive sampling pre-supposes that a given sequence of observations may be exactly represented by a linear combination of a small number of basis vectors. In practice, however, even small deviations from an exact…

Iterative algorithms with feedback are amongst the most powerful and versatile optimization methods for phase retrieval. Among these, the hybrid input-output algorithm has demonstrated practical solutions to giga-element nonlinear phase…

The recovery of a signal from the magnitudes of its transformation, like the Fourier transform, is known as the phase retrieval problem and is of big relevance in various fields of engineering and applied physics. In this paper, we present…

Higher-order low-rank tensors naturally arise in many applications including hyperspectral data recovery, video inpainting, seismic data recon- struction, and so on. We propose a new model to recover a low-rank tensor by simultaneously…

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…

Phase retrieval, a long-established challenge for recovering a complex-valued signal from its Fourier intensity measurements, has attracted significant interest because of its far-flung applications in optical imaging. To enhance accuracy,…

Phase retrieval is the classical problem of recovering a signal $x^* \in \mathbb{R}^n$ from its noisy phaseless measurements $y_i = \langle a_i, x^* \rangle^2 + \zeta_i$ (where $\zeta_i$ denotes noise, and $a_i$ is the sensing vector) for…

We consider the problem of signal recovery on graphs as graphs model data with complex structure as signals on a graph. Graph signal recovery implies recovery of one or multiple smooth graph signals from noisy, corrupted, or incomplete…