Low rank matrix recovery from column-wise phaseless measurements

Nayer, Seyedehsara; Vaswani, Namrata; Eldar, Yonina C.

doi:10.1109/ssp.2016.7551786

Cited by 8 publications

(19 citation statements)

References 17 publications

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“…Modifying TWF for the set of variables U , B needs to be done with care, and needs to include a step that ensures that one of U or B does not keep increasing. An early attempt along these lines is given in [1].…”

Section: Lrpr2: Low Rank Pr Via Alternating Minimizationmentioning

confidence: 99%

“…Email: namrata@iastate.edu. An early version of the initialization idea developed in this work was presented at the IEEE Statistical Signal Processing Workshop 2016 [1]. A short version of this work will be presented at ICASSP 2017 [2].…”

Section: Introductionmentioning

confidence: 99%

“…, q. (1) The measurement vectors, a i,k , are mutually independent. Our goal is to recover the matrix X from these mq phaseless measurements y i,k .…”

Section: Introductionmentioning

confidence: 99%

“…Two other works that also generalize WF [10], but to 1 For AltMinPhase, the initialization sample complexity (for achieving a given fixed error) is cn log 3 n while it is only cn log n per iteration for the rest of the algorithm. For resampled WF, it is cn log 2 n for initialization and cn log n for the rest of the algorithm, while for TWF, it is cn both for the initialization and for the complete algorithm.…”

Section: Introductionmentioning

confidence: 99%

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Low-Rank Phase Retrieval

Vaswani

Nayer

Eldar

2017

IEEE Trans. Signal Process.

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Abstract-We develop two iterative algorithms for solving the low rank phase retrieval (LRPR) problem. LRPR refers to recovering a low-rank matrix X from magnitude-only (phaseless) measurements of random linear projections of its columns. Both methods consist of a spectral initialization step followed by an iterative algorithm to maximize the observed data likelihood. We obtain sample complexity bounds for our proposed initialization approach to provide a good approximation of the true X. When the rank is low enough, these bounds are significantly lower than what existing single vector phase retrieval algorithms need. Via extensive experiments, we show that the same is also true for the proposed complete algorithms.

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Section: Lrpr2: Low Rank Pr Via Alternating Minimizationmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

“…, q. (1) The measurement vectors, a i,k , are mutually independent. Our goal is to recover the matrix X from these mq phaseless measurements y i,k .…”

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Low-Rank Phase Retrieval

Vaswani

Nayer

Eldar

2017

IEEE Trans. Signal Process.

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“…The only results in the literature that are directly comparable to Theorem 1.3 are [25,26]. These works show how M 0 can be recovered using an alternating minimization or gradient descent algorithm.…”

Section: Statistical Analysis Of Decentralized Sketchingmentioning

confidence: 98%

Approximately low-rank recovery from noisy and local measurements by convex program

Lee¹,

Srinivasa²,

Junge³

et al. 2021

Preprint

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Low-rank matrix models have been universally useful for numerous applications starting from classical system identification to more modern matrix completion in signal processing and statistics. The nuclear norm has been employed as a convex surrogate of the low-rankness since it induces a low-rank solution to inverse problems. While the nuclear norm for low-rankness has a nice analogy with the ℓ 1 norm for sparsity through the singular value decomposition, other matrix norms also induce low-rankness. Particularly as one interprets a matrix as a linear operator between Banach spaces, various tensor product norms generalize the role of the nuclear norm. We provide a tensornorm-constrained estimator for recovery of approximately low-rank matrices from local measurements corrupted with noise. A tensor-norm regulizer is designed adapting to the local structure. We derive statistical analysis of the estimator over matrix completion and decentralized sketching through applying Maurey's empirical method to tensor products of Banach spaces. The estimator provides a near optimal error bound in a minimax sense and admits a polynomial-time algorithm for these applications.

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