Low rank phase retrieval

Nayer, Seyedehsara

doi:10.31274/etd-20210609-131

Cited by 3 publications

(5 citation statements)

References 58 publications

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“…Recall that g := Û U b is an rlength vector and, conditioned on Û , ãi iid ∼ N (0, I). If m > cr log 4 r/ 2 5 , then, conditioned on x and Û , w.p. ≥ 1 − 4/ m8 ,…”

Section: The Next Lemma Bounds Maxmentioning

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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“…Recall that g := Û U b is an rlength vector and, conditioned on Û , ãi iid ∼ N (0, I). If m > cr log 4 r/ 2 5 , then, conditioned on x and Û , w.p. ≥ 1 − 4/ m8 ,…”

Section: The Next Lemma Bounds Maxmentioning

confidence: 99%

“…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]. the old Gerchberg-Saxton algorithm [4].…”

Section: Introductionmentioning

confidence: 99%

Low-Rank Phase Retrieval

Vaswani

Nayer

Eldar

2017

IEEE Trans. Signal Process.

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“…We call such methods "unstructured" because they assume no structure in the images. Recently, Nayer et al proposed AltMinLowRaP [13], an algorithm that theoretically improved their previous algorithm AltMinTrunc [12,15], that both solved the unstructured low-rank phase retrieval problem. AltMinLowRaP involved alternately minimizing the factor matrices U ∈ C n×r and B ∈ C q×r that constructed the low-rank matrix X = UB * .…”

Section: Unstructured Low-rank Phase Retrievalmentioning

confidence: 99%

“…Recently, there has been a surge of interest in solving the low-rank phase retrieval problem [12][13][14][15][16]. This problem can be viewed as a dynamic extension of the standard phase retrieval problem, where the objective is to recover a matrix of vectorized images rather than a single image.…”

Section: Introductionmentioning

confidence: 99%

Low-Rank Phase Retrieval with Structured Tensor Models

Kwon¹,

Li²,

Sarwate³

2022

Preprint

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We study the low-rank phase retrieval problem, where the objective is to recover a sequence of signals (typically images) given the magnitude of linear measurements of those signals. Existing solutions involve recovering a matrix constructed by vectorizing and stacking each image. These algorithms model this matrix to be low-rank and leverage the low-rank property to decrease the sample complexity required for accurate recovery. However, when the number of available measurements is more limited, these low-rank matrix models can often fail. We propose an algorithm called Tucker-Structured Phase Retrieval (TSPR) that models the sequence of images as a tensor rather than a matrix that we factorize using the Tucker decomposition. This factorization reduces the number of parameters that need to be estimated, allowing for a more accurate reconstruction in the under-sampled regime. Interestingly, we observe that this structure also has improved performance in the over-determined setting when the Tucker ranks are chosen appropriately. We demonstrate the effectiveness of our approach on real video datasets under several different measurement models.

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“…One example where both claims of the above result are useful but the result of Theorem 5.39 (or of Remark 5.40) of [1] does not suffice is in analyzing the initialization step of our recently proposed low-rank phase retrieval algorithm [2], [3]. In fact this is where we first used this generalization.…”

Section: A An Example Application Of Theorem 21mentioning

confidence: 99%

A Simple Generalization of a Result for Random Matrices with Independent Sub-Gaussian Rows

Vaswani,

Nayer

2016

Preprint

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Low rank phase retrieval

Cited by 3 publications

References 58 publications

Low-Rank Phase Retrieval

Low-Rank Phase Retrieval

Low-Rank Phase Retrieval with Structured Tensor Models

A Simple Generalization of a Result for Random Matrices with Independent Sub-Gaussian Rows

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