Inexact alternating optimization for phase retrieval with outliers

Qian, Cheng; Fu, Xiao; Sidiropoulos, Nicholas D.

doi:10.1109/eusipco.2016.7760506

Cited by 1 publication

(5 citation statements)

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“…For phase retrieval under Gaussian noise, over the past few years, several CRBs have been derived for different models, e.g., 2-D Fourier-based measurements [19], noise added prior to taking the magnitude [20] and noise added after taking the magnitude square [11], [21]. To the best of our knowledge, there is no available CRB formula for the signal model in (1). Here, we present the CRBs for two particular types of noise: Laplacian and Gaussian noise.…”

Section: Cram éR-rao Bound Analysismentioning

confidence: 99%

“…The simulations show that our approaches outperform the state-of-the-art algorithms in the presence of impulsive noise. A preliminary conference version of part of this work has been submitted to EUSIPCO 2016 [1]. The conference version includes one of the two basic algorithms, the Laplacian CRB, and limited simulations.…”

Section: Introductionmentioning

confidence: 99%

“…The choice hinges on the experimental setup, including the measurement apparatus; but (1) is more widely adopted by experimentalists. Contributions: We consider the phase retrieval problem under the model in (1) in the presence of impulsive noise, and focus on designing robust algorithms to handle it. To fend against impulsive noise, we adopt the p -fitting (0 < p < 2) based estimator that is known to be effective in dealing with outliers, and devise two optimization algorithms using twoblock inexact alternating optimization.…”

Section: Introductionmentioning

confidence: 99%

“…We also derive computationally light implementations using Nesterov-type and stochastic gradient updates. In order to assist in performance analysis and experimental design, we derive the CRB for the model in (1) and under different parameterizations, in the presence of Laplacian and Gaussian noise. Curiously, although related CRBs for different noisy measurement models have been previously derived in [11], [19]- [22], to the best of our knowledge, there is no available CRB for the model in (1) -and our work fills this gap.…”

Section: Introductionmentioning

confidence: 99%

“…A preliminary conference version of part of this work has been submitted to EUSIPCO 2016 [1]. The conference version includes one of the two basic algorithms, the Laplacian CRB, and limited simulations.…”

Section: Introductionmentioning

confidence: 99%

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Inexact Alternating Optimization for Phase Retrieval in the Presence of Outliers

Qian

Sidiropoulos

et al. 2017

IEEE Trans. Signal Process.

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Abstract-Phase retrieval has been mainly considered in the presence of Gaussian noise. However, the performance of the algorithms proposed under the Gaussian noise model severely degrades when grossly corrupted data, i.e., outliers, exist. This paper investigates techniques for phase retrieval in the presence of heavy-tailed noise -which is considered a better model for situations where outliers exist. An p-norm (0 < p < 2) based estimator is proposed for fending against such noise, and twoblock inexact alternating optimization is proposed as the algorithmic framework to tackle the resulting optimization problem. Two specific algorithms are devised by exploring different local approximations within this framework. Interestingly, the core conditional minimization steps can be interpreted as iteratively reweighted least squares and gradient descent. Convergence properties of the algorithms are discussed, and the Cramér-Rao bound (CRB) is derived. Simulations demonstrate that the proposed algorithms approach the CRB and outperform stateof-the-art algorithms in heavy-tailed noise.

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