Phase retrieval from STFT measurements via non-convex optimization

Bendory, Tamir; Eldar, Yonina C.

doi:10.1109/icassp.2017.7953062

Cited by 7 publications

(6 citation statements)

References 30 publications

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“…, where f d j is the j th Fourier vector in C d and γ ∈ R d has support [δ] produces an invertible system under a very mild condition. We further prove that this condition holds for almost all γ; this result is particularly interesting considering that γ ∈ C d has δ degrees of freedom, but must generate a spanning set for a subspace of dimension d(2δ − 1) when all shifts are taken in (7).…”

Section: Organization and Contributionsmentioning

confidence: 69%

“…Among the first treatments of local measurements are [7,20,33], in which it is shown that STFT (short-time Fourier transform [2,48]) measurements with specific properties can allow (sparse) phase retrieval in the noiseless setting, and several recovery methods have been proposed [9,27]. Similarly, the phase retrieval approach from [1] was extended to STFT measurements in [53] in order to produce recovery guarantees in the noiseless setting.…”

Section: Related Workmentioning

confidence: 99%

“…Herein we focus on the setup described in Section 1.2, while also accounting for noise as in (2). Thus, by design, it is clear that the vectors {S m j m * j S − } are all contained in the subspace T δ (H d ) of H d (defined in (7)), where d is the ambient dimension (meaning x 0 , m j ∈ C d ) and δ is the support size of the masks (so supp(m j ) ⊆ [δ]). Following the framework of Algorithm 1 we now focus on the linear system (9).…”

Section: Invertible Local Measurement Systemsmentioning

confidence: 99%

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Admissible Measurements and Robust Algorithms for Ptychography

Preskitt¹,

Saab²

2019

Preprint

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We study an approach to solving the phase retrieval problem as it arises in a phase-less imaging modality known as ptychography. In ptychography, small overlapping sections of an unknown sample (or signal, say x 0 ∈ C d ) are illuminated one at a time, often with a physical mask between the sample and light source. The corresponding measurements are the noisy magnitudes of the Fourier transform coefficients resulting from the pointwise product of the mask and the sample. The goal is to recover the original signal from such measurements.The algorithmic framework we study herein relies on first inverting a linear system of equations to recover a fraction of the entries in x 0 x * 0 and then using non-linear techniques to recover the magnitudes and phases of the entries of x 0 . Thus, this paper's contributions are three-fold. First, focusing on the linear part, it expands the theory studying which measurement schemes (i.e., masks, shifts of the sample) yield invertible linear systems, including an analysis of the conditioning of the resulting systems. Second, it analyzes a class of improved magnitude recovery algorithms and, third, it proposes and analyzes algorithms for phase recovery in the ptychographic setting where large shifts -up to 50% the size of the mask -are permitted.

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Section: Organization and Contributionsmentioning

confidence: 69%

Section: Related Workmentioning

confidence: 99%

Section: Invertible Local Measurement Systemsmentioning

confidence: 99%

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Admissible Measurements and Robust Algorithms for Ptychography

Preskitt¹,

Saab²

2019

Preprint

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“…In this generation process of image data, time series from tests are transformed into frequency spectrums by using short-time Fourier transform (STFT). For an original discrete signal sequence x(n), a pre-determined window function is used to divide the time series into many segments, and it is assumed the signal is pseudo-stationary over a short interval, and then Fourier transform is carried out on each window length (Bendory et al, 2017;Rashid and Louis, 2020). The transform process of STFT is shown in Figure 3.…”

Section: Generation Of Spectrum Image Datamentioning

confidence: 99%

A Novel Piezoceramic-Based Sensing Technology Combined With Visual Domain Networks for Timber Damage Quantification

et al. 2021

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Early detection of timber damage is essential for the safety of timber structures. In recent decades, wave-based approaches have shown great potential for structural damage assessment. Current damage assessment accuracy based on sensing signals in the time domain is highly affected by the varied boundary conditions and environmental factors in practical applications. In this research, a novel piezoceramic-based sensing technology combined with a visual domain network was developed to quantitatively evaluate timber damage conditions. Numerical and experimental studies reveal the stress wave propagation properties in different cases of timber crack depths. Through the spectrogram visualization process, all sensing signals in the time domain were transferred to images which contain both time and frequency features of signals collected from different crack conditions. A deep neural network (DNN) was adopted for image training, testing, and classification. The classification results show high efficiency and accuracy for identifying crack conditions for timber structures. The proposed technology can be further integrated with a fielding sensing system to provide real-time monitoring of timber damage in field applications.

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“…Then we apply Algorithm 1 to search for the solution of (13). In Algorithm 1, λ is the step size calculated by the backtracking method which can be seen in Algorithm 2.…”

Section: Algorithm For the Phase Retrieval With Background Informationmentioning

confidence: 99%

Phase retrieval with background information

Yuan

Wang

2019

Inverse Problems

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Phase retrieval problem has been studied in various applications. It is an inverse problem without the standard uniqueness guarantee. To make complete theoretical analyses and devise efficient algorithms to recover the signal is sophisticated. In this paper, we come up with a model called phase retrieval with background information which recovers the signal with the known background information from the intensity of their combinational Fourier transform spectrum. We prove that the uniqueness of phase retrieval can be guaranteed even considering those trivial solutions when the background information is sufficient. Under this condition, we construct a loss function and utilize the projected gradient descent method to search for the ground truth. We prove that the stationary point is the global optimum with probability 1. Numerical simulations demonstrate the projected gradient descent method performs well both for 1-D and 2-D signals. Furthermore, this method is quite robust to the Gaussian noise and the bias of the background information.

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Phase retrieval from STFT measurements via non-convex optimization

Cited by 7 publications

References 30 publications

Admissible Measurements and Robust Algorithms for Ptychography

Admissible Measurements and Robust Algorithms for Ptychography

A Novel Piezoceramic-Based Sensing Technology Combined With Visual Domain Networks for Timber Damage Quantification

Phase retrieval with background information

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