Iterative projection approach for phase retrieval of semi-sparse wave field

Fan, Rong; Wan, Qun; Wen, Fei; Chen, Hui; Liu, Yipeng

doi:10.1186/1687-6180-2014-24

Cited by 3 publications

(3 citation statements)

References 24 publications

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“…(27b) compared with the use of soft thresholding, for the remainder of this paper we will consider the use only of hard thresholding. We note that other algorithms exist that successfully use soft thresholding to promote sparsity [30,25,31]. We further note as a reminder that the use of soft thresholding comes from ℓ = 1 regularization as a sparsity-inducing term and that its use is as a convex and continuous relaxation of ℓ = 0 regularization in order to make the problem simpler to analyze; both regularization terms are effective at promoting sparsity to varying degrees depending on the particulars of the phase retrieval algorithm used and type of sparsifying transformation.…”

Section: Benchmarkingmentioning

confidence: 99%

Single-view phase retrieval of an extended sample by exploiting edge detection and sparsity

et al. 2016

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We propose a new approach to robustly retrieve the exit wave of an extended sample from its coherent diffraction pattern by exploiting sparsity of the sample's edges. This approach enables imaging of an extended sample with a single view, without ptychography. We introduce nonlinear optimization methods that promote sparsity, and we derive update rules to robustly recover the sample's exit wave. We test these methods on simulated samples by varying the sparsity of the edge-detected representation of the exit wave. Our tests illustrate the strengths and limitations of the proposed method in imaging extended samples.

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Section: Benchmarkingmentioning

confidence: 99%

Single-view phase retrieval of an extended sample by exploiting edge detection and sparsity

et al. 2016

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“…So far, all issues in the process of handing problem (11) have been solved. We update the variable x, z, y at the tth iteration by solving subproblems (12), (15), and (21), and update u 1 , u 2 by (23) iteratively. To monitor the convergence of our algorithm, we utilize the relative residual norm defined by [19] res ¼ jjjFx…”

Section: Y Subproblemmentioning

confidence: 99%

“…Recently, the sparsity prior for PR is focused by researchers [8][9][10][11][12]. Theoretically, the sparsity prior can be incorporated into the object constraint of any alternative projection algorithm to improve the performance.…”

Section: Introductionmentioning

confidence: 99%

Sparse representation utilizing tight frame for phase retrieval

Shi

Lian

Chen

2015

EURASIP J. Adv. Signal Process.

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We treat the phase retrieval (PR) problem of reconstructing the interest signal from its Fourier magnitude. Since the Fourier phase information is lost, the problem is ill-posed. Several techniques have been used to address this problem by utilizing various priors such as non-negative, support, and Fourier magnitude constraints. Recent methods exploiting sparsity are developed to improve the reconstruction quality. However, the previous algorithms of utilizing sparsity prior suffer from either the low reconstruction quality at low oversampled factors or being sensitive to noise. To address these issues, we propose a framework that exploits sparsity of the signal in the translation invariant Haar pyramid (TIHP) tight frame. Based on this sparsity prior, we formulate the sparse representation regularization term and incorporate it into the PR optimization problem. We propose the alternating iterative algorithm for solving the corresponding non-convex problem by dividing the problem into several subproblems. We give the optimal solution to each subproblem, and experimental simulations under the noise-free and noisy scenario indicate that our proposed algorithm can obtain a better reconstruction quality compared to the conventional alternative projection methods, even outperform the recent sparsity-based algorithms in terms of reconstruction quality.

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