Phase retrieval: A data-driven wavelet frame based approach

Pang, Tongyao; Li, Qingna; Wen, Zaiwen; Shen, Zuowei

doi:10.1016/j.acha.2019.05.004

Cited by 6 publications

(4 citation statements)

References 32 publications

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“…Furthermore, combining the average running time listed in Table 1, we can see that our methods still have the advantage of time consumption. From the compared results of the DDWF [34], i.e., for the kind of image (2D projection slices of the caffeine molecule) in Fig. 8, we also have better phase retrieval results.…”

Section: Convergence Behaviormentioning

confidence: 70%

“…However, due to the different measurements, we compare the proposed method with TVB [11] under mask Eq. ( 3), and the proposed model with RAAR [30], RAF [48], RWF [52], TAF [47], CDA [54], HIO [19], TWF [15], WF [9] and DDWF [34] with DCP measurement Eq. ( 4).…”

Section: Convergence Behaviormentioning

confidence: 99%

“…In [35], the low-complexity algorithms with a superior performance based on the majorization-minimization (MM) framework was proposed to handle the phase retrieval problem. In [34], the proximal alternating linearization algorithm was employed to handle the phase retrieval model. However, the convergence of their algorithm was guaranteed under some assumptions.…”

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confidence: 99%

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Finding robust minimizer for non-convex phase retrieval

Wu¹,

Huang²,

Gu³

et al. 2024

IPI

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The phase retrieval task has received considerable attention in recent years. Here, phase retrieval refers to the problem of recovering the clear image from magnitude-only data of its Fourier transform, or other linear transforms. As the observed magnitude signal is usually corrupted by heavy noise, retrieving the original object is rather difficult. In this paper, we investigate a regularization-based framelet method to recover the phase information and alleviate the influence of noise. Indeed, since phase retrieval is usually modeled by a non-convex model, how to find the solution efficiently is an intricate challenge. For this reason, we first reformulate the objective function as the difference between two convex functions. By introducing the boosted difference of convex algorithm (BDCA), the proposed scheme has good performance in handling the phase retrieval problem. Theoretically, we also present the convergence analysis of the numerical algorithm. To exhibit the effectiveness of our approach, we consider two classical regularizers with the proposed framework. Besides, two different measurement models are carefully studied to illustrate the robustness of our scheme. Numerical experiments demonstrate clearly that the proposed framelet method is effective and robust in tackling the non-convex phase retrieval task.

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Section: Convergence Behaviormentioning

confidence: 70%

Section: Convergence Behaviormentioning

confidence: 99%

mentioning

confidence: 99%

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Finding robust minimizer for non-convex phase retrieval

Wu¹,

Huang²,

Gu³

et al. 2024

IPI

View full text Add to dashboard Cite

show abstract

“…Bao et al showed the sub-sequence convergence of the iterative algorithm in [3], and gave a new globally convergent algorithm. Soon later, this data-driven tight frame model has been improved and applied to various problems [13,22,27,32,33,37,42,44]. However, as far as we know, these data-driven models mainly use L 2 fidelity, which is not suitable for the basic and significant impulsive noise removal problems.…”

Section: Introductionmentioning

confidence: 99%