Phase retrieval from incomplete data via weighted nuclear norm minimization
Phase retrieval from incomplete data via weighted nuclear norm minimization
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DOI：
10.1016/j.patcog.2022.108537
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发表时间：
2022-01
期刊：
影响因子：
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通讯作者：
Zhi Li;Ming Yan;T. Zeng;Guixu Zhang
中科院分区：
文献类型：
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作者：
Zhi Li;Ming Yan;T. Zeng;Guixu Zhang
从傅立叶变换的幅度中恢复未知物体是一个相位检索问题。在这里，我们考虑一个非常困难的情况，其中观察到的强度值不完整，并且受到椒盐噪声和随机值脉冲噪声的污染。为了利用对象图像内的低秩属性，我们使用正则化项来惩罚图像块组的高加权核范数值。对于观测中的异常值（脉冲噪声），采用 ℓ 1− 2 度量作为数据保真度项。然后我们将得到的优化问题分解为更小的问题，例如加权核范数近端映射和 ℓ 1− 2 最小化，因为非凸和非光滑子问题具有可用的封闭式解。还给出了收敛结果，并提供了数值实验来证明该方法的优越的重建质量。
Recovering an unknown object from the magnitude of its Fourier transform is a phase retrieval problem. Here, we consider a much difficult case, where those observed intensity values are incomplete and contaminated by both salt-and-pepper and random-valued impulse noise. To take advantage of the low-rank property within the image of the object, we use a regularization term which penalizes high weighted nuclear norm values of image patch groups. For outliers (impulse noise) in the observation, the ℓ 1− 2 metric is adopted as the data fidelity term. Then we break down the resulting optimization problem into smaller ones, for example, weighted nuclear norm proximal mapping and ℓ 1− 2 minimization, because the nonconvex and nonsmooth subproblems have available closed-form solutions. The convergence results are also presented, and numerical experiments are provided to demonstrate the superior reconstruction quality of the proposed method.