噪声数据的多频相位恢复
Multi-frequency phase retrieval from noisy data
摘要：
考虑了多频强度（功率）观测的相位反演问题。要重建的对象是复值的。提出了一种新的算法，实现了对象相位（绝对相位）检索和去噪泊松和高斯测量。该算法是来自最大似然公式与块匹配3D（BM3D）稀疏先验。这些先验导致两个滤波：一个是在复值多频对象图像的复域中，另一个是在实域中的对象相位。该算法是迭代的对象和测量变量之间的交替投影。对物体的傅里叶变换成像和随机相位调制进行了模拟实验，得到了随机物体衍射图样。结果表明，该算法的成功重建的复杂相位的对象具有高精度的性能，即使是非常嘈杂的数据。
英文摘要：
The phase retrieval from multi-frequency intensity (power) observations is considered. The object to be reconstructed is complex-valued. A novel algorithm is presented that accomplishes both the object phase (absolute phase) retrieval and denoising for Poissonian and Gaussian measurements. The algorithm is derived from the maximum likelihood formulation with Block Matching 3D (BM3D) sparsity priors. These priors result in two filtering: one is in the complex domain for complex-valued multi-frequency object images and another one in the real domain for the object phase. The algorithm is iterative with alternating projections between the object and measurement variables. The simulation experiments are produced for Fourier transform image formation and random phase modulations of the object, then the observations are random object diffraction patterns. The results demonstrate the success of the algorithm for reconstruction of the complex phase objects with the high-accuracy performance even for very noisy data.
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