基于复波前边缘稀疏性的Gini指数和Tamura系数的全息自聚焦比较
Comparison of Gini index and Tamura coefficient for holographic autofocusing based on the edge sparsity of the complex optical wavefront
摘要：
梯度稀疏度（SoG）是一种稳健的全息自聚焦准则，它计算复重聚焦全息图的梯度模量，并在其上应用稀疏度度量。在这里，我们比较了SoG中使用的两种不同的稀疏性度量选择，特别是基尼指数（GI）和田村系数（TC），用于密集/连接或稀疏样本的全息自动聚焦。我们提供了一个理论分析预测，对于均匀分布的图像数据，TC和GI表现出类似的行为，而对于自然稀疏的图像，包含一些高值的信号条目和许多低值的噪声背景像素，TC是更敏感的分布变化的信号和更耐背景噪声。这些预测也得到了实验结果的证实，实验结果使用基于SOG的全息自动聚焦在密集和连接的样本（如染色的乳腺组织切片）以及高度稀疏的样本（如孤立的贾第鞭毛虫囊肿）。通过这些实验，我们发现ToG和GoG在密集和连接的样本上提供几乎相同的自动聚焦性能，而对于自然稀疏的样本，GoG应该在紧密围绕对象的相对较小的感兴趣区域（ROI）上计算，而ToG在选择包含更多背景像素的较大ROI方面提供了更大的灵活性。
英文摘要：
The Sparsity of the Gradient (SoG) is a robust autofocusing criterion for holography, where the gradient modulus of the complex refocused hologram is calculated, on which a sparsity metric is applied. Here, we compare two different choices of sparsity metrics used in SoG, specifically, the Gini index (GI) and the Tamura coefficient (TC), for holographic autofocusing on dense/connected or sparse samples. We provide a theoretical analysis predicting that for uniformly distributed image data, TC and GI exhibit similar behavior, while for naturally sparse images containing few high-valued signal entries and many low-valued noisy background pixels, TC is more sensitive to distribution changes in the signal and more resistive to background noise. These predictions are also confirmed by experimental results using SoG-based holographic autofocusing on dense and connected samples (such as stained breast tissue sections) as well as highly sparse samples (such as isolated Giardia lamblia cysts). Through these experiments, we found that ToG and GoG offer almost identical autofocusing performance on dense and connected samples, whereas for naturally sparse samples, GoG should be calculated on a relatively small region of interest (ROI) closely surrounding the object, while ToG offers more flexibility in choosing a larger ROI containing more background pixels.
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