Template matching (TM) is a common methodology for target detection (TD) which allows detecting a target based on cross-correlation analysis between a reference pattern and the scene. State-of-the-art TD approaches do not consider the optical phase of the target as a discriminant in the detection process, because to recover the phase involves solving a computationally demanding inverse problem known as phase retrieval (PR). However, in applications such as microscopy and optical imaging, the optical phase contains valuable information that describes the shape and depth of the object. This work proposes a method for fast TD via TM, which considers the optical phase of the object in the reference pattern as a discriminant in a setup that records coded phaseless measurements (CPM). Specifically, the proposed TD methodology is established for far-field imaging. This approach consists of two steps: (i) fast approximation of the optical field from CPM based on compressive PR, including its optical phase information; (ii) cross-correlation analysis to detect the target using its optical phase. The approximation of the optical field considering its phase is performed by low-pass-filtering the leading eigenvector of a designed matrix, overcoming traditional approaches in terms of relative error. Since no explicit TD methodology that includes the optical phase as a discriminant exists in the literature, the proposed approach is compared to a method that reconstructs the optical field and then performs the detection step. Numerical results suggest that the proposed methodology detects a target under noisy scenarios using up to $\text{75}\%$ fewer measurements in the tested datasets. Also, the proposed TD using the filtered spectral method reduces the detection time in up to $\text{79}\%$ in the tested datasets, compared to a methodology that requires the reconstruction of the phase.

中文翻译：

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在压缩相位检索中通过模板匹配进行快速目标检测

模板匹配 (TM) 是一种常见的目标检测 (TD) 方法，它允许基于参考模式和场景之间的互相关分析来检测目标。最先进的 TD 方法在检测过程中不考虑目标的光学相位作为判别式，因为恢复相位涉及解决称为相位检索 (PR) 的计算要求高的逆问题。然而，在显微镜和光学成像等应用中，光学相位包含描述物体形状和深度的有价值的信息。这项工作提出了一种通过 TM 进行快速 TD 的方法，该方法将参考图案中物体的光学相位视为记录编码无相测量 (CPM) 的设置中的判别式。具体来说，提出的 TD 方法是为远场成像建立的。该方法包括两个步骤：（i）基于压缩 PR 的 CPM 光场的快速逼近，包括其光相位信息；(ii) 互相关分析以使用其光学相位检测目标。考虑其相位的光场近似是通过对设计矩阵的前导特征向量进行低通滤波来执行的，在相对误差方面克服了传统方法。由于文献中不存在将光相位作为判别式的明确 TD 方法，因此将所提出的方法与重建光场然后执行检测步骤的方法进行比较。数值结果表明，所提出的方法在测试数据集中使用最多 $\text{75}\%$ 更少的测量值来检测噪声场景下的目标。此外，与需要重建相位的方法相比，所提出的使用滤波光谱方法的 TD 在测试数据集中减少了高达 $\text{79}\%$ 的检测时间。