Fast Target Detection via Template Matching in Compressive Phase Retrieval

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.