Compressive phase-only filtering at extreme compression rates

We introduce an efficient method for the reconstruction of the correlation between a compressively measured image and a phase-only filter (POF). The proposed method is based on two properties of POF: such filtering is a unitary circulant transform, and the correlation plane it produces is usually sparse. The method can be applied to the measurements from single-pixel detectors, which opens a way for adding some functionalities of an optical correlator to these kind of cameras at no additional computational expense. We show that images measured at extremely high compression rates may still contain sufficient information for target classification and localization.