Optical single pixel detection for compressive sensing with unitary circulant matrices

Compressive sensing (CS) is a rapidly developing field of mathematics and signal processing with important contributions to the introduction of novel measurement methodologies and information recovery techniques in numerous fields of science and technology. Optical applications of CS include single pixel cameras for hyperspectral imaging, THz imaging, 3D imaging, and polarimetric imaging, phase recovery, compressive holography etc. In this paper we report on optical single-pixel detection for the direct reconstruction of a linearly filtered signal based on Walsh-Hadamard compressive measurements. For this purpose we propose a fast and efficient image reconstruction method which utilizes unitary circulant matrices at the reconstruction stage. Experimental results are obtained with a DMD-based single-pixel detector operating at visible frequencies.