Direct Single-Step Measurement of Hadamard Spectrum Using Single-Pixel Optical Detection

Spectrum can be acquired by Hadamard transform, and the spectrum energy concentrates on the upper-left corner according to the chosen Walsh-ordering Hadamard bases. Hence, measurement of the main spectrum coefficients can facilitate the reconstruction of objects. In this letter, we propose a method for directly calculating each Hadamard spectrum coefficient using only single-step measurement in single-pixel imaging (SPI) for high-contrast object reconstruction. The proposed method can significantly reduce the number of measurements in the SPI. In addition, an effective noise suppression strategy is further developed to recover high-contrast objects. The proposed method in the SPI is also tested in scattering environment. Experimental work is conducted to verify the feasibility and effectiveness of the proposed method.