Pseudo complementary measurement for traditional single-pixel cameras

A traditional single-pixel camera needs a large number of measurements to reconstruct the object with compressive sensing computation. Compared with the 1/0 matrices in classical measurement, the 1/-1 matrices in the complementary measurement has better property for reconstruction computation and returns better reconstruction results. However, each row of the 1/-1 matrices needs two measurements with the traditional single-pixel camera which results into double measurements compared with the 1/0 matrices. In this paper, we consider the pseudo complementary measurement which only takes the same amount of measurements with the row number of some properly designed 1/0 matrix to compute the total luminous flux of the objective and derives the measurement data of the corresponding 1/-1 matrix in a mathematical way. The numerical simulation and experimental result show that the pseudo complementary measurement is an efficient tool for the traditional single-pixel camera imaging under low measurement rate, which can combine the advantages of the classical and complementary measurements and significantly improve the peak signal-to-noise ratio.