Single-pixel imaging with Gao-Boole patterns

Single-pixel imaging (SPI) can perceive the world using only a single-pixel detector, but long sampling times with a series of patterns are inevitable for SPI, which is the bottleneck for its practical application. Developing new patterns to reduce the sampling times might provide opportunities to address this challenge. Based on the Kronecker product of Hadamard matrix, we here design a complete set of new patterns, called Gao-Boole patterns, for SPI. Compared to orthogonal Hadamard basis patterns with elements valued as +1 or -1, our Gao-Boole patterns are non-orthogonal ones and the element values are designed as +1 or 0. Using our Gao-Boole patterns, the reconstructed quality of a target image (N × N pixels) is as high as the Hadamard one but only with half pattern numbers of the Hadamard ones, for both full sampling (N² for Gao-Boole patterns, 2N² for Hadamard basis patterns) and undersampling cases in experiment. Effectively reducing the patterns numbers and sampling times without sacrificing imaging quality, our designed Gao-Boole patterns provide a superior option for structural patterns in SPI and help to steer SPI toward practical imaging application.