Single Pixel Imaging Based on Bicubic Interpolation Walsh Transform Matrix

Single pixel imaging is a new method, but imaging quality and speed are the main factors affecting its practicality. Building upon the attributes of the random measurement and deterministic matrices, a Walsh transformation matrix with bicubic interpolation is proposed. This matrix is formulated by integrating the Walsh matrix and a pseudo-random diagonal matrix using a structured construction method alongside bicubic interpolation. The structure of matrix and the effect of single pixel imaging using matrix are simulated and analyzed. The imaging effects of Gaussian, Bernoulli, Topeliz and bicubic interpolation Walsh transform matrix are simulated and analyzed. A single pixel experimental system is set up for experimental verification. The results show that the quality of reconstructed images with bicubic interpolation Walsh transformation matrix is better than that of bicubic interpolation Gold matrix and bicubic interpolation Walsh matrix, and there is no energy concentration in reconstructed images. The results indicate that, under a 25% low sampling rate, obtaining the image of the target object is achievable through a Walsh transformation matrix with bicubic interpolation. Additionally, the imaging performance of the Peudo-random measurement-Walsh Gold (PRM-WG) matrix is better than that of Peudo-random measurement-Hadamard Gold (PRM-HG), and Peudo-random measurement-Like_Walsh Gold (PRM-LG) matrices. These research insights contribute to optimizing single pixel imaging efficiency and lay a theoretical groundwork for advancing the real-world applications of single pixel imaging.