High-efficiency reconstruction of ghost imaging based on equivalent deformation of 2D Walsh transform

As a high-quality imaging scheme, the sampling and reconstruction of 1D Walsh transform ghost imaging is mathematically equivalent to 1D Walsh transform, i.e. single matrix multiplication. It is widely acknowledged that compared with the 1D Walsh transform, the 2D Walsh transform is advantageous in terms of simpler calculation and stronger energy concentration. However, the 2D Walsh transform cannot adapt well to 1D imaging systems because it requires matrix multiplication to be carried out twice. To address this problem, we employ the 'most natural' Walsh order basis patterns to obtain the bucket detection value, so that the effect of the 1D sampling process is the same as that in the 2D Walsh transform. Based on this relationship of equivalence, this scheme can recover the image accurately. Numerical simulations and experimental results demonstrate that 2D Walsh transform ghost imaging is capable of reconstructing a sharp image with fewer coefficients. Moreover, we propose a fast algorithm for the 2D Walsh transform, which is proven to require less reconstruction time than the 1D fast Walsh transform. We are committed to building an efficient imaging system that can save as much time as possible in both sampling and reconstruction. From a practical point of view, a broader application may be found in real-time and low-resolution video imaging. (paper)