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.

作为高质量的成像方案，一维沃尔什变换重影的采样和重建在数学上等效于一维沃尔什变换，即单矩阵乘法。众所周知，与一维沃尔什变换相比，二维沃尔什变换在简化计算和增强能量集中方面具有优势。但是，二维沃尔什变换不能很好地适应一维成像系统，因为它需要将矩阵乘法执行两次。为了解决这个问题，我们采用“最自然的”沃尔什阶基础图案来获得桶检测值，因此一维采样过程的效果与二维沃尔什变换的效果相同。基于这种等效关系，该方案可以准确地恢复图像。数值模拟和实验结果表明，二维沃尔什变换重影成像能够以较少的系数重建清晰的图像。此外，我们提出了一种用于2D Walsh变换的快速算法，事实证明，该算法比1D快速Walsh变换需要更少的重建时间。我们致力于构建一个高效的成像系统，该系统可以在采样和重建中节省尽可能多的时间。从实际的角度来看，可以在实时和低分辨率视频成像中找到更广泛的应用。我们致力于构建一个高效的成像系统，该系统可以在采样和重建中节省尽可能多的时间。从实际的角度来看，可以在实时和低分辨率视频成像中找到更广泛的应用。我们致力于构建一个高效的成像系统，该系统可以在采样和重建中节省尽可能多的时间。从实际的角度来看，可以在实时和低分辨率视频成像中找到更广泛的应用。