Separable Hadamard single-pixel imaging for high-resolution reconstruction

Hadamard single-pixel imaging (HSI) is an attractive computational imaging technique. However, existing approaches suffer from prohibitive data throughput and computational time, making high-resolution image reconstruction challenging. To overcome this bottleneck, we proposed a separable HSI (SHSI) model that drastically reduces storage and accelerates imaging speed, offering a novel, to the best of our knowledge, strategy for efficient high-resolution reconstruction. We first investigated the transformation relationship between Hadamard spectrum distribution and a bidirectional compressed sensing model and proved that a 2D sampling mask can be decomposed into specific combinations of 1D vectors from separable measurement matrices. Based on this, we further developed an iterative alternating optimization algorithm for solving the optimal separable sampling strategy. By exploiting the dual constraints of Hadamard spectrum characteristics and the measurement matrix, the algorithm decomposes 2D sampling masks into separable 1D vectors, enabling a real-time pattern generation with ultra-low storage and computational overhead. Simulations and experiments demonstrate that the proposed method enables high-efficiency and high-resolution (1024 × 1024) image reconstruction.