Abstract
Single-pixel imaging (SPI) based on Hadamard multiplexing enables efficient image acquisition with a reduced number of measurements, but its performance critically depends on the choice of subsampling strategy. In this work, we conduct a comprehensive evaluation of subsampling strategies for compressive Hadamard SPI, aiming to identify the method that selects the best-suited subset of Hadamard basis vectors. Natural images are known to contain most of their information in low spatial frequencies. Hence, the motivation for subsampling low-sequency patterns first, where sequency is the Hadamard analog of spatial frequency and corresponds to the number of sign changes in a Hadamard pattern, is intuitive but lacks theoretical grounding. This motivates the evaluation of multiple strategies which combine known subsampling schemes—deterministic, variable density sampling, and multilevel density sampling—with several reorderings of the Hadamard basis elements. These follow specific metrics defined on the Hadamard basis, including sequency, total variation, cake-cutting, and to our knowledge a novel data-driven variance-based ordering. In addition, spread spectrum and scrambled Hadamard approaches, relying on a randomization of the Hadamard basis, are considered. The performance of these strategies is assessed across different sampling ratios, Gaussian noise levels, and reconstruction methods, including pseudoinverse, ISTA, and a deep-learning-based approach (PinvNet), both on simulations and on an actual SPI setup. Results on a common, large dataset of images (BSDS500) indicate that deterministic selection of informative Hadamard patterns consistently outperforms probabilistic and randomized compressive sensing strategies. The proposed variance-based ordering achieves state-of-the-art performance for linear and sparsity-based reconstructions, while sequency ordering remains competitive for deep-learning-based reconstruction. These findings highlight the importance of selecting the most informative Hadamard patterns and open the way to data-driven approaches to assess their information content.