Real-Time Compressive Sensing Framework Using 2D Hadamard Total Sequency Ordering

Compressive sensing (CS) has emerged as a powerful framework for reducing the number of measurements required for accurate image reconstruction, making it especially relevant in applications such as medical imaging, wireless sensing, and single-pixel imaging. In CS, deterministic transforms like the Hadamard basis offer advantages in efficiency and hardware implementation. However, achieving high-quality reconstruction at low sampling ratios remains challenging, particularly because traditional random or fixed-order sampling patterns introduce redundancy and limit reconstruction performance. Existing Hadamard reordering methods, such as Walsh, cake-cutting, and weight ordering, partially address these issues but still struggle to balance reconstruction quality with computational efficiency in real-time or resource-limited environments. Deep learning-based CS approaches improve reconstruction accuracy but require large training datasets, high computational cost, and powerful hardware. To address these limitations, this study introduces a Total Sequency (TS)–based reordering of the Hadamard matrix, which prioritizes two-dimensional low-frequency patterns by counting sign changes across both rows and columns. This approach enhances sampling efficiency at very low sampling ratios while maintaining extremely low computational overhead. Integrated into a block-based CS pipeline, the proposed method delivers improved reconstruction accuracy at low sampling ratios, achieving average PSNR values of 19.61 dB, 22.21 dB, and 24.38 dB at sampling ratios of 0.01, 0.04, and 0.1, outperforming Walsh, cake-cutting, and weight ordering methods. Furthermore, it provides near-real-time reconstruction with processing times as low as 0.0014 seconds on a standard CPU, significantly faster than deep learning models such as CPP-Net. These findings demonstrate that TS-based Hadamard reordering bridges the gap between deterministic CS sampling and computational efficiency, making it highly suitable for portable imaging devices, wireless sensor networks, and other real-time, resource-constrained platforms.