Deep Compressive Single Pixel Imaging by Reordering Hadamard Basis: A Comparative Study

Single pixel imaging (SPI) combined with compressed sensing techniques can provide solutions for special optical imaging to avoid array detectors and raster scanning. However, the imaging speed should be further improved for real-time SPI and the challenge is to reduce the sampling time and post-processing time. This paper proposes a deep compressive and super-fast single pixel imaging protocol based on reordering Hadamard basis patterns and Fourier domain regularization inversion (FDRI) algorithm. Two reordered Hadamard basis patterns in terms of the improvement in the compressing ratio and reconstruction quality are proposed and compared to other methods. The deterministic Hadamard basis are reordered through their total variation (TV) in ascending order and total wavelet transformed coefficients (TW) in ascending order to have the best performance. Numerical simulation shows that this protocol can reconstruct a
$128\times 128$
pixels natural image at the sampling ratio of 5% with the peak-signal-to-noise ratio (PSNR) of 25.56 dB in 0.00039s. Terahertz near-field imaging experiment also verifies the proposed protocol. The inherent advantage and mechanism of reordering approaches are discussed and then revealed by comparing the coherent area generated by these reordered patterns. The TV order and TW order Hadamard basis patterns can be deterministically described mathematically and easily constructed. Meanwhile, it results in a significant improvement both in the compression ratio and image reconstruction quality. Finally, the realization this protocol in real SPI system in the future will bring the real-time SPI closer to practical applications.