Fast single-pixel imaging based on optimized reordering Hadamard basis

Abstract

Single-pixel imaging is a computational imaging scheme that offers novel solutions for multi-spectral imaging, feature-based imaging, polarimetric imaging, three-dimensional imaging, holographic imaging, and optical encryption. The single-pixel imaging scheme can be used for imaging in wave band such as infrared and micro wave imaging, or will be useful in the case where the array detector technique is difficult to meet the requirement such as the sensitivity or the volume. The main limitation for its application comes from a trade-off between spatial resolution and acquisition time, in other words, from relatively high measurement and reconstruction time. Although compressive sensing technique can be used to improve the acquisition time by reducing the number of samplings, the computational time to reconstruct an image is not fast enough to satisfy the real-time video. In this paper, we propose to reduce the required signal acquisition time by using a novel sampling scheme based on optimized ordering of the Hadamard basis, and improve the image reconstruction efficiency by using fast Walsh-Hadamard transform. In our method, the Hadamard basis is rearranged in the ascendant order of the values of its " sparsity” coefficients which are obtained through " Daubechies wavelets 1 (Haar wavelets)”, " Daubechies wavelets 2” wavelet transform and discrete cosine transform, and then compute each total sum of the transformed coefficients’ absolute value, respectively. The measurement order of the Hadamard basis is then rearranged directly according to Walsh order and random permutation order. The peak signal-to-noise ratio (PSNR) and structural similarity index (SSIM) of the retrieved images are computed and compared to test all the five reordering schemes above both in our numerical simulation and outdoor experiments. We find that the reordering method based on Haar wavelet transform is the best PSNR and SSIM and it can reconstruct image under a sampling ratio of 25% which corresponds to the recovering time in which 300 frame per second @64 × 64 pixels single-pixel imaging can be achieved. The optimized measurement order of Hadamard basis greatly simplifies post processing, resulting in significantly faster image reconstruction, which steps further toward high frame rate single-pixel imaging’s applications. Moreover, we propose a novel method to optimize measurement basis in single-pixel imaging, which may be useful in other basis optimizing, such as optimized random speckles, etc.