基于Hadamard矩阵优化排序的快速单像素成像

Fast single-pixel imaging based on optimized reordering Hadamard basis

为提升单像素成像速度,提出了基于Hadamard矩阵优化排序的压缩采样解决方案.利用数值仿真和室外实验对提出的5种排序方法进行了对比分析.研究结果表明:按Haar小波变换系数绝对值排序时单像素成像效果最优,排序对应到Walsh序后可利用快速变换重建图像,速度达300帧/秒@64×64像素;最优排序下,采样率25%仍可重建图像,采样速度可提升4倍.针对排序方法与成像信噪比关系,从关联成像角度给出了其物理解释:测量基矩阵元邻域数值相等的区域面积等效于光场二阶相干面积,当光场二阶相干面积随测量基由大到小排序时成像效果最优.本文研究成果可用于提升单像素成像速度,具有实用价值.

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 which300 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.