1.Quantum Engineering Research Center, China Aerospace Science and Technology Corporation, Beijing 100094, China 2.Beijing Institute of Aerospace Control Devices, Beijing 100039, China
Fund Project:Project supported by the Defense Industrial Technology Development Program, China (Grant No. JCKY2016601C005) and the National Natural Science Foundation of China (Grant No. 61805006).
Received Date:22 October 2018
Accepted Date:02 January 2019
Available Online:01 March 2019
Published Online:20 March 2019
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. Keywords:single-pixel imaging/ Walsh-Hadamard transform/ wavelet transform
单像素成像的基本原理示意图如图1所示, 待成像物体通过主透镜成像到数字微镜器件(digital micro-mirror device, DMD), 微镜受数字电路控制系统的控制, 按加载的调制矩阵$ {\varPhi } $, 每个微镜发生$ {+12}^{\circ} $或$ {-12} ^{\circ} $摆动, 摆动方向由矩阵$ {\varPhi } $的矩阵元决定, 例如矩阵元“1”对应$ {+12} ^{\circ} $方向翻转, 矩阵元“–1”对应$ {-12}^{\circ} $方向翻转. 物体的像被测量矩阵调制经由中继透镜汇聚到光电探测器转为电信号, 重复刷新DMD调制矩阵将得到因光强变化引起的一系列电信号, 该过程等价于调制图案与物体实像作内积的过程, 模拟的电信号经A/D进行模数转换变为数字信号, 数字信号将被采集到计算设备经过算法计算重建图像. 图 1 单像素成像原理示意图, 其中待成像物体经主透镜成像到DMD上, 经编码矩阵调制的光束被反射, 反射光由中继透镜汇聚到光电探测器, 探测器将光信号转为电信号, 电信号经过A/D转换由模拟信号转为数字信号, 重复刷新DMD调制矩阵将得到一系列数字信号, 将数字信号采集到计算设备即可利用算法重构图像 Figure1. Schematic diagram of the experimental setup. Lena is the object to be recovered; the main lens imaging Lena onto the DMD, which is modulated by matrices, then the light is reflected and collected by the relay lens into the photo-detector. As DMD modulation matrices refreshing continuously, the analog-to-digital converter (A/D) connected with the photo-detector receives a series of digital signals, which are finally sent to recover the image by the computer.
4.实验验证为验证上述的数值模拟仿真实验及分析结论, 开展了800m距离单像素凝视成像实验. 单像素原理样机调制器DMD为美国德州仪器公司生产的DLP4100, 微镜总数及排列为1920 × 1080, 微镜可$ \pm12^{\circ} $翻转, 每个微镜10.6 $ \text{μm} $. 实验时从DMD中间区域选取的调制区域为1024 × 1024, 16 × 16个微镜作为一个像素调制单元, 因此共64 × 64个像素调制单元, 微镜的调制速度设定为8 kHz. 首先, 计算机按Hadamard编码原则生成4096 × 4096大小的Hadamard矩阵; 其次, 将Hadamard矩阵的每一行重新按顺序排列成4096个64 × 64大小的矩阵; 然后将4096个64 × 64大小的矩阵利用直积的方式变为1024 × 1024像素, 再填0扩充到1920 × 1080, 将扩充后的序列加载到数字微镜阵列DMD的板载内存. DMD的调制速率设置为8 kHz, 采集得到一副图像需要0.512 s. 样机成像主镜为卡塞格林式天文望远镜, 口径为280 mm, 焦距为2800 mm. 探测器采用日本滨松H10723-20型PMT, 有效波段 350—900 nm. 数据采集卡采用16位精度的A/D转换模块. 为获得高SNR成像结果, 实验进行了100次全测量, 对应曝光时间51.2 s. 累加求平均后, 分别按5种规则排序: 按Haar小波变换、Db2小波变换和Dct的$ S(i) $值由小到大排序, 以及按Walsh序排序和按1到4096随机排序, 分别截取数据的25%用于图像重建, 截取的数据如图5所示. 从截取的数据图5可见, 对于相同图像, 不同测量基在数据表征上有显著区别, 利用数据的特征分布规律有望进行不成像识别, 此处不展开讨论. 数据虽有区别但仍不能直接给出重建效果优劣. 因此仍需利用这5种排序的1024个数据重建图像, 其结果如图6所示. 图6(a)为成像区域, 利用商用测距仪测得目标距离约800 m. 对该区域放大, 得到的相机拍摄图像如图6(b)所示, 该区域为选定的成像目标区域. 图6(c) 为利用单像素成像实验装置在全采样和测量次数$ m=4096 $条件下获得的成像结果. 图6(d)—(h)分别对应排序方法为Db2小波序、Dct序、Walsh序、随机排序和Haar小波排序下的图像重建结果. 通过对比发现, 只有图6(h), 即Haar小波变换排序方法可在25%、测量次数$ m=1024 $条件下依然能够成像, 且图像大部分信息得到还原. Haar小波变换排序相当于提升4倍采样速度和图像重建速度, 使得单幅图像采集与重建时间为0.125 s, 本实验中对应8帧/秒@$64\times 64 $像素成像. 而实际上, 算法计算速度上可满足至少300帧/秒@$ 64\times 64 $像素的单像素成像, 此时, 高速单像素成像主要受调制器调制速度的限制. 图 5 不同排序方法25%采样下的实验数据, 即Haar小波变换、Db2小波变换、Dct、Walsh排序和随机随机排序对应的实验数据 Figure5. Experimental data of different ordering methods: Haar wavelet, Db2 wavelet and Dct, Walsh order and random order.
图 6 室外实验结果和不同排序方法在25%采样下的重建图像 (a)目标区域, 对应距离800 m; (b)相机拍摄的目标图像; (c) 无压缩单像素成像, 64 × 64像素, 100幅图像累加结果; (d)—(h) 分别对应排序方法为Db2小波序、Dct序、Walsh序、随机排序和Haar小波排序下重图像重建结果 Figure6. Outdoor experiment and recovered images under 25% full sampling with different ordering methods: (a) The target region, with the distance 800 meters; (b) target image captured by camera; (c) image recovered by single-pixel camera, with 64 × 64 pixels, with 100 recovered images averaged; (d)?(h) images recovered corresponding to the ordering method of Db2 wavelet order, Dct order, Walsh order, random permutation order and Haar wavelet order, respectively.