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文中分别选取了传统二阶关联算法(GI)、传统差分关联算法(DGI)、计算差分关联算法(CGI)、随机二值矩阵正交匹配追踪算法(OMP)、阿达玛矩阵正交匹配追踪算法和阿达玛矩阵全变分正则化算法(TVAL3)对模拟测量值信号进行重构,并且对比了不同采样率下的成像效果。GI算法通过调制光路上的总光强Si与参考光路上的光强分布Ii (x,y)来计算得到待成像物体TGI (x,y):
$$ {T}_{{\rm{GI}}}(x,y)=\frac{1}{N}\sum _{i=1}^{N}\left({I}_{i}\left(x,y\right)-\left\langle{{I}_{i}(x,y}\right\rangle\right)({S}_{i}-\left\langle{{S}_{i}}\right\rangle) $$ (1) DGI算法在此基础上,将参考光路的光强分布做离散化求和处理。CGI算法对观测矩阵的选择性更多,通过DMD实现二值光场调制,提高了投影的对比度。OMP算法通过贪婪迭代找到观测矩阵中与当前残差相关性最好的一列,迭代剔除。TVAL3算法引入增广拉格朗日函数和交替方向变换,使用梯度下降法迭代求解[18]。
从图2和图3中可以看出,前两种算法得到的图像效果较差;CGI算法在全采样下,重构结果与原图几乎无差异,并且所需时间最短;OMP算法在采样率为0.3时可重构出图像的轮廓和部分细节,但所需时间最长;图3 (b)、(c)显示,TVAL3算法明显重构效果最优,采样率为0.1时就可以大致重构出图像的轮廓和细节特征,相似度为0.474,采样率为0.3时相似度可达0.773,并且计算速度比OMP算法快。
图 2 不同算法下的重构图像。(a)~(f) 分别采用传统二阶关联算法、传统差分关联算法、计算差分关联算法、随机二值矩阵OMP算法、阿达玛矩阵OMP算法和阿达玛矩阵TVAL3算法,采样率为0.1、0.3、0.6和1.0
Figure 2. Reconstructed images under different algorithms. The algorithms used in (a)-(f) are the traditional second-order correlation algorithm, the traditional differential correlation algorithm, the calculated differential correlation algorithm, the random binary matrix OMP algorithm, the Hadamard matrix OMP algorithm and the Hadamard matrix TVAL3 algorithm, and the sampling rates are 0.1, 0.3, 0.6 and 1.0
图 3 在不同采样率下使用不同重构算法的像质评价
Figure 3. Image quality evaluation using different reconstruction algorithms at different sampling rates (PSNR, SSIM, TIME)
上述仿真模拟仅针对无散射介质时单像素成像重构算法的比较。在光路上放置散射介质后,携带调制信息的光束会改变传播方向以及被介质吸收[19],在目标平面形成一个散射光晕。在散射介质成像实验中,散射介质影响的不只是成像光路,还有目标到探测器的一段探测光路。差分关联计算主要计算调制信号与经过调制的目标信号之间的联系,可以削减成像光路信号变化带来的不利影响。而压缩感知的特点是通过稀疏约束以少量信号来恢复高精度的原始信号,与采样率关系较大,与被散射介质强散射性削弱的探测光路信号有一些相似性,作为重构算法可以抵消非成像光路上的不利影响。
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以厚度1 mm的猪肉切片为散射介质,光源采用光纤卤钨灯和红外滤光片,对USAF-1951分辨率板进行成像,InGaAs探测器为单像素探测器进行信号采集,具体参数和光路如表1、图4所示。
表 1 实验中的关键器件参数
Table 1. Key device parameters in the experiment
Key device Parameter Light source Wave length: 260-2500 nm Lens 1 AR COATED 650-1050 nm, f=26 mm Lens 2 f=100 mm Infrared filter 800-2500 nm DMD Operating 350-2700 nm, 1024×768 pixel Projection lens f=35 mm Single point detector Operating 800-1750 nm Focusing lens AR COATED 650-1050 nm, f=60 mm 图 4 基于DMD的主动式单像素成像系统设计图。(a)无散射介质时;(b)散射介质在探测光路时;(c)散射介质在成像光路时
Figure 4. Layout of active single-pixel imaging system based on DMD. (a) When there is no scattering medium; (b) When the scattering medium in detection path; (c) When the scattering medium inimaging path
首先在无散射介质的情况下实施近红外单像素成像实验,采用分辨率为64×64的阿达玛矩阵,分别使用CGI算法和TVAL3算法在不同采样率下恢复。为了减少随机误差的影响,循环采集四次数据并取平均值作为实验结果的最终测量值。
CGI算法使用4096个测量值重构了目标图像,PSNR与SSIM分别为16.3051、0.6337。TVAL3算法在采样率为0.4时就可以重构出图像的轮廓和细节特征,PSNR与SSIM分别为16.9636、0.6326,如图5(b)所示,两种算法的重构效果相近。可以看出,在无散射介质时,基于压缩感知理论的TVAL3算法的成像质量优于基于关联成像理论的CGI算法。
图 5 无散射介质下两种算法的重构效果对比。 (a)第一张由CGI算法重构,后四张图由TVAL3算法重构,其采样率为0.4~0.7;(b)重构图像的PSNR、SSIM对比
Figure 5. Comparison of the reconstruction effects of the two algorithms with non-scattering medium. (a) The first image recovered by CGI, and the last four images are recovered by TVAL3, with a sampling rate of 0.4-0.7; (b) PSNR and SSIM comparison of reconstructed image
在图4所示的光路上加入散射介质后,介质的多重散射作用促使光束随机偏离原来的传播方向。成像光路上结构光的空间信息将被打乱[20-21],抵消了结构光照明可增加有效信息提取[22]的优势,造成成像质量下降。如图6 (a)、(b)所示,在结构光的传播路径上放置毛玻璃做散射介质。在d1距离处,光束经过毛玻璃后空间结构细节变得模糊,并且距离越远,图像越模糊,最终如图6 (b)所示,在d2距离处图像失去正方形形状,变成一个大的光斑。同样的,如果将散射介质放置在非成像光路中,光被混匀,可探测到的光束强度衰减。如图6(c)、(d)所示,均匀光经过物体和紧贴物体的毛玻璃后,光束的传播方向同样发生了变化,如同经过了一个光扩散板,并且随着距离变长,光束愈发扩散。
图 6 光束在毛玻璃散射作用下的表现。(a)~(b) 结构光是否经过散射介质后的强度分布对比;(e) 均匀光经过物体和散射介质后的强度分布,(c1)~(c2) 上方是直接拍摄的照片,下方是使用一张白纸做观察面、然后拍摄观察面得到的照片;(c3) 均匀光经过物体和散射介质后的强度分布;(d) 均匀光直接经过物体的强度分布
Figure 6. Performance of the light beam under the scattering of ground glass. (a)-(b) Intensity distribution comparison of structured light with or without scattering medium; (e) Uniform light passing through the object and scattering medium; The upper of (c1)-(c2) is a photo taken directly, and the below is a picture taken from the observation surface; (c3) Uniform light passing through the object and scattering medium; (d) Uniform light passing through the object
选择厚度约为1 mm的生物组织,分别固定在分辨率板的前面(图4 (c))与后面(图4 (b))。介质的散射作用会限制成像深度,使被介质包裹着的目标信号不容易被探测器接收到,并且探测到的微弱信号易与探测器噪声混杂。因此,在重构运算前,需要在测量值中减去无光和有光环境下探测器的暗噪声平均值。此外,在重复测量的数据中选择最大的数据作为测量值。经过预处理的测量值可以在一定限度内减小探测器噪声、环境光照、光源强度波动对测量值的影响。对于TVAL3算法,选取多个采样率进行图像重构并对比,调整了重构图像的灰度,增加非线性映射操作,增强了对比度。
图7的成像结果表明,生物组织散射介质对成像有一定程度的影响,重构图像质量下降。CGI算法得到的图像底噪多,其SSIM值略低于TVAL3算法,但PSNR值(10.1886、9.9831)均高于TVAL3算法重构图像的PSNR(9.170456)。当TVAL3算法的采样率减小时,图像结构越发不明显。
图 7 穿透散射介质成像结果。 (a) 散射介质在成像光路上的重构图像,分别使用CGI算法和TVAL3算法,后者采样率为1~0.6,其峰值信噪比与相似度的对比在(b)中;(c) 散射介质在探测光路上的重构图像,其峰值信噪比与相似度的对比在(d)中
Figure 7. Reconstructed image of penetrating scattering medium. (a) When the medium in imaging path, using CGI algorithm and TVAL3 algorithm, the latter sampling rate is 1-0.6, its peak signal-to-noise ratio and similarity. Comparison of (a) is in (b); (c) When scattering medium in detection path, and the comparison is in (d)
当涉及到动态成像时,单像素成像对成像时间也有要求。实验选用了高速切换状态的DMD对光束进行编码[23],其照明时间与探测器的响应时间相对应,因此不同场景下的数据采集时间相同,在静态成像下对成像结果影响不大。图8为在有散射介质的情况下两种算法分别重构图像所需的时间,可以看出CGI算法所需的时间远小于TVAL3算法。
图 8 CGI算法与TVAL3算法在穿透散射介质成像中的重构时间对比
Figure 8. Comparison of reconstruction time between CGI algorithm and TVAL3 algorithm in penetrating scattering media imaging
从以上实验结果可以看出,在有散射介质的情况下,CGI算法重构的图像质量略优于欠采样率的TVAL3算法,而可压缩性正是压缩感知理论的特点,采样率越低时,基于压缩感知理论的重构算法优势逐渐降低。
Scattering interference suppression for single-pixel imaging reconstruction of biological tissues
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摘要: 针对单像素成像重构中的散射介质影响而导致重构图像无法达到最佳效果的问题,研究了有无散射介质的情况下,关联算法和压缩感知算法的图像重构适用性。分析了散射介质在成像光路造成的调制信息空间结构变化和在探测光路造成的信号损耗对成像的影响,建立了近红外单像素成像系统,使用CGI算法和TVAL3算法实现了穿透生物组织散射介质的单像素成像实验。实验发现,在无散射介质时,TVAL3算法的重构时间、峰值信噪比和相似度等均优于CGI算法;而在有散射介质时,CGI算法的三项数值中有两项优于TVAL3算法,其最大重构时间(0.304091 s)小于TVAL3算法最小时间(1.766299 s),其最小峰值信噪比(9.9831 dB)高于TVAL3算法的最大值(9.170456 dB),其相似度(0.0982、0.1178)则位于TVAL3算法的范围内(0.099258~0.497622)。结果表明,基于关联成像理论的CGI算法较适合散射介质成像,基于压缩感知理论的TVAL3算法更适合无散射介质成像。Abstract: In view of the influence of the scattering medium in the reconstruction of single-pixel imaging, the reconstructed image cannot achieve the best effect. The applicability of the correlation algorithm and compressed sensing algorithm for image reconstruction with or without the scattering medium was investigated. The influence of the spatial structure change of modulated information in the imaging path and the signal loss in detection path caused by the medium was analyzed, a near-infrared single-pixel imaging system was established, and the single-pixel imaging of penetrating the biological tissues scattering medium with the CGI algorithm and the TVAL3 algorithm was realized. It was found that the reconstruction time, peak signal-to-noise ratio and SSIM of the TVAL3 were better than CGI when there was no medium; while two of the three values of the CGI were better when there was medium, its maximum reconstruction time (0.304091 s) was smaller than the minimum (1.766299 s) of the TVAL3, and its minimum PSNR (9.9831dB) was higher than the maximum (9.170456 dB) of the TVAL3, and its SSIM (0.0982,0.1178) lay within the range of the SSIM of the TVAL3 (0.099258-0.497622). The results show that the CGI based on correlation imaging theory is more suitable for imaging scattering media, and the TVAL3 based on compressed perception theory is more suitable for imaging non-scattering media.
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图 2 不同算法下的重构图像。(a)~(f) 分别采用传统二阶关联算法、传统差分关联算法、计算差分关联算法、随机二值矩阵OMP算法、阿达玛矩阵OMP算法和阿达玛矩阵TVAL3算法,采样率为0.1、0.3、0.6和1.0
Figure 2. Reconstructed images under different algorithms. The algorithms used in (a)-(f) are the traditional second-order correlation algorithm, the traditional differential correlation algorithm, the calculated differential correlation algorithm, the random binary matrix OMP algorithm, the Hadamard matrix OMP algorithm and the Hadamard matrix TVAL3 algorithm, and the sampling rates are 0.1, 0.3, 0.6 and 1.0
图 5 无散射介质下两种算法的重构效果对比。 (a)第一张由CGI算法重构,后四张图由TVAL3算法重构,其采样率为0.4~0.7;(b)重构图像的PSNR、SSIM对比
Figure 5. Comparison of the reconstruction effects of the two algorithms with non-scattering medium. (a) The first image recovered by CGI, and the last four images are recovered by TVAL3, with a sampling rate of 0.4-0.7; (b) PSNR and SSIM comparison of reconstructed image
图 6 光束在毛玻璃散射作用下的表现。(a)~(b) 结构光是否经过散射介质后的强度分布对比;(e) 均匀光经过物体和散射介质后的强度分布,(c1)~(c2) 上方是直接拍摄的照片,下方是使用一张白纸做观察面、然后拍摄观察面得到的照片;(c3) 均匀光经过物体和散射介质后的强度分布;(d) 均匀光直接经过物体的强度分布
Figure 6. Performance of the light beam under the scattering of ground glass. (a)-(b) Intensity distribution comparison of structured light with or without scattering medium; (e) Uniform light passing through the object and scattering medium; The upper of (c1)-(c2) is a photo taken directly, and the below is a picture taken from the observation surface; (c3) Uniform light passing through the object and scattering medium; (d) Uniform light passing through the object
图 7 穿透散射介质成像结果。 (a) 散射介质在成像光路上的重构图像,分别使用CGI算法和TVAL3算法,后者采样率为1~0.6,其峰值信噪比与相似度的对比在(b)中;(c) 散射介质在探测光路上的重构图像,其峰值信噪比与相似度的对比在(d)中
Figure 7. Reconstructed image of penetrating scattering medium. (a) When the medium in imaging path, using CGI algorithm and TVAL3 algorithm, the latter sampling rate is 1-0.6, its peak signal-to-noise ratio and similarity. Comparison of (a) is in (b); (c) When scattering medium in detection path, and the comparison is in (d)
表 1 实验中的关键器件参数
Table 1. Key device parameters in the experiment
Key device Parameter Light source Wave length: 260-2500 nm Lens 1 AR COATED 650-1050 nm, f=26 mm Lens 2 f=100 mm Infrared filter 800-2500 nm DMD Operating 350-2700 nm, 1024×768 pixel Projection lens f=35 mm Single point detector Operating 800-1750 nm Focusing lens AR COATED 650-1050 nm, f=60 mm -
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