Review of Research and Application of Terahertz Imaging Technology
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摘要: 太赫兹波（terahertz waves）位于红外波段与微波波段之间，相比其他波段具有高透射性、低能量性、相干性、指纹光谱以及瞬态性等特点。随着太赫兹成像技术在空间通信、雷达探测、航天航空以及生物医疗等领域的广泛应用，已经表现出传统成像技术（如可见光、超声波和X射线成像）无法比拟的优势。本文首先对太赫兹时域光谱（THz-TDS）成像技术以及室温（非制冷）微测辐射热计太赫兹成像技术的发展现状进行介绍，再介绍太赫兹成像技术的典型应用，最后指出太赫兹成像技术在发展中存在的限制因素并给出合理的建议。Abstract: Terahertz (THz) waves are located between the infrared and microwave bands. Compared with other bands, they have the characteristics of high transmission, low energy, coherence and transient nature. With the widespread application of terahertz imaging technology in the fields of space communication, radar detection, aerospace and biomedicine, it has been shown that THz imaging offers advantages over traditional imaging technologies (such as ultrasonic imaging and X-ray imaging). This paper first introduces the development status of THz time-domain spectroscopy (THz-TDS) imaging technology and room temperature (uncooled) microbolometer THz imaging technology. Subsequently, typical applications of THz imaging technology are presented. Finally, the limiting factors of THz imaging technology are discussed.
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Keywords:
- terahertz /
- time-domain spectroscopy /
- microbolometer /
- imaging technology
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0. 引言
多模态图像融合[1]是指从不同模态的源图像中提取重要信息，合成一幅比单一源图像更清晰、内容更全面的图像，便于人眼的观察和计算机的处理。
近年来，随着多尺度几何分析[2]、稀疏表示[3]、深度学习[4]等理论的发展，多模态图像融合技术取得了很大的进展。Bulanon等[5]采用拉普拉斯金字塔变换将源图像中的特征按照不同的尺度分解到不同的分解层上，由此来融合源图像中的显著特征；Zhan等人[6]提出了基于离散小波变换（discrete wavelet transform, DWT）的红外与可见光图像融合方法，虽然DWT在保留图像细节方面具有良好的性能，但缺乏平移不变性，导致融合图像的边界不连续。Liu等[7]提出了一种基于自适应稀疏表示（adaptive sparse representation，ASR）的多模态图像融合算法，融合的高频子带中保留了源图像的结构特征，但融合结果对比度极低、细节丢失严重。文献[8]提出了一种基于卷积神经网络（convolutional neural network，CNN）的图像融合算法，能同时实现显著性水平测评和权重分配，但融合结果中丢失了较多的细节信息。文献[9]提出了一种基于自适应脉冲耦合神经网络（adaptive pulse coupled neural network，APCNN）的非下采样轮廓波变换（non-subsampled contourlet transform，NSCT）域图像融合算法，由于APCNN模型中的连接强度设置为常数影响了融合结果的精度，且NSCT对各向异性的信息表示能力较弱，导致融合图像中丢失了边缘信息，针对此问题，文献[10]将非下采样剪切波变换（non-subsampled shearlet transform, NSST）和APCNN相结合，解决了NSCT方向有限的问题，且具有平移不变性[11]，因此被广泛应用[10-13]。以上算法虽然在一定程度上提高了融合图像的质量，但都存在图像的边缘细节丢失、视觉效果差等问题。
为了增加融合图像中的细节信息，提出了一种基于NSST-DWT-ICSAPCNN的多模态图像融合方法。采用NSST对源图像进行多尺度、多方向的分解得到高频和低频子带图像。考虑到NSST对细节处理精度仍不够高，而DWT在保留图像细节方面具有良好的性能，因此采用DWT进一步分解低频子带，提取源图像中容易被NSST分解忽略的细节信息。此外，为了增强中心神经元受到周围神经元的影响程度，将局部标准差的Sigmoid函数作为连接强度来构建改进型连接强度自适应脉冲耦合神经网络（improved connection strength adaptive pulse coupled neural network, ICSAPCNN），由于APCNN具有全局耦合特性和脉冲同步特性[14]，因此能更好地利用高频子带图像的全局特征。本文结合NSST、DWT、ICSAPCNN的互补特性融合多模态图像，通过实验验证了所提算法的有效性。
1. 基本理论
1.1 非下采样剪切波变换
NSST分解过程有两步，第一步采用非下采样金字塔滤波器组（NSPF）对待融合的源图像进行n级尺度分解，实现图像的多尺度化。第二步采用剪切滤波器（SFB）实现高频子带的多方向化，第k级方向分解个数为2k。最终得到n+1个子带图像[11]，即1个低频和n个高频子带图像，均与源图像的大小相同。
NSST不仅可以在多方向和多尺度上表示图像，还具有平移不变性，并且其分解过程中没有使用下采样运算，消除了伪吉布斯现象。NSST二级分解过程如图 1所示，本文中NSST分解的级数设置为4，方向数设为[8, 8, 16, 16]。
1.2 离散小波变换
DWT可以将源图像分解成一系列的能量子带和细节子带图像，分解过程使用一组高通、低通滤波器来执行，如图 2所示：先对图像ai中每行构成的一维数据进行一维小波分解，得到高、低频信息。再对每列构成的一维数据做相同的操作，最终得到4个子带图像：ai－1，hj－11，hj－12，hj－13。其中，ai－1由行低通、列低通得到，包含图像的近似信息，hj－11由行低通、列高通得到，hj－12由行高通、列低通得到，hj－13由行高通、列高通得到。hj－11，hj－12，hj－13分别包含水平、垂直、对角方向上的边缘细节信息[15]。
1.3 自适应脉冲耦合神经网络
APCNN模型是通过模拟猫的大脑视觉皮层中同步脉冲发放现象而建立起来的一个简化模型[16]，它不需要任何的训练过程，而是基于迭代计算，其数学方程描述如式(1)~(5)所示：
$$ F_{ij}[n]＝S_{ij} $$ (1) $$ {L_{ij}}[n] = {V_L}\sum\limits_{kl} {{W_{ijkl}}{Y_{kl}}[n - 1]} $$ (2) $$ {U_{ij}}[n] = {{\text{e}}^{ - {\alpha _{\text{F}}}}}{U_{ij}}[n - 1] + {F_{ij}}[n](1 + \beta {L_{ij}}[n]) $$ (3) $$ {Y_{ij}}[n] = \left\{ {\begin{array}{*{20}{c}} {1,\quad {U_{ij}}[n] \gt {E_{ij}}[n - 1]} \\ {0,\quad {U_{ij}}[n] \leqslant {E_{ij}}[n - 1]} \end{array}} \right. $$ (4) $$ {E_{ij}}[n] = {{\text{e}}^{ - {\alpha _{\text{E}}}}}{E_{ij}}[n - 1] + {V_E}{Y_{ij}}[n] $$ (5) 输入图像中的像素点(i, j)与APCNN模型中的神经元之间存在一一对应的关系[17]，神经元获取外部刺激输入的通道有两个，一个是反馈输入Fij，由像素点(i, j)的灰度绝对值Sij决定，另一个是连接输入Lij，其中VL是放大系数，Wijkl为突触连接矩阵。将Fij和Lij进行非线性相乘调制后得到神经元的内部活动项Uij，其中αF为反馈输入的衰减时间常数。当Uij大于动态阈值Eij时发放脉冲Yij，神经元产生一次点火。当神经元点火时，Eij立刻增大，然后又按照指数逐渐衰减，直到神经元再次发放脉冲，其中αE为动态阈值的衰减常数，VE为脉冲的放大系数。当迭代结束时，得到点火频率映射图。
2. 改进的多模态图像融合过程
基于本文方法的图像融合流程如图 3所示，采用NSST对源图像IA、IB进行分解得到高低频子带；再对低频子带进行DWT分解得到低频能量子带和细节子带，并采用最大值选择规则融合能量子带，利用ICSAPCNN分别对细节子带和高频子带进行融合；对能量子带和细节子带进行DWT逆变换得到融合的低频子带；最后采用NSST逆变换重构出融合图像IF。
2.1 低频子带融合规则
本文结合区域能量（RE）和梯度能量（EOG）融合低频系数，选择M×N区域窗口，具体步骤如下：
Step 1 根据式(6)分别计算两幅低频能量子带图像的区域能量RE1和RE2。
$$ {\text{R}}{{\text{E}}_X}(i,j) = \sum\nolimits_{i \leqslant M} {\sum\nolimits_{j \leqslant N} {{L_X}{{(i,j)}^2}} } $$ (6) Step 2 根据式(7)分别计算两幅低频能量子带图像的梯度能量EOG1和EOG2。
$$ {\text{EO}}{{\text{G}}_X}(i,j) = \sum\nolimits_{i \leqslant M} {\sum\nolimits_{j \leqslant N} {{{\left| {{G_X}(i,j)} \right|}^2}} } $$ (7) 式中：LX(i, j)和GX(i, j)分别表示(i, j)位置的低频能量子带系数值和梯度值。
$$ {G_X}(i,j) = \sqrt {{{({L_X}(i,j) - {L_X}(i + 1,j))}^2} + {{({L_X}(i,j) - {L_X}(i,j + 1))}^2}} $$ (8) Step 3 将RE和EOG相乘作为低频的显著性水平度量（ALM），定义如式(9)所示：
$$ {\text{AL}}{{\text{M}}_X}(i,j) = {\text{R}}{{\text{E}}_X}(i,j) * {\text{EO}}{{\text{G}}_X}(i,j) $$ (9) 上式(6)~(9)中，X∈{1, 2}。
Step 4 根据极大值规则选择ALM较大的点所对应的低频系数作为融合的低频系数LF(i, j)：
$$ {L_{\text{F}}}(i,j) = \left\{ {\begin{array}{*{20}{c}} {{L_1}(i,j),}&{{\text{AL}}{{\text{M}}_1}(i,j) \geqslant {\text{AL}}{{\text{M}}_2}(i,j)} \\ {{L_2}(i,j),}&{{\text{AL}}{{\text{M}}_1}(i,j) \lt {\text{AL}}{{\text{M}}_2}(i,j)} \end{array}} \right. $$ (10) 2.2 高频子带融合规则
2.2.1 改进的连接强度
连接强度取值范围为(0, 1)，调节着神经元之间的相互影响程度。本文利用Sigmoid函数表示APCNN模型的连接强度βij，避免了将连接强度设置为常数时模型的不灵活性。考虑到人眼视觉神经系统中各个神经元的连接强度不会完全相同，令连接强度由输入图像的局部标准差决定，标准差越大的区域对应的高频子带中包含更多的显著特征，连接强度随之增大，从而增强神经元受到周围神经元的影响程度，提高了ICSAPCNN对高频子带全局信息的利用程度。
$$ {\beta _{ij}} = \frac{1}{{(1 + \exp ( - {\sigma _{ij}}))}} $$ (11) 式中：σij为局部标准差，其定义如式(12)所示；$ \overline {{x_{ij}}} $为区域内以神经元(i, j)为中心的灰度均值；xkl为周围神经元(k, l)的灰度值；m为区域内神经元的总数。
$$ {\sigma _{ij}} = \sqrt {\frac{1}{m}\sum\nolimits_{k = 1}^3 {\sum\nolimits_{l = 1}^3 {{{({x_{kl}} - \overline {{x_{ij}}} )}^2}} } } $$ (12) 2.2.2 融合规则
ICSAPCNN模型中各神经元由某一高频子带刺激后，将得到对应的点火频率映射图，点火次数表征高频系数中包含细节信息的显著程度，次数越大，对应位置所包含的细节信息越丰富。因此选择点火次数较大的点所对应的系数作为融合的高频系数，高频子带和低频细节子带具体的融合步骤如下：
Step 1 初始化ICSAPCNN模型，将输入激励Sij设为高频子带（低频细节子带）图像像素点(i, j)的灰度值，并令Lij[n]＝Uij[n]＝Yij[n]＝Eij[n]＝0。
Step 2 根据式(11)计算改进的连接强度βij，其余参数根据文献[9]设定。
Step 3 根据式(13)计算模型每次迭代结束后的点火次数：
$$ T_{ij}^{s,l}[n] = T_{ij}^{s,l}[n - 1] + Y_{ij}^{s,l}[n] $$ (13) Step 4 根据式(14)选择融合的高频系数（低频细节子带系数）。
$$ H_{\text{F}}^{s,l}(i,j) = \left\{ {\begin{array}{*{20}{c}} {H_{\text{A}}^{s,l}(i,j),}&{T_{\text{A}}^{s,l}(i,j) \geqslant T_{\text{B}}^{s,l}(i,j)} \\ {H_{\text{B}}^{s,l}(i,j),}&{T_{\text{A}}^{s,l}(i,j) \lt T_{\text{B}}^{s,l}(i,j)} \end{array}} \right. $$ (14) 式(13)~(14)中：s、l分别对应高频子带（低频细节子带）的第s层、第l个方向。式(14)中A、B分别对应两幅高频子带图像或两幅低频细节子带图像。
3. 实验结果与分析
3.1 实验设置
本文所有实验均在Windows10，MATLAB 2019a软件上运行。为了验证本文方法的有效性，实验所用到的多模态图像包括6组红外图像（Infrared）与可见光图像（Visible），8组计算机断层扫描图像（CT）与核磁共振图像（MRI）。与近几年的4种图像融合方法做对比，文献[7]采用基于ASR的融合方法，文献[8]采用基于CNN的融合方法，文献[9]和文献[10]均采用基于多尺度变换和APCNN的融合方法（分别记为NSCT-APCNN、NSST-APCNN），本文实验分析中展示了部分多模态源图像的融合结果。
3.2 客观评估指标
Zheng等人在文献[18]中总结了很多评估融合图像质量的客观指标，本文选取的评估指标包括熵QEN，互信息QMI，标准差QSD，视觉信息保真度QVIFF，非线性相关信息熵QIE，基于Tsallis的熵QTE。对于本文所有的客观评估指标，其值越大，融合后的图像质量越高，融合效果越好。
3.3 仿真结果与分析
本文列出了部分源图像的融合结果，图 4(a)和图 4(b)分别是“road”可见光和红外源图像，图 4(c)~(g)为对两幅源图像应用不同方法得到的融合结果。观察可知：使用ASR和CNN方法的融合结果中能量严重丢失，公路上的行人分辨率极低，视觉效果差；使用NSCT-APCNN和NSST-APCNN方法的融合结果中人物边缘模糊，细节信息丢失；本文利用Sigmoid函数表示连接强度，在两幅高频子带对应位置的标准差相差较小时ICSAPCNN模型也能表现出较好的效果。由局部放大图可知，基于本文方法的结果中人物清晰，辨识度高，保留了源图像中的重要信息。图 5(a)和图 5(b)~(g)分别是“tree”可见光和红外源图像，图 5(c)为对两幅源图像应用不同方法得到的融合结果。观察融合结果可知基于本文方法的融合结果最清晰，融合效果最好。由不同方法融合“road”和“tree”两组红外与可见光源图像的客观评估指标值如表 1所示，显然，由本文方法得到的客观评估指标值均较高。由不同方法融合6组红外和可见光源图像的客观评估指标结果的平均值如表 2所示，由表 2可知，除了QSD和QTE，其余4个指标QEN、QMI、QVIFF、QIE均为最优，与主观视觉效果保持一致，验证了本文方法对于红外与可见光图像融合的有效性。
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图 4 “road”红外和可见光图像以及融合结果Figure 4. The "road" infrared and visible source images and fusion results![]()
图 5 “tree”红外和可见光图像以及融合结果Figure 5. The "tree" infrared and visible source images and fusion results表 1 两组红外与可见光图像客观评估指标值Table 1. Values of objective evaluation index for 2 groups of infrared and visible imagesImages Metrics ASR[7] CNN[8] NSCT-APCNN[9] NSST-APCNN[10] NSST-DWT-ICSAPCNN Road QEN 7.1339 7.4964 7.3703 7.331 7.4247 QMI 3.0046 3.2051 3.0786 3.2336 3.0167 QSD 38.3922 48.4964 45.5887 44.5039 51.7009 QVIFF 0.4469 0.5842 0.5206 0.5078 0.6275 QIE 0.8055 0.8054 0.8052 0.8053 0.8062 QTE 0.5749 0.5207 0.5401 0.5454 0.5886 Tree QEN 6.3464 7.1022 6.9596 6.9152 7.1043 QMI 1.2234 1.1755 1.3188 1.7535 2.1287 QSD 24.3398 37.2648 32.8565 31.4357 34.8227 QVIFF 0.3177 0.4706 0.3822 0.3798 0.4261 QIE 0.8033 0.8043 0.8035 0.8035 0.8040 QTE 0.4090 0.2861 0.2981 0.3279 0.3282 表 2 六组红外与可见光图像客观评估指标平均值Table 2. Average values of objective evaluation index for 6 groups of infrared and visible imagesMetrics ASR[7] CNN[8] NSCT-APCNN[9] NSST-APCNN[10] NSST-DWT-ICSAPCNN QEN 6.2345 6.8978 6.9633 6.9094 7.0247 QMI 2.8656 3.2917 3.6756 4.1826 4.3438 QSD 24.7236 38.7514 37.0670 35.4332 38.6467 QVIFF 0.3761 0.5399 0.5445 0.5032 0.5514 QIE 0.8063 0.8076 0.8086 0.8090 0.8097 QTE 0.7311 0.6582 0.6534 0.6971 0.6841 图 6(a)和图 6(b)分别为致死性脑卒中CT和MRI源图像，图 6(c)~(g)为对两幅医学源图像应用不同方法得到的融合结果。观察仿真结果图可知：使用ASR方法的融合结果亮度较暗，对比度严重丢失，视觉效果差；使用CNN方法的融合结果存在能量丢失现象；使用NSCT-APCNN和NSST-APCNN的融合方法是直接对低频子带图像进行融合，这种做法不能充分提取到源图像的细节信息；本文利用DWT进一步分解低频子带图像，提取源图像中容易被NSST分解忽略的信息，由局部放大图可知，得到的融合结果（图 6(g)）中保留了源图像较多的细节信息，且对比度与源图像保持一致，视觉效果最好。图 7(a)~(b)分别为脑膜瘤CT和MRI源图像，图 7(c)~(g)为融合结果，观察可知，基于本文方法的融合结果细节信息最丰富，融合效果最好。由不同方法融合两组医学源图像的客观评估值如表 3所示，显然，由本文方法得到的客观评估指标值均较高。由不同融合方法融合8组医学图像的客观评估指标结果的平均值如表 4所示，由表 4可知，除了QSD，其他5个评估指标均为最优，与主观视觉效果一致，验证了本文方法对于多模态医学图像融合的有效性。
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图 6 致死性脑卒中CT和MRI图像以及融合结果Figure 6. The fatal stroke CT and MRI source images and fusion results![]()
图 7 脑膜瘤CT和MRI图像以及融合结果Figure 7. The meningoma CT and MRI source images and fusion results表 3 两组医学图像客观评估指标值Table 3. Values of objective evaluation index for 2 groups of medical imagesImages Metrics ASR[7] CNN[8] NSCT-APCNN[9] NSST-APCNN[10] NSST-DWT-ICSAPCNN fatal stroke QEN 4.5440 4.8244 5.0632 4.8747 5.1693 QMI 2.5170 2.8593 2.7118 2.8665 2.7618 QSD 72.3351 90.2448 90.0339 84.2365 88.4652 QVIFF 0.2691 0.3333 0.3259 0.3100 0.3131 QIE 0.8051 0.8055 0.8054 0.8051 0.8054 QTE 0.6663 0.7252 0.7277 0.7102 0.7896 meningoma QEN 4.1794 4.2013 4.3485 4.6852 4.6013 QMI 2.5408 2.9163 2.9516 3.0001 3.0665 QSD 72.0789 88.7470 92.8914 90.2904 91.3901 QVIFF 0.4940 0.6192 0.6279 0.5624 0.6292 QIE 0.8056 0.8059 0.8062 0.8064 0.8064 QTE 0.7907 0.7923 0.8445 0.8733 0.8804 表 4 八组医学图像客观评估指标平均值Table 4. Average values of objective evaluation index for 8 groups of medical imagesMetrics ASR[7] CNN[8] NSCT-APCNN[9] NSST-APCNN[10] NSST-DWT-ICSAPCNN QEN 4.3242 4.6515 4.7943 4.7715 4.8254 QMI 2.6843 2.9002 2.8697 2.8998 2.9848 QSD 66.6290 83.3568 85.9244 85.7634 85.7755 QVIFF 0.3561 0.4417 0.4562 0.4491 0.4647 QIE 0.8057 0.8061 0.8061 0.8062 0.8062 QTE 0.7033 0.7494 0.7608 0.7593 0.7818 4. 结论
为了在融合过程中提取更多的图像信息，提出了一种基于NSST-DWT-ICSAPCNN的多模态图像融合方法。对源图像经NSST分解得到的低频子带图像做DWT分解，解决了部分源图像细节丢失的问题。此外，将低频子带图像的区域能量和梯度能量相结合作为显著性水平度量，有效地保留了图像的能量和边缘细节信息。采用ICSAPCNN获取低频细节子带图像和高频子带图像的点火频率映射图，提高了对低频细节子带和高频子带图像全局信息的利用程度。实验结果显示所提算法相比于其他4种多模态图像融合算法，在主观视觉和客观评估指标方面均表现最优，同时验证了本文方法对于多模态红外和可见光图像与多模态医学图像均有较好的融合效果。下一步将继续研究双树复小波变换（Dual Tree Complex Wavelet Transform，DTCWT）、双密度双树复小波变换（Double Density Dual Tree Complex Wavelet Transform，DDDTCWT）对低频子带图像做进一步分解的效果。
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图 1 太赫兹辐射产生方法(a) 光电导效应；(b)光整流效应；(c)空气等离子体效应
Figure 1. (a) Photo conductance effect; (b) Optical rectification effect; (c) Air plasma effect
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图 4 太赫兹成像系统及样品的太赫兹图像：(a) 太赫兹脉冲焦线成像系统；(b) 金属孔阵列样品以及其在0.204 THz、0.407 THz、0.815 THz、1.600 THz处的太赫兹图像[20]
Figure 4. Terahertz imaging system and terahertz images of samples: (a) THz pulse focal imaging system; (b) THz images of metal hole array samples and samples at 0.204 THz, 0.407 THz, 0.815 THz, 1.600 THz[20]
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图 15 太赫兹成像技术在安全检查方面的应用：(a) 为中国电科38所研制太赫兹人体安检仪系统成像；(b) 为诺⋅格公司研制的太赫兹安检仪成像
Figure 15. The application of THz imaging technology in security inspection: (a) Imaging for the THz human security detector system developed by China Electric Power 38 Institute; (b) Imaging for the THz security detector developed by Northrop Grumman
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