WO2023109717A1 - Terahertz time domain signal noise reduction method, and terahertz image reconstruction method and system - Google Patents
Terahertz time domain signal noise reduction method, and terahertz image reconstruction method and system Download PDFInfo
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- the invention belongs to the field of terahertz signal processing and image reconstruction, and more specifically relates to a terahertz time-domain signal noise reduction method, image reconstruction method and system.
- Terahertz has the characteristics of no ionization and no damage. The vibration and rotational energy levels of various organic molecules fall in the terahertz band. Combined use with other technologies. Terahertz spectroscopy detection and imaging technology has broad application prospects in the study of biological macromolecular properties, medical diagnosis, security inspection, material detection and environmental monitoring.
- the terahertz time-domain signal of the tested sample collected by the terahertz time-domain spectroscopy system can reflect the amplitude and phase information of the terahertz pulse, and can extract the photoelectric properties of the tested sample in the terahertz band.
- the sample to be measured when two-dimensional scanning is performed on the sample to be measured, it can be based on the maximum value, minimum value or amplitude value at a specific time point of the terahertz time domain signal at each point of the sample, or based on the Fourier transform of the time domain signal.
- the amplitude value at a certain frequency in the spectrum, or the size of the optical parameter of the sample at a certain frequency extracted based on the time-domain signal is used to perform terahertz imaging on the tested sample.
- the purpose of the present invention is to provide a terahertz time-domain signal noise reduction method, image reconstruction method and system, aiming to solve the unsatisfactory noise reduction effect caused by modal mixing in terahertz spectrum detection and imaging applications The problem.
- the present invention provides a terahertz time-domain signal noise reduction method, which is characterized in that it comprises the following steps:
- the original signal is separated into noise and a noise-reduced signal through independent component analysis.
- the empirical mode decomposition may also be set empirical mode decomposition, complementary set empirical mode decomposition or variational mode decomposition.
- step S1 the empirical mode decomposition result of the terahertz time domain signal x(t) is expressed as
- step S2 specifically includes the following steps:
- the threshold filtering in step S3 is soft threshold filtering, hard threshold filtering or adaptive threshold filtering.
- step S5 is fast independent component analysis or Fourier independent component analysis.
- Another aspect of the present invention provides a terahertz image reconstruction method, comprising the following steps:
- the two-dimensional imaging of the measured sample includes: using terahertz point-by-point scanning imaging or terahertz focal plane imaging, combined with transmission imaging or reflection imaging.
- Another aspect of the present invention provides a terahertz image reconstruction system, including:
- the imaging module performs two-dimensional imaging on the tested sample to obtain noise-containing terahertz time-domain signals at each point on the tested sample;
- a noise reduction processing module configured to perform noise reduction processing on the noise-containing terahertz signals of each point, to obtain the noise-reduced signal of each point on the sample under test;
- the image reconstruction module selects the maximum value, the minimum value, or the intensity at a specific time point of the noise-reduced signal, or selects a certain frequency in the frequency spectrum after the Fourier transform of the noise-reduced signal.
- the result comparison module is used to display and compare the reconstructed terahertz images of different samples under test
- the noise reduction processing module further includes:
- the empirical mode decomposition module is used to perform empirical mode decomposition on the noise-containing terahertz time-domain signal to obtain multiple eigenmode functions
- the threshold filtering module receives the processing result of the empirical mode decomposition module, uses the correlation coefficient to select the noise-dominated eigenmode function, uses the threshold to filter the noise-dominated eigenmode function selected above, filters out the signal part, and obtains the noise part Modal components, using part of the modal components of the filtered noise to construct a virtual noise channel;
- the independent component analysis module receives the processing result of the threshold filtering module, and separates the original signal into noise and a noise-reduced signal through independent component analysis.
- the invention proposes a method and system for noise reduction and image reconstruction of terahertz time domain signals based on empirical mode decomposition, threshold filtering and independent component analysis.
- the modes containing noise components obtained by empirical mode decomposition are screened by threshold filtering, useful signal components are eliminated, and a purer virtual noise channel is obtained, and then the noise and noise in the noisy signal are decomposed by independent component analysis.
- the effective signal can better solve the modal aliasing problem in the empirical mode decomposition, and greatly improve the signal-to-noise ratio of the processed signal.
- the above-mentioned signal denoising method can be used to perform two-dimensional imaging of the measured sample, which can be based on the maximum value, minimum value or amplitude value at a specific time point of the terahertz signal after noise reduction at each point of the sample, or based on the noise reduction signal.
- the amplitude value at a certain frequency in the frequency spectrum after Fourier transform, or the size of the optical parameters of the sample at a certain frequency extracted based on the noise reduction signal reconstructs the terahertz image of the tested sample, which significantly improves the terahertz image.
- Hertzian imaging signal-to-noise ratio and enhanced contrast for different samples can be used to perform two-dimensional imaging of the measured sample, which can be based on the maximum value, minimum value or amplitude value at a specific time point of the terahertz signal after noise reduction at each point of the sample, or based on the noise reduction signal.
- Fig. 1 is the flow chart of the present invention for the denoising processing of the terahertz time-domain signal containing noise in the sample;
- Fig. 2 is a flowchart of terahertz imaging of samples in the present invention
- Figure 3 is a comparison chart of the noise-containing signal and the noise-reduced signal processed by different methods when the noise level is 8dB;
- Figure 4 is a comparison chart of the signal-to-noise ratio and cross-correlation coefficient results of the noise-reduced signal processed by different methods under different noise levels;
- Figure 5 is a schematic diagram of the terahertz reflection imaging results of layered fiber-reinforced polymer composites (with defects inside) provided by the embodiment of the present invention; wherein, Figure 5(a) is the original signal of a single point of the sample, and Figure 5(b) is Corresponding to the signal after noise reduction using the method of the present invention, Fig. 5(c) is based on the amplitude value at a specific time point of the reflected terahertz time-domain signal for the defect layer of the layered fiber-reinforced polymer composite (with defects inside).
- 5(d) is the terahertz imaging result of the defect layer of the layered fiber-reinforced polymer composite material (with defects inside) based on the amplitude value of the noise-reduced signal at a specific time point based on the method of the present invention.
- the present invention proposes a method for denoising terahertz time-domain signals based on empirical mode decomposition, threshold filtering and independent component analysis, the steps comprising:
- the original signal is separated into noise and noise-reduced signal through independent component analysis
- the terahertz time-domain signal in step 1) may be the terahertz time-domain signal of the sample to be measured based on the measurement of the transmission-type terahertz time-domain spectroscopy system or the measurement based on the reflection-type terahertz time-domain spectroscopy system.
- the empirical mode decomposition described in step 2) may also be set empirical mode decomposition, complementary set empirical mode decomposition, or variational mode decomposition.
- the threshold filtering described in step 4) may be various threshold filtering methods such as soft threshold filtering, hard threshold filtering, or adaptive threshold filtering.
- the independent component analysis described in step 6) can be fast independent component analysis, Fourier independent component analysis.
- the present invention also proposes a method for reconstructing terahertz images based on empirical mode decomposition, threshold filtering and independent component analysis.
- the steps include:
- the specific selection index can be set according to the comparison requirements of the user; and the specific selected The time point and frequency point can also be adjusted according to the user's comparison needs, which is not limited here;
- the two-dimensional imaging of the measured sample described in step 1 adopts terahertz point-by-point scanning imaging or terahertz focal plane imaging, combined with transmission imaging or reflection imaging.
- the samples described in step 1 are various sample forms capable of terahertz imaging.
- the present invention also proposes a system for reconstructing terahertz images based on empirical mode decomposition, threshold filtering and independent component analysis, including
- an imaging module which performs two-dimensional imaging on the tested sample to obtain noise-containing terahertz time-domain signals at each point on the tested sample;
- a noise reduction processing module which is used to perform noise reduction processing on the noise-containing terahertz signal of each point, and obtain the noise-reduced signal of each point on the sample to be tested;
- the image reconstruction module selects the maximum value, the minimum value, or the intensity at a specific time point of the noise-reduced signal, or selects one of the spectrum after the Fourier transform of the noise-reduced signal Amplitude values at frequencies, or selecting the size of optical parameters at a certain frequency extracted based on the noise reduction signal, to reconstruct the terahertz image of the measured sample;
- a result comparison module used to display and compare the reconstructed terahertz images of different tested samples.
- the noise reduction processing module further includes:
- Empirical mode decomposition module used for empirical mode decomposition of terahertz time domain signals containing noise to obtain multiple eigenmode functions;
- Threshold filtering module Receive the processing result of the empirical mode decomposition module, use the correlation coefficient to select the noise-dominated eigenmode function, use the threshold to filter the noise-dominated eigenmode function selected above, filter out the signal part, and obtain the noise part Modal component, using the modal component of the filtered noise part to construct a virtual noise channel;
- Independent component analysis module receives the processing result of the threshold filtering module, and separates the original signal into noise and noise-reduced signal through independent component analysis.
- the embodiment of the present invention proposes a method for denoising a terahertz time-domain signal based on empirical mode decomposition, soft threshold filtering and fast independent component analysis, and the steps include:
- Step 1 Obtain a terahertz time-domain signal containing noise in the sample
- Step 2 Decompose and calculate the obtained noisy signal by using empirical mode decomposition to obtain multiple eigenmode functions.
- the calculation method is as follows:
- Step 3 Use the correlation coefficient to select the noise-dominated eigenmode function, and regard the high-frequency eigenmode function c i (t) with a correlation coefficient less than 0.2 and the next eigenmode function c i+1 (t) as noise
- the dominant eigenmode function the formula for calculating the correlation coefficient between each eigenmode function and the original signal is:
- Step 4 Use the soft threshold to filter the noise-dominated eigenmode function selected above, filter out the signal part, and obtain the modal component y i (t) of the noise part,
- the specific calculation method is:
- N is the signal length.
- Step 5 Construct a virtual noise channel by using the modal component of the noise part obtained by the above soft threshold
- Step 6 Use fast independent component analysis to distinguish noise and useful signals, and obtain noise reduction results.
- the method of adding different Gaussian white noises to pure terahertz time-domain signals is firstly used to form terahertz time-domain signals with different noise levels.
- existing noise reduction method low-pass filter, empirical mode decomposition, empirical mode decomposition and independent component analysis to combine
- signal noise reduction method proposed by the present invention to process respectively, when noise level is 8dB, pure signal , the noise-containing signal and the noise-reduced signal processed by different methods are shown in Figure 3.
- two-dimensional point-by-point scanning combined with reflective imaging is used to carry out the Imaging, the steps are as follows: (1) perform two-dimensional imaging on the layered fiber-reinforced polymer composite material (with defects inside), and obtain noise-containing terahertz time-domain signals of each point on the tested sample; (2) use the signal of the present invention
- the noise reduction method obtains the signal after noise reduction of each point of the measured layered fiber-reinforced polymer composite material (with defects inside); (3) select the amplitude of the original signal and the signal after noise reduction at 22.03ps respectively,
- the terahertz image of the defect layer of the tested layered fiber-reinforced polymer composite (with defects inside) is reconstructed.
- the time point 22.03ps is selected for the following reasons: According to the layered distribution of the layered fiber-reinforced polymer composite (with defects inside), the refractive index of the material and the depth position of the defect layer in the sample, the calculation of the terahertz pulse at The flight time required for the interface reflection of the defect layer corresponds to the time point of the time domain signal at 22.03ps.
- the present invention significantly improves the signal-to-noise ratio of the terahertz image. Noise ratio, and significantly enhance the contrast between different samples, to achieve a beneficial technical effect.
- the invention provides a new imaging method for terahertz imaging and promotes the development of this field.
- the present invention is a method and system for noise reduction and image reconstruction of terahertz signals based on empirical mode decomposition, threshold filtering, and independent component analysis.
- threshold filtering the noise-containing modes obtained by empirical mode decomposition are screened to obtain virtual noise channels, and then the noise and effective signals in the noisy signals are distinguished through independent component analysis, which better solves the problem of empirical mode decomposition.
- it greatly improves the signal-to-noise ratio of the denoised signal.
- the imaging signal-to-noise ratio and contrast are significantly improved.
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Abstract
The present invention belongs to the fields of terahertz signal processing and image reconstruction. Disclosed are a terahertz time domain signal noise reduction method, and a terahertz image reconstruction method and system. By means of a threshold filtering method, modes, which are obtained by means of empirical mode decomposition and include noise, are screened to obtain a virtual noise channel, and a signal including noise is then separated, by means of independent component analysis, into the noise and a signal that has been subjected to noise reduction, such that the mode aliasing problem occurring during empirical mode decomposition is better solved; and compared with existing methods, the method greatly increases the signal-to-noise ratio of the signal that has been subjected to noise reduction. When the method is then used for imaging, compared with existing imaging methods, the method significantly increases the imaging signal-to-noise ratio and the contrast ratio.
Description
本发明属于太赫兹信号处理和图像重建领域，更具体地，涉及一种太赫兹时域信号降噪方法、图像重建方法和系统。The invention belongs to the field of terahertz signal processing and image reconstruction, and more specifically relates to a terahertz time-domain signal noise reduction method, image reconstruction method and system.
太赫兹具有无电离、无损伤等特性，多种有机分子的振动和转动能级落在太赫兹波段，太赫兹波谱检测和成像技术对工作环境和样品形式要求不高，操作简单，并可方便与其他技术进行联合使用。太赫兹波谱检测和成像技术在研究生物大分子特性、医学诊断、安检、材料检测和环境监测等方面具有广阔的应用前景。太赫兹时域光谱系统采集得到的被测样品的太赫兹时域信号可反映太赫兹脉冲的振幅和相位信息，可提取出被测样品在太赫兹波段的光电性质。进一步可对被测样品进行二维扫描时，可根据样品各点太赫兹时域信号的最大值、最小值或特定时间点下的幅度值，或者基于对时域信号进行傅里叶变换后的频谱中某一个频率下的幅度值，或者基于时域信号提取的样品在某一个频率下的光学参数的大小，对被测样品进行太赫兹成像。Terahertz has the characteristics of no ionization and no damage. The vibration and rotational energy levels of various organic molecules fall in the terahertz band. Combined use with other technologies. Terahertz spectroscopy detection and imaging technology has broad application prospects in the study of biological macromolecular properties, medical diagnosis, security inspection, material detection and environmental monitoring. The terahertz time-domain signal of the tested sample collected by the terahertz time-domain spectroscopy system can reflect the amplitude and phase information of the terahertz pulse, and can extract the photoelectric properties of the tested sample in the terahertz band. Furthermore, when two-dimensional scanning is performed on the sample to be measured, it can be based on the maximum value, minimum value or amplitude value at a specific time point of the terahertz time domain signal at each point of the sample, or based on the Fourier transform of the time domain signal The amplitude value at a certain frequency in the spectrum, or the size of the optical parameter of the sample at a certain frequency extracted based on the time-domain signal, is used to perform terahertz imaging on the tested sample.
但是在太赫兹时域光谱系统中，会有来源于激光和光电器件的不稳定性、环境干扰、黑体辐射、光电器件中的电子噪声等各种噪声的影响，导致太赫兹时域信号的信噪比在某些情况下较低。特别是在太赫兹源强度较低或者被测样品在太赫兹波段吸收较强时，噪声对于太赫兹时域信号分析和成像的影响更为严重。对太赫兹时域信号进行有效降噪处理对于样品性质分析和成像识别具有十分重要的意义。However, in the terahertz time-domain spectroscopy system, there will be various noises from the instability of lasers and optoelectronic devices, environmental interference, black body radiation, electronic noise in optoelectronic devices, etc., resulting in signal loss of terahertz time-domain signals The noise ratio is lower in some cases. Especially when the intensity of the terahertz source is low or the measured sample has strong absorption in the terahertz band, the impact of noise on the analysis and imaging of the terahertz time-domain signal is more serious. Effective noise reduction processing of terahertz time-domain signals is of great significance for sample property analysis and imaging identification.
研究人员提出了多种太赫兹时域信号的降噪方法。例如，为了滤除高频噪声，最常用的一种手段是通过低通滤波器滤除特定频段的噪声对太赫兹信号的影响，但此方法只能去除含噪信号中的高频噪声，对低频区域的噪声无法去除，且降噪的频率区域需要自己设定，不具有自适应性；研究人员也利用经验模态分解将原太赫兹信号自适应地分解成多个本征模式函数，选取其中特定的本征模式函数进行加和重构，降低噪声影响。Researchers have proposed a variety of noise reduction methods for terahertz time-domain signals. For example, in order to filter out high-frequency noise, the most commonly used method is to filter out the influence of noise in a specific frequency band on the terahertz signal through a low-pass filter, but this method can only remove high-frequency noise in noisy signals The noise in the low-frequency region cannot be removed, and the frequency region for noise reduction needs to be set by itself, which is not adaptive; researchers also use empirical mode decomposition to adaptively decompose the original terahertz signal into multiple eigenmode functions, and select Among them, the specific eigenmode functions are summed and reconstructed to reduce the influence of noise.
2019年Zhou等人将经验模态分解进一步与独立成分分析相结合，应用于光声成像信号的降噪，通过经验模态分解出的噪声主导的本征模式函数构建噪声通道，再利用独立成分分析分离出噪声与信号，实现了比单独利用经验模态分解进行降噪更好的效果。上述经验模态分解与独立成分分析相结合的方法，也存在明显不足——因为经验模态分解所具有的固有缺陷，往往在含噪模态中会存在严重的模态混叠现象，模态混叠现象导致在这些噪声主导的本征模式函数中噪声与信号混在一起，利用这些本征模式函数构建噪声通道，势必会丢失有用的信号信息，极大地影响了降噪效果。特别是对于太赫兹波谱检测和成像应用时，对于层状样品测试时的多重反射会在采集到的太赫兹信号中存在很多有用的微弱多层反射信号分量，若基于上述经验模态分解与独立成分分析相结合方法进行降噪时，模态混叠的现象会丢失很多有用的多层反射信号信息，信号降噪和图像重建效果很不理想，急需改进和优化。In 2019, Zhou et al. further combined empirical mode decomposition with independent component analysis and applied it to the noise reduction of photoacoustic imaging signals. The noise-dominated eigenmode function obtained by empirical mode decomposition was used to construct the noise channel, and then the independent component The analysis separates the noise and the signal, and achieves a better effect than using the empirical mode decomposition alone for noise reduction. The method of combining empirical mode decomposition and independent component analysis above also has obvious deficiencies—because of the inherent defects of empirical mode decomposition, there will often be serious mode aliasing in noisy modes, and the mode The aliasing phenomenon causes noise and signal to be mixed together in these noise-dominated eigenmode functions. Using these eigenmode functions to construct a noise channel will inevitably lose useful signal information and greatly affect the noise reduction effect. Especially for terahertz spectral detection and imaging applications, there will be many useful weak multi-layer reflection signal components in the collected terahertz signal for the multiple reflections in the layered sample test. If based on the above empirical mode decomposition and independent When the component analysis is combined with the method for noise reduction, the phenomenon of mode aliasing will lose a lot of useful multi-layer reflection signal information, and the signal noise reduction and image reconstruction effects are not ideal, which urgently needs improvement and optimization.
发明内容Contents of the invention
针对相关技术的缺陷，本发明的目的在于提供一种太赫兹时域信号降噪方法、图像重建方法和系统，旨在解决太赫兹波谱检测和成像应用时模态混叠导致降噪效果不理想的问题。In view of the defects of related technologies, the purpose of the present invention is to provide a terahertz time-domain signal noise reduction method, image reconstruction method and system, aiming to solve the unsatisfactory noise reduction effect caused by modal mixing in terahertz spectrum detection and imaging applications The problem.
为实现上述目的，本发明提供了一种太赫兹时域信号降噪方法，其特征在于，包括以下步骤：In order to achieve the above object, the present invention provides a terahertz time-domain signal noise reduction method, which is characterized in that it comprises the following steps:
S1.将含有噪声的太赫兹时域信号进行经验模态分解，得到多个本征模式函数；S1. Perform empirical mode decomposition on the noisy terahertz time domain signal to obtain multiple eigenmode functions;
S2.利用相关系数选择噪声主导的本征模式函数；S2. Using the correlation coefficient to select a noise-dominated eigenmode function;
S3.使用阈值过滤所述噪声主导的本征模式函数，再滤除信号部分，得到噪声部分的模态分量；S3. Use a threshold to filter the noise-dominated eigenmode function, and then filter out the signal part to obtain the modal component of the noise part;
S4.利用所述噪声部分的模态分量构建虚拟噪声通道；S4. Constructing a virtual noise channel by using the modal components of the noise part;
S5.利用所述虚拟噪声通道，通过独立成分分析将原信号分离为噪声与降噪后信号。S5. Using the virtual noise channel, the original signal is separated into noise and a noise-reduced signal through independent component analysis.
进一步地，所述经验模态分解，还可以是集合经验模态分解、互补集合经验模态分解或变分模态分解。Further, the empirical mode decomposition may also be set empirical mode decomposition, complementary set empirical mode decomposition or variational mode decomposition.
进一步地，步骤S1中，太赫兹时域信号x(t)的经验模态分解结果表示为Further, in step S1, the empirical mode decomposition result of the terahertz time domain signal x(t) is expressed as
进一步地，所述步骤S2具体包括以下步骤：Further, the step S2 specifically includes the following steps:
采用相关系数挑选出噪声主导的本征模式函数，将相关系数小于0.2的高频本征模式函数c
i(t)以及下一个本征模式函数c
i+1(t)视为噪声主导的本征模式函数。
Use the correlation coefficient to select the noise-dominated eigenmode function, and regard the high-frequency eigenmode function c i (t) with a correlation coefficient less than 0.2 and the next eigenmode function c i+1 (t) as the noise-dominated eigenmode function feature mode function.
进一步地，所述步骤S3所述的阈值过滤是软阈值过滤、硬阈值过滤或自适应阈值过滤。Further, the threshold filtering in step S3 is soft threshold filtering, hard threshold filtering or adaptive threshold filtering.
进一步地，所述步骤S5所述的独立成分分析是快速独立成分分析或傅里叶独立成分分析。Further, the independent component analysis described in step S5 is fast independent component analysis or Fourier independent component analysis.
本发明的另一方面提供了一种太赫兹图像重建方法，包括以下步骤：Another aspect of the present invention provides a terahertz image reconstruction method, comprising the following steps:
对被测样品进行二维成像，得到所述被测样品上各点含有噪声的太赫兹时域信号；performing two-dimensional imaging on the tested sample to obtain noise-containing terahertz time-domain signals at each point on the tested sample;
采用上述的太赫兹时域信号降噪方法，得到所述被测样品上各点的降噪后信号；Using the above-mentioned terahertz time-domain signal noise reduction method to obtain the noise-reduced signal of each point on the tested sample;
根据不同应用需求，选取所述降噪后信号的最大值、最小值或特定时间点下的强度，或选取对降噪信号进行傅里叶变换后的频谱中某一个频率下的幅度值，或选取基于降噪信号提取的某一个频率下的光学参数的大小，重构所述被测样品的太赫兹图像。According to different application requirements, select the maximum value, the minimum value or the strength at a specific time point of the noise-reduced signal, or select the amplitude value at a certain frequency in the frequency spectrum after the Fourier transform of the noise-reduced signal, or The size of the optical parameter at a certain frequency extracted based on the noise reduction signal is selected to reconstruct the terahertz image of the measured sample.
进一步地，所述对被测样品进行二维成像包括：采用太赫兹逐点扫描成像或太赫兹焦平面成像，并结合透射式成像或反射式成像。Further, the two-dimensional imaging of the measured sample includes: using terahertz point-by-point scanning imaging or terahertz focal plane imaging, combined with transmission imaging or reflection imaging.
本发明的又一方面提供了一种太赫兹图像重建系统，包括：Another aspect of the present invention provides a terahertz image reconstruction system, including:
成像模块，对被测样品进行二维成像，得到所述被测样品上各点含有噪声的太赫兹时域信号；The imaging module performs two-dimensional imaging on the tested sample to obtain noise-containing terahertz time-domain signals at each point on the tested sample;
降噪处理模块，用于对所述各点的含有噪声的太赫兹信号进行降噪处理，得到被测样品上各点在降噪后的信号；A noise reduction processing module, configured to perform noise reduction processing on the noise-containing terahertz signals of each point, to obtain the noise-reduced signal of each point on the sample under test;
图像重构模块，根据不同应用需求，选取所述降噪后信号的最大值、最小值或特定时间点下的强度，或选取对降噪信号进行傅里叶变换后的频谱中某一个频率下的幅度值，或选取基于降噪信号提取的某一个频率下的光学参数的大小，重构所述被测样品的太赫兹图像；The image reconstruction module, according to different application requirements, selects the maximum value, the minimum value, or the intensity at a specific time point of the noise-reduced signal, or selects a certain frequency in the frequency spectrum after the Fourier transform of the noise-reduced signal The amplitude value, or select the size of the optical parameter at a certain frequency extracted based on the noise reduction signal, to reconstruct the terahertz image of the measured sample;
结果比对模块，用于将不同所述被测样品的重构的太赫兹图像进行展示及比对；The result comparison module is used to display and compare the reconstructed terahertz images of different samples under test;
其中，降噪处理模块进一步包括：Wherein, the noise reduction processing module further includes:
经验模态分解模块，用于对含有噪声的太赫兹时域信号进行经验模态分解，得到多个本征模式函数；The empirical mode decomposition module is used to perform empirical mode decomposition on the noise-containing terahertz time-domain signal to obtain multiple eigenmode functions;
阈值过滤模块，接收经验模态分解模块的处理结果，利用相关系数选择噪声主导的本征模式函数，使用阈值过滤上述选择出的噪声主导的本征模式函数，滤除信号部分，得到噪声部分的模态分量，利用过滤得到的噪声的部分模态分量构建虚拟噪声通道；The threshold filtering module receives the processing result of the empirical mode decomposition module, uses the correlation coefficient to select the noise-dominated eigenmode function, uses the threshold to filter the noise-dominated eigenmode function selected above, filters out the signal part, and obtains the noise part Modal components, using part of the modal components of the filtered noise to construct a virtual noise channel;
独立成分分析模块，接收阈值过滤模块的处理结果，通过独立成分分析将原信号分离为噪声与降噪后信号。The independent component analysis module receives the processing result of the threshold filtering module, and separates the original signal into noise and a noise-reduced signal through independent component analysis.
本发明提出了一种基于经验模态分解、阈值过滤和独立成分分析对太赫兹时域信号降噪和图像重建的方法和系统。通过阈值过滤的方式对由经验模态分解得到的含有噪声分量的模态进行筛选，剔除有用信号成分，获得更为纯粹的虚拟噪声通道，再通过独立成分分析分解出含噪信号中的噪声与有效信号，较好地解决了经验模态分解中存在的模态混叠问题，极大地提高了处理后信号的信噪比。进一步可利用上述信号降噪方法，对被测样品进行二维成像，可根据样品各点降噪后太赫兹信号的最大值、最小值或特定时间点下的幅度值，或者基于对降噪信号进行傅里叶变换后的频谱中某一个频率下的幅度值，或者基于降噪信号提取的样品在某一个频率下的光学参数的大小，重构出被测样品的太赫兹图像，显著提高太赫兹成像信噪比和增强不同样品对比度。The invention proposes a method and system for noise reduction and image reconstruction of terahertz time domain signals based on empirical mode decomposition, threshold filtering and independent component analysis. The modes containing noise components obtained by empirical mode decomposition are screened by threshold filtering, useful signal components are eliminated, and a purer virtual noise channel is obtained, and then the noise and noise in the noisy signal are decomposed by independent component analysis. The effective signal can better solve the modal aliasing problem in the empirical mode decomposition, and greatly improve the signal-to-noise ratio of the processed signal. Further, the above-mentioned signal denoising method can be used to perform two-dimensional imaging of the measured sample, which can be based on the maximum value, minimum value or amplitude value at a specific time point of the terahertz signal after noise reduction at each point of the sample, or based on the noise reduction signal The amplitude value at a certain frequency in the frequency spectrum after Fourier transform, or the size of the optical parameters of the sample at a certain frequency extracted based on the noise reduction signal, reconstructs the terahertz image of the tested sample, which significantly improves the terahertz image. Hertzian imaging signal-to-noise ratio and enhanced contrast for different samples.
图1是本发明对样品含有噪声的太赫兹时域信号降噪处理流程图；Fig. 1 is the flow chart of the present invention for the denoising processing of the terahertz time-domain signal containing noise in the sample;
图2是本发明对样品进行太赫兹成像流程图；Fig. 2 is a flowchart of terahertz imaging of samples in the present invention;
图3是噪声水平为8dB时含噪信号和不同方法处理的降噪后信号对比图；Figure 3 is a comparison chart of the noise-containing signal and the noise-reduced signal processed by different methods when the noise level is 8dB;
图4是不同噪声水平下，不同方法处理的降噪后信号的信噪比以及互相关系数结果对比图；Figure 4 is a comparison chart of the signal-to-noise ratio and cross-correlation coefficient results of the noise-reduced signal processed by different methods under different noise levels;
图5为本发明实施例提供的对层状纤维增强聚合物复合材料(内部含有缺陷)太赫兹反射成像结果示意图；其中，图5(a)为样品单点原始信号，图5(b)为对应的利用本发明方法降噪后信号，图5(c)为基于反射太赫兹时域信号特定时间点下幅度值对层状纤维增强聚合物复合材料(内部含有缺陷)的缺陷层进行太赫兹成像的结果，图5(d)为基于本发明方法的降噪后信号特定时间点下幅度值对层状纤维增强聚合物复合材料(内部含有缺陷)的缺陷层进行太赫兹成像结果。Figure 5 is a schematic diagram of the terahertz reflection imaging results of layered fiber-reinforced polymer composites (with defects inside) provided by the embodiment of the present invention; wherein, Figure 5(a) is the original signal of a single point of the sample, and Figure 5(b) is Corresponding to the signal after noise reduction using the method of the present invention, Fig. 5(c) is based on the amplitude value at a specific time point of the reflected terahertz time-domain signal for the defect layer of the layered fiber-reinforced polymer composite (with defects inside). The imaging result, Fig. 5(d) is the terahertz imaging result of the defect layer of the layered fiber-reinforced polymer composite material (with defects inside) based on the amplitude value of the noise-reduced signal at a specific time point based on the method of the present invention.
为了使本发明的目的、技术方案及优点更加清楚明白，以下结合附图及实施例，对本发明进行进一步详细说明。应当理解，此处所描述的具体实施例仅仅用以解释本发明，并不用于限定本发明。此外，下面所描述的本发明各个实施方式中所涉及到的技术特征只要彼此之间未构成冲突就可以相互组合。In order to make the object, technical solution and advantages of the present invention clearer, the present invention will be further described in detail below in conjunction with the accompanying drawings and embodiments. It should be understood that the specific embodiments described here are only used to explain the present invention, not to limit the present invention. In addition, the technical features involved in the various embodiments of the present invention described below can be combined with each other as long as they do not constitute a conflict with each other.
本发明提出了一种基于经验模态分解、阈值过滤和独立成分分析对太赫兹时域信号进行降噪的方法，步骤包括：The present invention proposes a method for denoising terahertz time-domain signals based on empirical mode decomposition, threshold filtering and independent component analysis, the steps comprising:
1)获取被测样品的含有噪声的太赫兹时域信号；1) Acquiring the noise-containing terahertz time-domain signal of the sample under test;
2)将含有噪声的太赫兹时域信号进行经验模态分解，得到多个本征模式函数；2) Decompose the noise-containing terahertz time-domain signal through empirical mode decomposition to obtain multiple eigenmode functions;
3)利用相关系数选择噪声主导的本征模式函数；3) Use the correlation coefficient to select the noise-dominated eigenmode function;
4)使用阈值过滤上述选择出的噪声主导的本征模式函数，滤除信号部分，得到噪声部分的模态分量；4) Filter the noise-dominated eigenmode function selected above using a threshold, filter out the signal part, and obtain the modal component of the noise part;
5)利用过滤得到的噪声部分的模态分量构建虚拟噪声通道；5) constructing a virtual noise channel by using the modal component of the noise part obtained by filtering;
6)利用虚拟噪声通道，通过独立成分分析将原信号分离为噪声与降噪后信号；6) Using the virtual noise channel, the original signal is separated into noise and noise-reduced signal through independent component analysis;
其中，步骤1)所述的太赫兹时域信号，可以是基于透射式太赫兹时域波谱系统测量或基于反射式太赫兹时域波谱系统测量，得到的被测样品的太赫兹时域信号。Wherein, the terahertz time-domain signal in step 1) may be the terahertz time-domain signal of the sample to be measured based on the measurement of the transmission-type terahertz time-domain spectroscopy system or the measurement based on the reflection-type terahertz time-domain spectroscopy system.
其中，步骤2)所述的经验模态分解，也可以是集合经验模态分解、互补集合经验模态分解、变分模态分解。Wherein, the empirical mode decomposition described in step 2) may also be set empirical mode decomposition, complementary set empirical mode decomposition, or variational mode decomposition.
其中，步骤4)所述的阈值过滤，可以是软阈值过滤、硬阈值过滤、或是自适应阈值过滤等各种阈值过滤方法。Wherein, the threshold filtering described in step 4) may be various threshold filtering methods such as soft threshold filtering, hard threshold filtering, or adaptive threshold filtering.
其中，步骤6)所述的独立成分分析，可以是快速独立成分分析、傅里叶独立成分分析。Wherein, the independent component analysis described in step 6) can be fast independent component analysis, Fourier independent component analysis.
此外，本发明还提出了一种基于经验模态分解、阈值过滤和独立成分分析对太赫兹图像重建的方法，步骤包括：In addition, the present invention also proposes a method for reconstructing terahertz images based on empirical mode decomposition, threshold filtering and independent component analysis. The steps include:
1)对被测样品进行二维成像，得到所述被测样品上各点含有噪声的太赫兹时域信号；1) performing two-dimensional imaging on the tested sample to obtain noise-containing terahertz time-domain signals at each point on the tested sample;
2)基于上述的信号降噪方法，得到所述被测样品上各点的降噪后信号；2) Based on the above-mentioned signal noise reduction method, obtain the noise-reduced signal of each point on the tested sample;
3)根据不同应用需求，选取所述降噪后信号的最大值、最小值或特定时间点下的强度，或选取对降噪信号进行傅里叶变换后的频谱中某一个频率下的幅度值，或选取基于降噪信号提取的某一个频率下的光学参数的大小，重构所述被测样品的太赫兹图像；具体选取指标，可以依据用户的比对需求进行设定；而具体选取的时间点和频率点，也是可以根据用户的比对需求进行调整的，此处不以此为限；3) According to different application requirements, select the maximum value, the minimum value or the strength at a specific time point of the noise-reduced signal, or select the amplitude value at a certain frequency in the frequency spectrum after the Fourier transform of the noise-reduced signal , or select the size of the optical parameter at a certain frequency extracted based on the noise reduction signal, and reconstruct the terahertz image of the sample under test; the specific selection index can be set according to the comparison requirements of the user; and the specific selected The time point and frequency point can also be adjusted according to the user's comparison needs, which is not limited here;
其中，步骤1所述的对被测样品进行二维成像，采用太赫兹逐点扫描成像或太赫兹焦平面成像，并结合透射式成像或反射式成像。Wherein, the two-dimensional imaging of the measured sample described in step 1 adopts terahertz point-by-point scanning imaging or terahertz focal plane imaging, combined with transmission imaging or reflection imaging.
其中，步骤1所述样品为各种可进行太赫兹成像的样品形式。Wherein, the samples described in step 1 are various sample forms capable of terahertz imaging.
此外，本发明还提出了一种基于经验模态分解、阈值过滤和独立成分分析对太赫兹图像重建的系统，包括In addition, the present invention also proposes a system for reconstructing terahertz images based on empirical mode decomposition, threshold filtering and independent component analysis, including
1)成像模块，对被测样品进行二维成像，得到所述被测样品上各点含有噪声的太赫兹时域信号；1) an imaging module, which performs two-dimensional imaging on the tested sample to obtain noise-containing terahertz time-domain signals at each point on the tested sample;
2)降噪处理模块，用于对所述各点的含有噪声的太赫兹信号进行降噪处理，得到被测样品上各点在降噪后的信号；2) a noise reduction processing module, which is used to perform noise reduction processing on the noise-containing terahertz signal of each point, and obtain the noise-reduced signal of each point on the sample to be tested;
3)图像重构模块，根据不同应用需求，选取所述降噪后信号的最大值、最小值或特定时间点下的强度，或选取对降噪信号进行傅里叶变换后的频谱中某一个频率下的幅度值，或选取基于降噪信号提取的某一个频率下的光学参数的大小，重构所述被测样品的太赫兹图像；3) The image reconstruction module, according to different application requirements, selects the maximum value, the minimum value, or the intensity at a specific time point of the noise-reduced signal, or selects one of the spectrum after the Fourier transform of the noise-reduced signal Amplitude values at frequencies, or selecting the size of optical parameters at a certain frequency extracted based on the noise reduction signal, to reconstruct the terahertz image of the measured sample;
4)结果比对模块，用于将不同所述被测样品的重构的太赫兹图像进行展示及比对。4) A result comparison module, used to display and compare the reconstructed terahertz images of different tested samples.
其中，降噪处理模块，进一步包括：Wherein, the noise reduction processing module further includes:
经验模态分解模块：用于对含有噪声的太赫兹时域信号进行经验模态分解，得到多个本征模式函数；Empirical mode decomposition module: used for empirical mode decomposition of terahertz time domain signals containing noise to obtain multiple eigenmode functions;
阈值过滤模块：接收经验模态分解模块的处理结果，利用相关系数选择噪声主导的本征模式函数，使用阈值过滤上述选择出的噪声主导的本征模式函数，滤除信号部分，得到噪声部分的模态分量，利用过滤得到的噪声部分的模态分量构建虚拟噪声通道；Threshold filtering module: Receive the processing result of the empirical mode decomposition module, use the correlation coefficient to select the noise-dominated eigenmode function, use the threshold to filter the noise-dominated eigenmode function selected above, filter out the signal part, and obtain the noise part Modal component, using the modal component of the filtered noise part to construct a virtual noise channel;
独立成分分析模块：接收阈值过滤模块的处理结果，通过独立成分分析将原信号分离为噪声与降噪后信号。Independent component analysis module: receives the processing result of the threshold filtering module, and separates the original signal into noise and noise-reduced signal through independent component analysis.
下面结合一个优选实施例，对上述实施例中涉及的内容进行说明。The content involved in the above embodiment will be described below in conjunction with a preferred embodiment.
本发明实施例提出了一种基于经验模态分解、软阈值过滤和快速独立成分分析对太赫兹时域信号进行降噪的方法，步骤包括：The embodiment of the present invention proposes a method for denoising a terahertz time-domain signal based on empirical mode decomposition, soft threshold filtering and fast independent component analysis, and the steps include:
步骤1：获取样品含有噪声的太赫兹时域信号；Step 1: Obtain a terahertz time-domain signal containing noise in the sample;
步骤2：采用经验模态分解对得到的含噪信号进行分解计算，得到多个本征模式函数。计算方法如下：Step 2: Decompose and calculate the obtained noisy signal by using empirical mode decomposition to obtain multiple eigenmode functions. The calculation method is as follows:
(1)找出含噪信号x(t)中的所有局部最大值和最小值点；(1) Find all local maximum and minimum points in the noisy signal x(t);
(2)分别得到(1)中的上包络线x
max(t)和下包络线x
min(t)；
(2) Obtain the upper envelope x max (t) and the lower envelope x min (t) in (1) respectively;
(3)计算上包络线和下包络线的均值：(3) Calculate the mean value of the upper and lower envelopes:
m
1(t)＝(x
max(t)+x
min(t))/2；
m 1 (t) = (x max (t) + x min (t))/2;
(4)得到x(t)去掉均值的新数据序列h
1(t)：
(4) Obtain the new data sequence h 1 (t) of x(t) minus the mean value:
h
1(t)＝x(t)-m
1(t)；
h 1 (t)=x(t)-m 1 (t);
(5)检查h
1(t)是否满足本征模式函数的条件，一般情况下，需要对h
1(t)重复上述处理过程，直到满足本征模式函数的定义要求(1.在全部时间范围内，局部极值点数和过零点数必须相等，或最多相差一个；2.在任意时刻，上包络线和下包络线的平均值必须为零)为止，最终获得第一个本征模式函数c
1(t)；
(5) Check whether h 1 (t) satisfies the conditions of the eigenmode function. In general, it is necessary to repeat the above process for h 1 (t) until it meets the definition requirements of the eigenmode function (1. , the number of local extremum points and the number of zero-crossing points must be equal, or have a difference of at most one; 2. At any time, the average value of the upper and lower envelopes must be zero), and finally the first eigenmode is obtained function c 1 (t);
(6)令r
1(t)＝x(t)-c
1(t)，以r
1(t)为时域信号，重复上述处理步骤，则可以得到其他本征模式函数：c
2(t)，c
3(t)，...，c
n(t)和余项r
n(t)。至此，含噪信号的经验模态分解结果可以表示为：
(6) Let r 1 (t)=x(t)-c 1 (t), take r 1 (t) as the time-domain signal, repeat the above processing steps, then you can get other eigenmode functions: c 2 (t ), c 3 (t), ..., c n (t) and the remainder r n (t). So far, the empirical mode decomposition result of the noisy signal can be expressed as:
步骤3：采用相关系数挑选出噪声主导的本征模式函数，将相关系数小于0.2的高频本征模式函数c
i(t)以及下一个本征模式函数c
i+1(t)视为噪声主导的本征模式函数，各本征模式函数与原信号相关系数计算公式为：
Step 3: Use the correlation coefficient to select the noise-dominated eigenmode function, and regard the high-frequency eigenmode function c i (t) with a correlation coefficient less than 0.2 and the next eigenmode function c i+1 (t) as noise The dominant eigenmode function, the formula for calculating the correlation coefficient between each eigenmode function and the original signal is:
步骤4：采用软阈值过滤上述选择出的噪声主导的本征模式函数，滤除信号部分，得到噪声部分的模态分量y
i(t)，
Step 4: Use the soft threshold to filter the noise-dominated eigenmode function selected above, filter out the signal part, and obtain the modal component y i (t) of the noise part,
计算方式具体为：The specific calculation method is:
y
i(t)＝c
i(t)-Z
i(t)；
y i (t) = c i (t) - Z i (t);
其中，
σ＝median(|c
i(t)-median(c
i(t))|)/0.6745，N为信号长度。
in, σ=median(| ci (t)-median( ci (t))|)/0.6745, N is the signal length.
步骤5：利用上述软阈值得到的噪声部分的模态分量构建虚拟噪声通道；Step 5: Construct a virtual noise channel by using the modal component of the noise part obtained by the above soft threshold;
步骤6：采用快速独立成分分析，区分出噪声与有用信号，得到降噪结果。Step 6: Use fast independent component analysis to distinguish noise and useful signals, and obtain noise reduction results.
为验证本发明对太赫兹时域信号的降噪性能，首先采用纯净太赫兹时域信号添加不同高斯白噪声的方式，形成含有不同噪声水平的太赫兹时域信号。分别利用现有降噪方法(低通滤波器、经验模态分解、经验模态分解与独立成分分析相结合)和本发明提出的信号降噪方法进行处理，在噪声水平为8dB时，纯净信号、含噪信号和不同方法处理的降噪后信号如图3所示，不同噪声水平下，不同方法处理的降噪后信号的信噪比以及与纯净 信号的互相关系数对比结果如图4所示，本发明提出的方法对于含有不同噪声水平的太赫兹时域信号的处理结果的信噪比和互相关系数都优于现有降噪方法，达到了有益的技术效果。In order to verify the noise reduction performance of the present invention on terahertz time-domain signals, the method of adding different Gaussian white noises to pure terahertz time-domain signals is firstly used to form terahertz time-domain signals with different noise levels. Utilize existing noise reduction method (low-pass filter, empirical mode decomposition, empirical mode decomposition and independent component analysis to combine) and signal noise reduction method proposed by the present invention to process respectively, when noise level is 8dB, pure signal , the noise-containing signal and the noise-reduced signal processed by different methods are shown in Figure 3. Under different noise levels, the comparison results of the signal-to-noise ratio of the noise-reduced signal processed by different methods and the cross-correlation coefficient with the pure signal are shown in Figure 4 It is shown that the signal-to-noise ratio and cross-correlation coefficient of the processing results of the terahertz time-domain signals containing different noise levels by the method proposed by the present invention are superior to the existing noise reduction methods, achieving beneficial technical effects.
为验证本发明提出的太赫兹图像重构方法的效果，在一个具体的实施例中，采用二维逐点扫描结合反射成像的方式，对层状纤维增强聚合物复合材料(内部含有缺陷)进行成像，步骤如下：(1)对层状纤维增强聚合物复合材料(内部含有缺陷)进行二维成像，得到被测样品上各点的含有噪声太赫兹时域信号；(2)利用本发明信号降噪方法，得到所述被测层状纤维增强聚合物复合材料(内部含有缺陷)各点的降噪后信号；(3)分别选取原信号和降噪后信号在22.03ps下的幅值，重构出被测层状纤维增强聚合物复合材料(内部含有缺陷)缺陷层的太赫兹图像。此成像应用中，时间点22.03ps选取原因如下：依据层状纤维增强聚合物复合材料(内部含有缺陷)的层状分布、材料折射率和缺陷层在样品内的深度位置，计算太赫兹脉冲在缺陷层界面反射所需飞行时间，对应时域信号时间点为22.03ps。In order to verify the effect of the terahertz image reconstruction method proposed in the present invention, in a specific embodiment, two-dimensional point-by-point scanning combined with reflective imaging is used to carry out the Imaging, the steps are as follows: (1) perform two-dimensional imaging on the layered fiber-reinforced polymer composite material (with defects inside), and obtain noise-containing terahertz time-domain signals of each point on the tested sample; (2) use the signal of the present invention The noise reduction method obtains the signal after noise reduction of each point of the measured layered fiber-reinforced polymer composite material (with defects inside); (3) select the amplitude of the original signal and the signal after noise reduction at 22.03ps respectively, The terahertz image of the defect layer of the tested layered fiber-reinforced polymer composite (with defects inside) is reconstructed. In this imaging application, the time point 22.03ps is selected for the following reasons: According to the layered distribution of the layered fiber-reinforced polymer composite (with defects inside), the refractive index of the material and the depth position of the defect layer in the sample, the calculation of the terahertz pulse at The flight time required for the interface reflection of the defect layer corresponds to the time point of the time domain signal at 22.03ps.
样品单点太赫兹信号降噪处理前后的结果和相应太赫兹成像结果如图5所示。采用原太赫兹时域信号，缺陷位置不可见。采用本发明提出的新成像方法，缺陷位置清晰可见(黑色虚线框所示)，显著增强不同样品间的对比度。本发明提出的成像方法的太赫兹图像在目标缺陷区域信噪比14.15dB，传统的成像方法的太赫兹图像在目标缺陷区域信噪比9.25dB，可见，本发明显著提升了太赫兹图像的信噪比，并显著增强不同样品间的对比度，达到了有益的技术效果。本发明对太赫兹成像提供了一个新的成像方法，促进了本领域的发展。The results before and after the single-point terahertz signal denoising of the sample and the corresponding terahertz imaging results are shown in Figure 5. With the original terahertz time domain signal, the defect position is not visible. By adopting the new imaging method proposed by the present invention, the defect position can be clearly seen (shown by the black dotted frame), and the contrast between different samples can be significantly enhanced. The signal-to-noise ratio of the terahertz image of the imaging method proposed in the present invention is 14.15dB in the target defect area, and the signal-to-noise ratio of the terahertz image of the traditional imaging method is 9.25dB in the target defect area. It can be seen that the present invention significantly improves the signal-to-noise ratio of the terahertz image. Noise ratio, and significantly enhance the contrast between different samples, to achieve a beneficial technical effect. The invention provides a new imaging method for terahertz imaging and promotes the development of this field.
综上所述，本发明是一种基于经验模态分解、阈值过滤、独立成分分析对太赫兹信号降噪和图像重建的方法和系统。通过阈值过滤的方法对由经验模态分解得到的含有噪声模态进行筛选获得虚拟噪声通道，再通过独立成分分析区分出含噪信号中的噪声与有效信号，较好地解决了经验模态分 解中会存在的模态混叠问题，与现有方法相比，极大地提高了降噪后信号的信噪比。在进一步用于成像时，与现有成像方法相比，显著提高了成像信噪比和对比度。In summary, the present invention is a method and system for noise reduction and image reconstruction of terahertz signals based on empirical mode decomposition, threshold filtering, and independent component analysis. Through the method of threshold filtering, the noise-containing modes obtained by empirical mode decomposition are screened to obtain virtual noise channels, and then the noise and effective signals in the noisy signals are distinguished through independent component analysis, which better solves the problem of empirical mode decomposition. Compared with the existing methods, it greatly improves the signal-to-noise ratio of the denoised signal. When further used for imaging, compared with existing imaging methods, the imaging signal-to-noise ratio and contrast are significantly improved.
本领域的技术人员容易理解，以上所述仅为本发明的较佳实施例而已，并不用以限制本发明，凡在本发明的精神和原则之内所作的任何修改、等同替换和改进等，均应包含在本发明的保护范围之内。It is easy for those skilled in the art to understand that the above descriptions are only preferred embodiments of the present invention, and are not intended to limit the present invention. Any modifications, equivalent replacements and improvements made within the spirit and principles of the present invention, All should be included within the protection scope of the present invention.
Claims (10)
- 一种太赫兹时域信号降噪方法，其特征在于，包括以下步骤：A terahertz time-domain signal denoising method, characterized in that it comprises the following steps:S1.将含有噪声的太赫兹时域信号进行经验模态分解，得到多个本征模式函数；S1. Perform empirical mode decomposition on the noisy terahertz time domain signal to obtain multiple eigenmode functions;S2.利用相关系数选择噪声主导的本征模式函数；S2. Using the correlation coefficient to select a noise-dominated eigenmode function;S3.使用阈值过滤所述噪声主导的本征模式函数，再滤除信号部分，得到噪声部分的模态分量；S3. Use a threshold to filter the noise-dominated eigenmode function, and then filter out the signal part to obtain the modal component of the noise part;S4.利用所述噪声部分的模态分量构建虚拟噪声通道；S4. Constructing a virtual noise channel by using the modal components of the noise part;S5.利用所述虚拟噪声通道，通过独立成分分析将原信号分离为噪声与降噪后信号。S5. Using the virtual noise channel, the original signal is separated into noise and a noise-reduced signal through independent component analysis.
- 如权利要求1所述的太赫兹时域信号降噪方法，其特征在于，所述经验模态分解是经典经验模态分解、集合经验模态分解、互补集合经验模态分解或变分模态分解。The method for denoising terahertz time-domain signals according to claim 1, wherein the empirical mode decomposition is classical empirical mode decomposition, ensemble empirical mode decomposition, complementary ensemble empirical mode decomposition or variational mode break down.
- 如权利要求1所述的太赫兹时域信号降噪方法，其特征在于，步骤S1中，太赫兹时域信号x(t)的经验模态分解结果表示为The method for denoising a terahertz time-domain signal according to claim 1, wherein in step S1, the empirical mode decomposition result of the terahertz time-domain signal x(t) is expressed as
- 如权利要求3所述的太赫兹时域信号降噪方法，其特征在于，所述步骤S2具体包括以下步骤：The terahertz time-domain signal denoising method according to claim 3, wherein said step S2 specifically comprises the following steps:采用相关系数挑选出噪声主导的本征模式函数，将相关系数小于0.2的高频本征模式函数c i(t)以及下一个本征模式函数c i+1(t)视为噪声主导的本征模式函数。 Use the correlation coefficient to select the noise-dominated eigenmode function, and regard the high-frequency eigenmode function c i (t) with a correlation coefficient less than 0.2 and the next eigenmode function c i+1 (t) as the noise-dominated eigenmode function feature mode function.
- 如权利要求1所述的太赫兹时域信号降噪方法，其特征在于，所述步骤S3所述的阈值过滤是软阈值过滤、硬阈值过滤或自适应阈值过滤。The method for denoising a terahertz time-domain signal according to claim 1, wherein the threshold filtering in step S3 is soft threshold filtering, hard threshold filtering or adaptive threshold filtering.
- 如权利要求1所述的太赫兹时域信号降噪方法，其特征在于，所述太赫兹时域信号是基于透射式太赫兹时域波谱系统测量或基于反射式太赫兹时域波谱系统测量，所得到的被测样品的太赫兹时域信号。The method for reducing noise of a terahertz time-domain signal according to claim 1, wherein the terahertz time-domain signal is measured based on a transmission-type terahertz time-domain spectroscopy system or based on a reflection-type terahertz time-domain spectroscopy system, The obtained terahertz time-domain signal of the tested sample.
- 如权利要求1所述的太赫兹时域信号降噪方法，其特征在于，所述步骤S5所述的独立成分分析是快速独立成分分析或傅里叶独立成分分析。The method for denoising terahertz time-domain signals according to claim 1, wherein the independent component analysis in step S5 is fast independent component analysis or Fourier independent component analysis.
- 一种太赫兹图像重建方法，其特征在于，包括以下步骤：A method for reconstructing a terahertz image, comprising the following steps:对被测样品进行二维成像，得到所述被测样品上各点含有噪声的太赫兹时域信号；performing two-dimensional imaging on the tested sample to obtain noise-containing terahertz time-domain signals at each point on the tested sample;采用权利要求1-7任一项所述的太赫兹时域信号降噪方法，得到所述被测样品上各点的降噪后信号；Using the terahertz time-domain signal noise reduction method described in any one of claims 1-7 to obtain the noise-reduced signal of each point on the measured sample;根据不同应用需求，选取所述降噪后信号的最大值、最小值或特定时间点下的强度，或选取对降噪信号进行傅里叶变换后的频谱中某一个频率下的幅度值，或选取基于降噪信号提取的某一个频率下的光学参数的大小，重构所述被测样品的太赫兹图像。According to different application requirements, select the maximum value, the minimum value or the strength at a specific time point of the noise-reduced signal, or select the amplitude value at a certain frequency in the frequency spectrum after the Fourier transform of the noise-reduced signal, or The size of the optical parameter at a certain frequency extracted based on the noise reduction signal is selected to reconstruct the terahertz image of the measured sample.
- 如权利要求8所述的太赫兹图像重建方法，其特征在于，所述对被测样品进行二维成像包括：采用太赫兹逐点扫描成像或太赫兹焦平面成像，并结合透射式成像或反射式成像。The terahertz image reconstruction method according to claim 8, wherein the two-dimensional imaging of the measured sample comprises: using terahertz point-by-point scanning imaging or terahertz focal plane imaging, combined with transmission imaging or reflection imaging.
- 一种太赫兹图像重建系统，其特征在于，包括：A terahertz image reconstruction system is characterized in that it comprises:成像模块，对被测样品进行二维成像，得到所述被测样品上各点含有噪声的太赫兹时域信号；The imaging module performs two-dimensional imaging on the tested sample to obtain noise-containing terahertz time-domain signals at each point on the tested sample;降噪处理模块，用于对所述各点的含有噪声的太赫兹信号进行降噪处理，得到被测样品上各点降噪后的信号；A noise reduction processing module, configured to perform noise reduction processing on the noise-containing terahertz signal at each point, to obtain a noise-reduced signal at each point on the sample to be tested;图像重构模块，根据不同应用需求，选取所述降噪后信号的最大值、最小值或特定时间点下的强度，或选取对降噪信号进行傅里叶变换后的频谱中某一个频率下的幅度值，或选取基于降噪信号提取的某一个频率下的光学参数的大小，重构所述被测样品的太赫兹图像；The image reconstruction module, according to different application requirements, selects the maximum value, the minimum value, or the intensity at a specific time point of the noise-reduced signal, or selects a certain frequency in the frequency spectrum after the Fourier transform of the noise-reduced signal The amplitude value, or select the size of the optical parameter at a certain frequency extracted based on the noise reduction signal, to reconstruct the terahertz image of the measured sample;结果比对模块，用于将不同所述被测样品的重构的太赫兹图像进行展示及比对；The result comparison module is used to display and compare the reconstructed terahertz images of different samples under test;其中，降噪处理模块进一步包括：Wherein, the noise reduction processing module further includes:经验模态分解模块，用于对含有噪声的太赫兹时域信号进行经验模态分解，得到多个本征模式函数；The empirical mode decomposition module is used to perform empirical mode decomposition on the noise-containing terahertz time-domain signal to obtain multiple eigenmode functions;阈值过滤模块，接收经验模态分解模块的处理结果，利用相关系数选择噪声主导的本征模式函数，使用阈值过滤上述选择出的噪声主导的本征模式函数，滤除信号部分，得到噪声部分的模态分量，利用过滤得到的噪声部分的模态分量构建虚拟噪声通道；The threshold filtering module receives the processing result of the empirical mode decomposition module, uses the correlation coefficient to select the noise-dominated eigenmode function, uses the threshold to filter the noise-dominated eigenmode function selected above, filters out the signal part, and obtains the noise part Modal component, using the modal component of the filtered noise part to construct a virtual noise channel;独立成分分析模块，接收阈值过滤模块的处理结果，通过独立成分分析将原信号分离为噪声与降噪后信号。The independent component analysis module receives the processing result of the threshold filtering module, and separates the original signal into noise and a noise-reduced signal through independent component analysis.
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