WO2019178794A1 - 一种荧光寿命的测量方法及装置 - Google Patents

一种荧光寿命的测量方法及装置 Download PDF

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WO2019178794A1
WO2019178794A1 PCT/CN2018/079924 CN2018079924W WO2019178794A1 WO 2019178794 A1 WO2019178794 A1 WO 2019178794A1 CN 2018079924 W CN2018079924 W CN 2018079924W WO 2019178794 A1 WO2019178794 A1 WO 2019178794A1
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matrix
measurement
sparse
sampling
fluorescence lifetime
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PCT/CN2018/079924
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French (fr)
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屈军乐
陈秉灵
严伟
林丹樱
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深圳大学
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    • G—PHYSICS
    • G01—MEASURING; TESTING
    • G01N—INVESTIGATING OR ANALYSING MATERIALS BY DETERMINING THEIR CHEMICAL OR PHYSICAL PROPERTIES
    • G01N21/00—Investigating or analysing materials by the use of optical means, i.e. using sub-millimetre waves, infrared, visible or ultraviolet light
    • G01N21/62—Systems in which the material investigated is excited whereby it emits light or causes a change in wavelength of the incident light
    • G01N21/63—Systems in which the material investigated is excited whereby it emits light or causes a change in wavelength of the incident light optically excited
    • G01N21/64—Fluorescence; Phosphorescence

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  • the invention belongs to the field of photoelectric detection, and in particular relates to a method and a device for measuring fluorescence lifetime.
  • Modern methods of fluorescence lifetime measurement include: Strobe Techniques, Phase Modulation Methods, Streak Cameras, Upcon-version Methods, and Time-Dependent Single-Photon Counting ( Time-Correlated Single-Photon Counting, TCSPC).
  • single photon counting is a powerful means of detecting very weak light.
  • the technique extracts the optical signal from the thermal noise digitally by distinguishing the photoelectron pulses excited by a single photon in the detector (PMT).
  • An important component of TCSPC technology is the Time Amplitude Converter (TAC), which is used to record the time interval between two different electrical signals.
  • TAC Time Amplitude Converter
  • the detector PMT converts the optical signal into an electrical signal and simultaneously initiates the recording of the TAC; when the sample is excited by the pulsed light, the fluorescent signal is delayed by a certain time and is also converted into a power by the PMT. Signal, terminate the TAC record.
  • the time interval signal recorded by the TAC is transmitted to the multi-channel analyzer (MCA) in the form of electrical pulses, and a point is recorded in the time channel corresponding to the MCA. After a large number of photons are accumulated, a fluorescence decay curve is formed. Statistical distribution.
  • the TAC since the TAC only records the first emitted photon signal after the excitation pulse, if more than two emitted photons are generated in a certain excitation pulse, only the first photon will be recorded, so that the signal frequency accumulation of the short-time channel is high.
  • the measured fluorescence decay curve will be significantly twisted. Therefore, in the detection process of TCSPC, the laser power must be reduced so that the energy contained in each laser pulse is small enough that each time the sample is excited, it is much smaller than a fluorescent photon reaching the photocathode of the detector. The purpose of this is to avoid the number of photons.
  • TCSPC is a time-consuming method for measuring fluorescence lifetime.
  • the present invention provides a method and apparatus for measuring fluorescence lifetime, and aims to provide a faster method for measuring fluorescence lifetime.
  • the invention provides a method for measuring fluorescence lifetime, comprising:
  • Each row of the preset measurement matrix is used as a sampling mode, and each non-zero value position in the sampling mode is used as a sparse signal channel for time-gated delay sampling, and is gated by time-gated hardware in each sampling mode.
  • the invention also provides a measuring device for fluorescence lifetime, comprising:
  • a reconstruction module configured to perform signal reconstruction by applying an inverse transform of a known sparse transform matrix to the sparse coefficient
  • the present invention has the beneficial effects that the method and the device for measuring the fluorescence lifetime of the present invention use each line of the preset random matrix as a sampling mode, and the non-zero value in each sampling mode.
  • the position is controlled by the time-gated hardware to delay sampling the sample in each sampling mode, and the photon number of the sparse signal channel in the current sampling mode is added together to obtain a compressed sensing measurement value, and each sampling mode is repeated.
  • the present invention implements multiple sampling mode settings through a measurement matrix to implement time gating function and pass Time gating function to select the time channel of photon accumulation, combined with time-gated hard
  • the delay sampling is performed to obtain the measured value, and the obtained measured value is combined with the compressed sensing algorithm for signal reconstruction, so that the problem that the TCSPC technology takes a long time is avoided, and the time-gated fluorescence lifetime resolution is avoided.
  • the problem is that it enables faster imaging and improves the measurement speed of fluorescence lifetime.
  • FIG. 1 is a schematic diagram of time-based fluorescence lifetime compression sensing sampling according to an embodiment of the present invention
  • FIG. 2 is a schematic flow chart of a method for measuring a fluorescence lifetime according to an embodiment of the present invention
  • FIG. 4 is a schematic diagram of a BPDN signal reconstruction result of a discrete Fourier transform (DFT) according to an embodiment of the present invention
  • FIG. 5 is a schematic diagram of a BPDN signal reconstruction result of an orthogonal exponential function set (Oexp-Basis) sparse basis provided by an embodiment of the present invention
  • FIG. 6 is a schematic diagram of a BPDN signal reconstruction result of DFT sparse base deconvolution according to an embodiment of the present invention
  • FIG. 7 is a schematic block diagram of a method for measuring fluorescence lifetime according to an embodiment of the present invention.
  • the present invention provides a method and a device for measuring fluorescence lifetime, which utilizes a gate control technique to achieve short-time photon filtering of a photon "stacking effect" under high excitation power, and achieves low sampling with compression sensing technology.
  • the rate of signal acquisition to reconstruct the source signal of high sampling rate improves the measurement speed of fluorescence lifetime.
  • Compressed Sensing proposes a new sampling theory that can compress and sample signals at much lower than the Nyquist sampling rate. Simply put, as long as the signal is compressible or sparse in a certain transform domain, then a sensor matrix that is uncorrelated with the transform base can be used to project the signal into a low-dimensional space, which proves that such a projection contains the original signal. Sufficient information, and then solve the optimization problem to reconstruct the original signal from these small projections with very high probability. Compressed sensing provides an experimental solution for signal digitization while sampling and compressing at an ultra-low rate, greatly reducing the sampling time cost of the sensor. If the signal itself is a sparse signal, there is no problem, even if the signal is not sparse, as long as the appropriate signal sparse representation space can be found, the compression sampling can be effectively performed.
  • the original signal x is a one-dimensional signal of length N
  • the sparsity is k (it is unknown at the moment)
  • the measurement matrix ⁇ of M ⁇ N (M ⁇ N) dimension corresponds to the subsampling process (known)
  • the general natural signal x itself is not sparse and requires sparse representation on a sparse basis.
  • the sensing matrix A must satisfy the Constrained Isometry Property (RIP) condition, and under the condition of satisfying RIP, to accurately reconstruct the k-sparse signal s, it is necessary to repeat M ⁇ cklog(N). /k) Sub-measurement (c is a small constant).
  • RIP Constrained Isometry Property
  • c is a small constant.
  • the theory of compressed sensing mainly includes three key technologies: the sparse representation of the signal, the design of the measurement matrix and the research of the reconstruction algorithm.
  • the first is the sparse representation of the signal.
  • the signal In the actual compressed sensing measurement, the signal is often not sparse. It is necessary to find the most sparse representation of the signal by using appropriate transformation. The more sparse the representation of the signal, the number of measurements required to reconstruct the signal with high precision. The smaller it is.
  • the most easily thought of sparse transform is the Fourier transform. If the signal is not sparse in the time domain, the signal can be transformed into a frequency domain sparse representation by Fourier transform; if the signal is not sparse in the frequency domain, it can pass Fourier.
  • the inverse transform turns the signal into a time domain sparse representation.
  • transformations such as Laplace transform, wavelet transform, and tightly supported wavelet Curvelets, Contourlets, and so on.
  • the design of the measurement matrix Since the Gaussian random matrix is almost irrelevant to the sparse basis of any signal, the number of measurements required is small and the applicability is wide, but the disadvantage is that the matrix element requires a large storage space, and because of its non- The characterization of the structure leads to its high complexity and is not easy to implement on hardware. Therefore, in order to facilitate the implementation on the hardware, a random Bernoulli matrix, a partial Hadamard matrix or a sparse random matrix can be used.
  • the appropriate algorithm to reconstruct the source signal is mainly divided into two categories, one is the greedy algorithm of l 0 norm, such as matching tracking (MP), orthogonal matching tracking (OMP), compressed sampling matching tracking (CoSaMP). ); one is the l 1 norm convex optimization algorithm, which mainly includes base tracking (BP), gradient projection, minimum angle regression and other algorithms.
  • l 0 norm such as matching tracking (MP), orthogonal matching tracking (OMP), compressed sampling matching tracking (CoSaMP).
  • l 1 norm convex optimization algorithm which mainly includes base tracking (BP), gradient projection, minimum angle regression and other algorithms.
  • the response to ultrashort pulses is a single exponential decay function.
  • the different luminescent groups of the fluorescent substance contribute differently to the decay of the overall fluorescence intensity, so the fluorescence decay curve of the system is a multi-exponential function model:
  • the experimentally measured fluorescence decay curve is the convolution of the overall instrument response function h(t) and the impulse response function e(t):
  • the main detection methods of fluorescence lifetime are divided into phase modulation frequency domain detection method and time domain detection method, while time domain detection method is subdivided into three main methods: time gate detection, time-correlated single photon counting and stripe camera.
  • time gate detection time-correlated single photon counting
  • stripe camera What we want to develop is a fluorescence lifetime detection count based on time-gate compressed sensing sampling. The technical scheme is shown in Figure 1.
  • a method for measuring the fluorescence lifetime provided by the embodiment of the present invention is specifically described below, and the measurement method is a fast fluorescence lifetime measurement method based on time gate compression sensing sampling:
  • a method for measuring fluorescence lifetime according to the present invention includes:
  • Step S1 each row of the preset measurement matrix is used as a sampling mode, and each non-zero value position in the sampling mode is used as a sparse signal channel for time-gated delay sampling, and each sampling is performed by time-gated hardware.
  • the generating process of the preset measurement matrix is: constructing a measurement matrix that conforms to the principle of time-gated delay sampling by using an existing compressed sensing algorithm;
  • the measurement matrix provided by the embodiment of the present invention is a random Bernoulli measurement matrix or a sparse random measurement matrix; wherein the design method of the random Bernoulli measurement matrix is: constructing a size of M ⁇ N matrix ⁇ , where each element independently obeys the Bernoulli distribution, ie:
  • the design method of the sparse random measurement matrix is: forming an all-zero element M ⁇ N matrix ⁇ , and then randomly selecting elements of d positions in each column of the matrix, wherein d is any greater than 0 and less than N. Natural number.
  • each row of the measurement matrix ⁇ represents an independent measurement yi, and the non-zero elements in each row represent the time channel of the compressed sample; traversing all the rows, that is, obtaining a set of M ⁇ 1 dimensional measurements.
  • Embodiments of the present invention provide two methods for independently measuring yi: First, a time-gated intensified CCD-based wide-field fluorescence lifetime imaging system is selected, and an element corresponding to a measurement matrix ⁇ i-th row having a value of 1 is selected.
  • the time channel is sequentially exposed and accumulated to form a positive sample, and the first photon number is accumulated, and then the time channel corresponding to the -1 element is sequentially exposed and accumulated to form a negative sample, and the second photon number is obtained.
  • a photon number accumulation and the second photon number cumulative subtraction constitute a compressed sensing independent measurement value yi.
  • the threshold value of the absolute value of the voltage can be increased to obtain more probe photons, and the delay sampling function or time gating function of the TCSPC acquisition card is used to select
  • the time channel accumulated by the photon is positively sampled according to the element value of the measurement matrix, and the first photon number is accumulated, and the negative value is -1, the second photon number is accumulated, and the first photon is used.
  • the cumulative sum of the number and the second photon number constitutes a compressed sensing independent measurement value yi.
  • Step S2 using the compressed sensing measurement value combined with the inverse transformation of the measurement matrix ⁇ M ⁇ N and the sparse transformation matrix
  • the compressed sampling model is:
  • y is the compressed sensing measurement and A is the sensing matrix.
  • ⁇ is the measurement matrix, s is the sparse coefficient, and ⁇ is the Lagrangian factor.
  • the experimentally measured fluorescence decay curve is a convolution of the overall instrument response function h(t) and the impulse response function e(t), and the mathematical model of equation (7) does not Consider the impact of the instrument response function. If you need to consider the instrument response function, you need to improve the formula (7) accordingly.
  • the convolution theorem the Fourier transform of the convolution of two functions is equal to the multiplication of the respective function Fourier transforms, ie
  • the model formula (7) will be corrected to the mathematical model following the instrument response function as follows:
  • y is the compressed sensing measurement and A is the sensing matrix.
  • h is the instrument response function
  • ⁇ is the measurement matrix
  • s is the sparse coefficient
  • ⁇ is the Lagrangian factor.
  • Step S3 performing signal reconstruction by applying an inverse transform of a known sparse transform matrix to the sparse coefficient
  • the fluorescence decay curve is obtained by inverse Fourier transform
  • Equation (4) can be re-understood from the perspective of linear transformation, and the impulse response function e(t) is linearly represented by a sparse basis ⁇ exp(-t/ ⁇ k ) ⁇ composed of an exponential function of a few different lifetimes ⁇ k , weight ⁇ k is a linear transform coefficient.
  • the life component is specified to be 3-5 kinds, and the visible weight ⁇ k is very sparse.
  • the compressed sensing model that directly uses the exponential function set ⁇ exp(-t/ ⁇ k ) ⁇ as the coefficient transform to fit the formula (7) will not successfully recover the original signal.
  • the possible reason is that the exponential function set ⁇ exp(- t/ ⁇ k ) ⁇ is not an orthogonal basis. If the Gram-Schmidt method is used to orthogonalize the exponential function set (Oexp-Basis for short), the signal recovery result similar to the Fourier transform base can be obtained. However, even if the exponential function set after orthogonalization is applied to the deconvolution model of equation (8), the source signal cannot be recovered successfully. The possible reason is that the orthogonalized exponential function set does not satisfy the convolution theorem.
  • Fourier transform will be used in the deconvolution model formula (8)
  • the least squares method can be used to solve 2K undetermined coefficients ⁇ k and ⁇ k .
  • 3 is a full-spectrum sampling of fluorescence lifetime of a fluorescent bead according to an embodiment of the present invention.
  • the ordinate is displayed on a logarithmic coordinate, the scatter indicates an experimentally measured fluorescence lifetime decay curve, and the solid line indicates a least squares exponential decay. Curve.
  • DFT discrete Fourier transform
  • the distortion of the rising edge of the pulse may be due to the fact that equation (7) does not consider the effect of the convolution of the instrument response function, and the signal-to-noise ratio is not high due to the characteristics of the DFT itself.
  • the DFT potential characteristics that affect the signal-to-noise ratio include that the DFT sparsity is not strong and the denoising ability is not strong.
  • the DFT can cause the jitter of the reconstructed signal caused by the relatively strong Gibbs effect.
  • the embodiment of the present invention uses the mathematical model of the formula (7) to perform the BPDN signal weight.
  • the results are shown in Figure 5. From the results, Oexp-Basis's denoising ability is obviously superior to DFT, which is related to the relatively strong sparsity of Oexp-Basis, but the phenomenon of partial distortion of the rising edge of the pulse still exists. This does not consider the instrument with formula (7).
  • the convolution effect of the response function is related.
  • the embodiment of the present invention uses the mathematical model of the formula (8) to implement deconvolution signal reconstruction, and the model can only process the instrument response function to a known situation.
  • the model needs to be improved.
  • DFT deconvolution can effectively improve the signal reconstruction accuracy of the rising edge of the pulse and the short-lived part, but the Gibbs effect of DFT still exists.
  • the deconvolution effect of Oexp-Basis is not ideal. The possible reason is that Oexp-Basis does not fully satisfy the convolution theorem.
  • the present invention provides a time-based fluorescence lifetime compression sensing sampling and reconstruction technical solution, has a theoretical guidance of a rigorous mathematical model, has available instruments for satisfying compressed sensing sampling, and has a mature compressed sensing program algorithm. Ensure source signal reconstruction.
  • a method for measuring fluorescence lifetime wherein a plurality of sampling modes are set by a measurement matrix to implement a time gating function, and a time gate function is used to select a time channel for photon accumulation, and a time gate is combined
  • the control hardware performs delay sampling to obtain the measured value, and then uses the obtained measured value combined with the compressed sensing algorithm to reconstruct the signal, thereby avoiding the problem that the TCSPC technology takes a long time and avoids the time-gated fluorescence lifetime resolution.
  • the low problem enables faster imaging and improved measurement of fluorescence lifetime.
  • the embodiment of the invention further provides a measuring device for fluorescence lifetime, as shown in FIG. 7, the device comprises:
  • the acquisition module 1 is configured to use each row of the preset measurement matrix as a sampling mode, and each non-zero value position in the sampling mode is used as a sparse signal channel for time-gated delay sampling, and is time-controlled hardware.
  • a solution module 2 for utilizing the compressed sensing measurement value combined with an inverse transformation of the measurement matrix ⁇ M ⁇ N and a sparse transformation matrix
  • a reconstruction module 3 configured to perform signal reconstruction by applying an inverse transform of a known sparse transform matrix to the sparse coefficient
  • the related content of the fluorescence lifetime measuring device can be specifically referred to the measurement method of the fluorescence lifetime described in the embodiment shown in FIG. 2, and details are not described herein.

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Abstract

一种荧光寿命的测量方法，包括：首先，以预置的测量矩阵的每一行作为一个采样模式，每一个所述采样模式下的非零值位置作为一个时间门控延迟采样的稀疏信号通道，在每个采样模式下对样品进行延迟采样，将当前采样模式下的稀疏信号通道的光子数累加在一起获得一个压缩感知测量值，重复各采样模式获取系列压缩感知测量值；然后，利用所述压缩感知测量值并结合测量矩阵在 l 1范数最优化算法下求解方程得到稀疏系数；最后，通过已知的稀疏矩阵逆变换作用于所述稀疏系数，进行信号重构，得到荧光寿命衰减曲线，以实现荧光寿命的测量；该方法提高了荧光寿命的测量速度。一种运用上述方法测量荧光寿命的装置。

Description

一种荧光寿命的测量方法及装置 技术领域
本发明属于光电检测领域，尤其涉及一种荧光寿命的测量方法及装置。
背景技术
荧光寿命测量的现代方法主要包括：闪频技术(Strobe Techniques)、相调制法(Phase Modulation Methods)、相机条纹(Streak Cameras)、上转换法(Upcon-version Methods)和时间相关单光子计数法(Time-Correlated Single-Photon Counting,TCSPC)。
其中，单光子计数是检测极微弱光的有力手段，该技术通过分辨单个光子在检测器(PMT)中激发出来的光电子脉冲，把光信号从热噪声中以数字化的方式提取出来。TCSPC技术的一个重要部件是时幅转换器(TAC)，用于记录不同两个电信号的时间间隔。当激发光源发射一束短脉冲光，探测器PMT将光信号转换为一个电信号，同时启动TAC的记录；当样品被脉冲光激发后，延迟一定的时间发射荧光信号同样被PMT转换为一个电信号，终止TAC的记录。这样被TAC记录下来的时间间隔信号会以电脉冲的形式传达给多通道分析器(MCA)，并在MCA对应的时间通道内记录一个点，经大量光子数的累计，就会形成荧光衰减曲线的统计分布。
但由于TAC只记录激发脉冲后的第一个发射光子信号，如果在某一激发脉冲产生两个以上的发射光子，则只有第一个光子会被记录，使得短时间通道的信号频次堆积偏高，测量得到的荧光衰减曲线会有明显扭变。因此，在TCSPC的探测过程必须降低激光功率，使每一个激光脉冲所含能量足够小，以至于每次激发样品时远小于一个荧光光子到达探测器的光阴极，这样做的目的是避免光子数暴累的“堆积效应(Pileup Effect)”，也就是让大量受激分子通过非辐射的 方式去活，这种情况下单次脉冲激发出多个光子的概率很小。这意味着TCSPC的光子计数效率非常低，需要相当长时间的计数才能满足衰减曲线的测量精度要求。
由此可见，TCSPC是一种耗时较长的荧光寿命测量方法。
发明内容
本发明提供一种荧光寿命的测量方法及装置，旨在提供一种更快速的荧光寿命测量方法。
本发明提供了一种荧光寿命的测量方法，包括：
以预置的测量矩阵的每一行作为一个采样模式，每一个所述采样模式下的非零值位置作为一个时间门控延迟采样的稀疏信号通道，通过时间门控硬件在每个采样模式下对样品进行延迟采样，将当前采样模式下的稀疏信号通道的光子数累加在一起获得一个压缩感知测量值y i，重复各采样模式获取系列压缩感知测量值y＝{y i},i＝1,2,...,M；
利用所述压缩感知测量值并结合由所述测量矩阵Φ M×N与稀疏变换矩阵的逆变换
Figure PCTCN2018079924-appb-000001
构成的传感矩阵A在l 1范数最优化算法下求解压缩采样模型，得到稀疏系数s＝{a k},k＝1,2,...,N；
通过已知的稀疏变换矩阵的逆变换作用于所述稀疏系数，进行信号重构
Figure PCTCN2018079924-appb-000002
得到荧光寿命衰减曲线I(t)＝{x j},j＝1,2,...,N，以实现荧光寿命的测量。
本发明还提供了一种荧光寿命的测量装置，包括：
采集模块，用于以预置的测量矩阵的每一行作为一个采样模式，每一个所述采样模式下的非零值位置作为一个时间门控延迟采样的稀疏信号通道，通过时间门控硬件在每个采样模式下对样品进行延迟采样，将当前采样模式下的稀疏信号通道的光子数累加在一起获得一个压缩感知测量值y i，重复各采样模式获取系列压缩感知测量值y＝{y i},i＝1,2,...,M；
求解模块，用于利用所述压缩感知测量值并结合由所述测量矩阵Φ M×N与稀 疏变换矩阵的逆变换
Figure PCTCN2018079924-appb-000003
构成的传感矩阵A在l 1范数最优化算法下求解压缩采样模型，得到稀疏系数s＝{a k},k＝1,2,...,N；
重构模块，用于通过已知的稀疏变换矩阵的逆变换作用于所述稀疏系数，进行信号重构
Figure PCTCN2018079924-appb-000004
得到荧光寿命衰减曲线I(t)＝{x j},j＝1,2,...,N，以实现荧光寿命的测量。
本发明与现有技术相比，有益效果在于：本发明提供的一种荧光寿命的测量方法及装置，以预置的随机矩阵的每一行作为一个采样模式，每一个采样模式下的非零值位置作为一个信号通道，通过时间门控硬件在每个采样模式下对样品进行延迟采样，将当前采样模式下的稀疏信号通道的光子数累加在一起获得一个压缩感知测量值，重复各采样模式获取系列压缩感知测量值；利用所述压缩感知测量值并结合测量矩阵在l 1范数最优化算法下求解压缩采样模型，得到稀疏系数；最后通过已知的稀疏变换矩阵的逆变换作用于所述稀疏系数，进行信号重构，得到荧光寿命衰减曲线，以实现荧光寿命的测量；本发明与现有技术相比，通过测量矩阵实现多个采样模式的设置，以实现时间门控功能，并通过时间门控功能来选择光子累计的时间通道，并结合时间门控硬件进行延迟采样，从而得到测量值，再利用得到的测量值结合压缩感知算法进行信号重构，使得既避免了TCSPC技术耗时较长的问题，又避免了时间门控的荧光寿命分辨率低的问题，使得能够更快速的成像，提高荧光寿命的测量速度。
附图说明
图1是本发明实施例提供的基于时间门的荧光寿命压缩感知采样示意图；
图2是本发明实施例提供的一种荧光寿命的测量方法的流程示意图；
图3是本发明实施例提供的荧光珠的TCSPC全采样荧光衰减曲线图；
图4是本发明实施例提供的离散傅里叶变换(DFT)的BPDN信号重构结果示意图；
图5是本发明实施例提供的正交指数函数集(Oexp-Basis)稀疏基的BPDN信 号重构结果示意图；
图6是本发明实施例提供的DFT稀疏基去卷积的BPDN信号重构结果示意图；
图7是本发明实施例提供的一种荧光寿命的测量方法的模块示意图。
具体实施方式
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。
由于现有技术中存在利用TCSPC(时间门控)方法进行荧光寿命测量时，测量速度慢的技术问题。
为了解决上述技术问题，本发明提出一种荧光寿命的测量方法及装置，利用门控技术来实现高激发功率下光子“堆积效应”的较短时间光子的过滤，并配合压缩感知技术实现低采样率的信号采集来重构高采样率的源信号，提高了荧光寿命的测量速度。
下面先介绍压缩感知技术的理论框架：
压缩感知(Compressed Sensing，CS)提出一种新的采样理论，能够以远低于Nyquist采样速率对信号进行压缩采样。简单地说，只要信号可压缩或在某个变换域是稀疏的，那么就可以用一个与变换基不相关的传感矩阵将信号投影到一个低维空间，可以证明这样的投影包含了原信号的足够信息，然后通过求解一个最优化问题就可以从这些少量的投影中以极高概率重构出原信号。压缩感知为信号数字化提供一种采样与压缩同时以超低速率进行的实验方案，大大降低传感器的采样时间成本。如果信号本身是稀疏信号则没有问题，即使信号不稀疏，只要能找到合适的信号稀疏表示空间，就可以有效地进行压缩采样。
假设原信号x为长度N的一维信号，稀疏度为k(此刻它是未知)；M×N(M<<N)维的测量矩阵Φ对应着亚采样过程(是已知)，它将高维信号x投影到低维空间， 得到长度M的一维测量值y＝Φx(也是已知)。因此，压缩感知问题就是在已知测量值y和测量矩阵Φ的基础上，求解欠定方程组y＝Φx得到原信号x。然而，一般的自然信号x本身并不是稀疏的，需要在某种稀疏基上进行稀疏表示。令s＝Ψx，Ψ为稀疏基矩阵，s为稀疏系数。最终变成了求解线性方程组y＝ΦΨ -1s中的未知稀疏系数s，通常把测量矩阵和稀疏基矩阵合并在一起称为传感矩阵A＝ΦΨ -1。具体数学描述如下：
Figure PCTCN2018079924-appb-000005
这个过程称之为信号重构，其中||s|| 0是指l 0范数，即稀疏信号s的非0元素个数。然而最小l 0范数是一个NP问题，通常需要对该问题转换为求最小l 1范数问题，使最优化问题变成一个凸优化问题，便于求解。如果测量过程存在噪声，须引入松弛因子σ，也就是把一个非凸线性规划问题松弛为凸的二次规划问题。此时，l 1范数优化问题可表示为：
Figure PCTCN2018079924-appb-000006
根据压缩感知理论的要求，传感矩阵A必须满足约束等距性(Restriced Isometry Property,RIP)条件，并且在满足RIP条件下，要精确重构k稀疏信号s，需要重复进行M≥cklog(N/k)次测量(c为一个很小的常数)。约束等距性的严格定义为，任意给定的k稀疏向量v以及常数0<δ<1满足一下不等式：
Figure PCTCN2018079924-appb-000007
但是，验证传感矩阵A是否满足RIP条件是一个组合复杂度问题，不容易直接验证，因此R.Baraniuk从理论上证明RIP的一个等价条件是测量矩阵Φ和稀疏基Ψ之间不相干，即这两个矩阵之间不能相互地线性表示。E.Candès和T.Tao还证明了当测量矩阵Φ采用高斯分布的随机矩阵时，传感矩阵A能以很大的概率满足RIP条件，采用适当的重构算法能以很大的概率去精确恢复源信号。
概括来说，压缩感知理论主要包括三个关键技术：信号的稀疏表示、测量矩阵的设计与重构算法的研究。首先是信号的稀疏表示，在实际的压缩感知测 量中，信号往往不具稀疏性，需要利用适当的变换找到信号的最稀疏表示，信号的表示越稀疏，则高精度重构信号所需的测量次数就越小。最容易想到的稀疏变换就是傅里叶变换，如果信号在时域不稀疏，则可以通过傅里叶变换将信号转化为频域稀疏表示；如果信号在频域不稀疏，则可以通过傅里叶逆变换将信号转为时域稀疏表示。当然还有其他变换，如拉普拉斯变换，小波变换以及紧支撑小波Curvelets、Contourlets等。其次是测量矩阵的设计，由于高斯随机矩阵几乎与任意信号的稀疏基都不相干，因此所需测量次数较少，适用性广，但缺点是矩阵元素所需储存空间较大，并且由于其非结构化的特点导致其复杂度高，在硬件上不容易实现。所以为了便于硬件上的实现，可以采用随机伯努利矩阵、部分哈达玛矩阵或稀疏随机矩阵。最后是合适的算法来重构源信号，主要分为两大类，一类是l 0范数的贪婪算法，如匹配追踪(MP)、正交匹配追踪(OMP)、压缩采样匹配追踪(CoSaMP)等；一类是l 1范数凸优化算法，主要包括基追踪(BP)、梯度投影、最小角度回归等算法。就目前主流的两种重构算法而言，基于l 1范数最小的凸优化重构算法精度高，但计算量巨大，不适用于大规模信号处理；贪婪算法则重构速度最快，但信号重构质量比不上凸优化；此外，迭代阈值法也得到了广泛应用，此类算法较容易实现，计算量适中。
下面再介绍荧光寿命压缩感知的数学模型
在荧光寿命探测中，对超短脉冲的响应为单指数衰减函数。在复杂体系中，荧光物质的不同发光基团对总体荧光强度衰变的贡献不同，所以体系荧光衰减曲线为多指数函数模型：
Figure PCTCN2018079924-appb-000008
其中，τ k为第k种荧光寿命，α k为第k种荧光寿命的权值。实际上，任何光源都有一定的宽度，再加上仪器响应时间的影响，实验测得的荧光衰减曲线为总体仪器响应函数h(t)和脉冲响应函数e(t)的卷积：
Figure PCTCN2018079924-appb-000009
其中，整体仪器响应函数
Figure PCTCN2018079924-appb-000010
为激光脉冲波形I(t)和系统接受响应函数R(t)的卷积。
目前荧光寿命的主要探测手段分为相位调制频域探测法和时域探测法，而时域探测法又细分为时间门探测、时间相关单光子计数和条纹相机三种主要方法。我们要发展的是一种基于时间门压缩感知采样的荧光寿命探测计数，技术方案如图1所示。
下面再具体介绍本发明实施例提供的一种荧光寿命的测量方法，所述测量方法是基于时间门压缩感知采样的快速荧光寿命测量方法：
结合图1-2所示，为本发明提供的一种荧光寿命的测量方法，包括：
步骤S1，以预置的测量矩阵的每一行作为一个采样模式，每一个所述采样模式下的非零值位置作为一个时间门控延迟采样的稀疏信号通道，通过时间门控硬件在每个采样模式下对样品进行延迟采样，将当前采样模式下的稀疏信号通道的光子数累加在一起获得一个压缩感知测量值y i，重复各采样模式获取系列压缩感知测量值y＝{y i},i＝1,2,...,M；
具体地，所述预置的测量矩阵的生成过程为：利用已有的压缩感知算法构造符合时间门控延迟采样原理的测量矩阵；
具体地，为了便于硬件实现，本发明实施例提供的所述测量矩阵为随机伯努利测量矩阵或稀疏随机测量矩阵；其中，所述随机伯努利测量矩阵的设计方法为：构造一个大小为M×N矩阵Φ，其中每一个元素独立服从伯努利分布，即：
Figure PCTCN2018079924-appb-000011
所述稀疏随机测量矩阵的设计方法为：先生成一个全零元素M×N矩阵Φ，然后在所述矩阵的每一列随机选取d个位置的元素置1，其中，d为任意大于0小于N的自然数。
结合图1所示，所述测量矩阵Φ的每一行代表一次独立测量yi，每一行中 的非零元素代表压缩采样的时间通道；遍历所有的行，即得到一组M×1维的测量值向量y＝{yi},i＝1,2,…,M。本发明实施例提供两种关于独立测量yi的方法：一，采用基于时间门iCCD(time-gated intensified CCD)的宽场荧光寿命成像系统，选择测量矩阵Φ第i行数值为1的元素所对应的时间通道进行顺序曝光并累加构成正采样，得到第一光子数累计，然后对数值为-1元素所对应时间通道进行顺序曝光并累加构成负采样，得到第二光子数累计，利用所述第一光子数累计和所述第二光子数累计相减构成一个压缩感知独立测量值yi。二，采用基于TCSPC逐点扫描的荧光寿命成像系统进行采样，可将电压绝对值的阈值提高来获取更多的探测光子，同时利用TCSPC采集卡自带的延迟采样功能或时间门控功能来选择光子累计的时间通道，并根据测量矩阵中元素值为1则进行正采样，得到第一光子数累计，反之数值为-1的进行负采样，得到第二光子数累计，利用所述第一光子数累计和所述第二光子数累计相减构成一个压缩感知独立测量值yi。
步骤S2，利用所述压缩感知测量值并结合由所述测量矩阵Φ M×N与稀疏变换矩阵的逆变换
Figure PCTCN2018079924-appb-000012
构成的传感矩阵A在l 1范数最优化算法下求解压缩采样模型，得到稀疏系数s＝{a k},k＝1,2,...,N；
具体地，所述压缩采样模型为：
Figure PCTCN2018079924-appb-000013
其中，y为压缩感知测量值，A为传感矩阵，
Figure PCTCN2018079924-appb-000014
Φ为测量矩阵，s为稀疏系数，λ为拉格朗日因子。
具体地，在压缩感知理论框架下，我们采用傅里叶变换将时域信号f(t)变换到频域的稀疏表示
Figure PCTCN2018079924-appb-000015
这里稀疏基即为傅里叶变换
Figure PCTCN2018079924-appb-000016
利用所述测量矩阵Φ和傅里叶逆变换矩阵
Figure PCTCN2018079924-appb-000017
构成传感矩阵
Figure PCTCN2018079924-appb-000018
待重构信号为荧光衰减曲线x＝f(t)，稀疏信号为其傅里叶变换
Figure PCTCN2018079924-appb-000019
采用基追踪降噪(Basis Pursuit De-Noising，BPDN)的l 1凸优化算法对稀疏信号s进行重构。
需要说明的是，由公式(5)可知，实验测得的荧光衰减曲线为总体仪器响应函数h(t)和脉冲响应函数e(t)的卷积，公式(7)的数学模型中并没有考虑仪器响应函数的影响。如需要考虑仪器响应函数，则需要对公式(7)作相应改进。根据卷积定理，两个函数卷积的傅里叶变换等于各自函数傅里叶变换相乘，即
Figure PCTCN2018079924-appb-000020
模型公式(7)将被修正为如下考虑仪器响应函数之后的数学模型：
Figure PCTCN2018079924-appb-000021
其中，y为压缩感知测量值，A为传感矩阵，
Figure PCTCN2018079924-appb-000022
h为仪器响应函数，Φ为测量矩阵，s为稀疏系数，λ为拉格朗日因子。
步骤S3，通过已知的稀疏变换矩阵的逆变换作用于所述稀疏系数，进行信号重构
Figure PCTCN2018079924-appb-000023
得到荧光寿命衰减曲线I(t)＝{x j},j＝1,2,...,N，以实现荧光寿命的测量。
具体地，利用傅里叶逆变换求得荧光衰减曲线
Figure PCTCN2018079924-appb-000024
补充说明关于拉普拉斯变换稀疏基
可从线性变换角度来重新理解公式(4)，脉冲响应函数e(t)被以少数不同寿命τ k的指数函数构成的稀疏基{exp(-t/τ k)}所线性表示，权值α k为线性变换系数。一般在荧光寿命曲线拟合中，会指定寿命成分为3-5种，可见权值α k是非常稀疏的。但是，直接采用指数函数集{exp(-t/τ k)}作为系数变换来套入公式(7)的压缩感知模型将不能成功恢复出原始信号，可能的原因在于指数函数集{exp(-t/τ k)}不是正交基。如果采用Gram-Schmidt方法对指数函数集进行正交化(简称Oexp-Basis)则可以得到类似于傅里叶变换基的信号恢复结果。但是，即便是正交化之后的指数函数集应用于公式(8)的去卷积模型也无法成功恢复源信号，可能的原因在于正交化的指数函数集并不满足卷积定理。
鉴于以上分析，我们希望获得一种稀疏变换基能够同时兼顾傅里叶所满足的卷积定理而又充分考虑像指数函数集那样的极度稀疏性质。最容易联想到的 稀疏变换就是拉普拉斯变换。从拉普拉斯变换的定义
Figure PCTCN2018079924-appb-000025
可以看出拉普拉斯变换复数域参数p＝μ+iω的虚部即为傅里叶变换，而实部则为指数函数变换，同时拉普拉斯变换是正交变换且充分满足卷积定理。
将脉冲响应函数公式(4)代入拉普拉斯的定义，得到
Figure PCTCN2018079924-appb-000026
其中，
Figure PCTCN2018079924-appb-000027
表示拉普拉斯变换，并利用拉普拉斯变换性质公式
Figure PCTCN2018079924-appb-000028
这里我们引进一个过渡矩阵Λ，假设
Figure PCTCN2018079924-appb-000029
则脉冲响应函数的拉普拉斯变换为
Figure PCTCN2018079924-appb-000030
α＝{α k},k＝1,2,…,K。将去卷积模型公式(8)中将傅里叶变换
Figure PCTCN2018079924-appb-000031
替换成拉普拉斯变换
Figure PCTCN2018079924-appb-000032
重构出来的稀疏信号s为脉冲响应函数的拉普拉斯变换，因此有s＝Λα等式成立，再利用过渡矩阵定义公式(10)就可以确定指数函数的权值分布系数α k。在利用s＝Λα等式计算系数α k的时候，τ k一般取有限的几个值，如但指数拟合的时候取值K＝1，双指数拟合的时候取值K＝2，以此类推K＝{1,2,3,4,5}集合中的一个。s的维度N>>K，所以线性方程s＝Λα是个超定方程，利用最小二乘法就可以求解其中2K个待定系数τ k和α k。
下面举具体实施例来验证本发明提供的荧光寿命的测量方法是否可行：
图3为本发明实施例提供的TCSPC系统对荧光珠进行荧光寿命全谱采样，纵坐标采用对数坐标显示，散点表示实验测得荧光寿命衰减曲线，实线表示指数衰减的最小二乘拟合曲线。
图4为本发明实施例提供的利用离散傅里叶变换(Discrete Fourier Transform,DFT)作为稀疏基，并采用公式(7)所示的数学模型进行BPDN信号重构，散点为TCSPC数据曲线，虚线为指数最小二乘拟合曲线，实线为CS重构曲线。从恢复结果来看，DFT作为稀疏基的信号重构效果并不理想，虽然能够反映源信号 大体趋势，但重构信噪比不高，重构曲线在脉冲上升沿部分严重失真，势必会造成后续的拟合计算在短寿命部分的严重偏差。分析原因，脉冲上升沿的失真可能是由于公式(7)没有考虑仪器响应函数卷积的效应，而信噪比不高则是由DFT本身特性所致。影响信噪比的DFT潜在特性包括，DFT稀疏性不强导致去噪能力不强，加之DFT能够引起比较强烈的Gibbs效应造成重构信号的抖动。
前面已经讨论过，如果采用正交指数函数集(Oexp-Basis)作为稀疏基则可以得到比较好的稀疏变换效果，在此稀疏变换下本发明实施例采用公式(7)数学模型进行BPDN信号重构结果如图5所示。从结果来看，Oexp-Basis的去噪能力明显优越于DFT，这跟Oexp-Basis具有比较强烈的稀疏特性有关，但脉冲上升沿部分失真的现象依然存在，这跟公式(7)没有考虑仪器响应函数的卷积效应有关。
为了获取短寿命部分更精确的信号重构结果，本发明实施例采用公式(8)的数学模型来实现去卷积的信号重构，此模型目前只能够处理仪器响应函数为已知的情况，对于仪器响应函数未知的盲去卷积则需对模型作改进。如图6，从去卷积的效果来看，DFT去卷积能够有效改善脉冲上升沿以及短寿命部分的信号重构精度，但DFT的Gibbs效应依然存在。然而Oexp-Basis的去卷积效果并不理想，可能的原因在于Oexp-Basis并不充分满足卷积定理。
综上，本发明提供的基于时间门的荧光寿命压缩感知采样及重构的技术方案可行，有严格数学模型的理论指导，有满足压缩感知采样的现行仪器设备可用，有成熟的压缩感知程序算法保证源信号重构。
本发明实施例提供的一种荧光寿命的测量方法，通过测量矩阵实现多个采样模式的设置，以实现时间门控功能，并通过时间门控功能来选择光子累计的时间通道，并结合时间门控硬件进行延迟采样，从而得到测量值，再利用得到的测量值结合压缩感知算法进行信号重构，使得既避免了TCSPC技术耗时较长的问题，又避免了时间门控的荧光寿命分辨率低的问题，使得能够更快速的成像，提高荧光寿命的测量速度。
本发明实施例还提供了一种荧光寿命的测量装置，如图7所示，所述装置包括：
采集模块1，用于以预置的测量矩阵的每一行作为一个采样模式，每一个所述采样模式下的非零值位置作为一个时间门控延迟采样的稀疏信号通道，通过时间门控硬件在每个采样模式下对样品进行延迟采样，将当前采样模式下的稀疏信号通道的光子数累加在一起获得一个压缩感知测量值y i，重复各采样模式获取系列压缩感知测量值y＝{y i},i＝1,2,...,M；
求解模块2，用于利用所述压缩感知测量值并结合由所述测量矩阵Φ M×N与稀疏变换矩阵的逆变换
Figure PCTCN2018079924-appb-000033
构成的传感矩阵A在l 1范数最优化算法下求解压缩采样模型，得到稀疏系数s＝{a k},k＝1,2,...,N；
重构模块3，用于通过已知的稀疏变换矩阵的逆变换作用于所述稀疏系数，进行信号重构
Figure PCTCN2018079924-appb-000034
得到荧光寿命衰减曲线I(t)＝{x j},j＝1,2,...,N，以实现荧光寿命的测量。
需要说明的是，荧光寿命的测量装置的相关内容具体可参阅图2所示实施例中描述的荧光寿命的测量方法，此处不做赘述。
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。

Claims (8)

  1. 一种荧光寿命的测量方法，其特征在于，所述方法包括：
    以预置的测量矩阵的每一行作为一个采样模式，每一个所述采样模式下的非零值位置作为一个时间门控延迟采样的稀疏信号通道，通过时间门控硬件在每个采样模式下对样品进行延迟采样，将当前采样模式下的稀疏信号通道的光子数累加在一起获得一个压缩感知测量值y i，重复各采样模式获取系列压缩感知测量值y＝{y i},i＝1,2,...,M；
    利用所述压缩感知测量值并结合由所述测量矩阵Φ M×N与稀疏变换矩阵的逆变换
    Figure PCTCN2018079924-appb-100001
    构成的传感矩阵A在l 1范数最优化算法下求解压缩采样模型，得到稀疏系数s＝{a k},k＝1,2,...,N；
    通过已知的稀疏变换矩阵的逆变换作用于所述稀疏系数，进行信号重构
    Figure PCTCN2018079924-appb-100002
    得到荧光寿命衰减曲线I(t)＝{x j},j＝1,2,...,N，以实现荧光寿命的测量。
  2. 如权利要求1所述的荧光寿命的测量方法，其特征在于，所述预置的测量矩阵的生成过程为：利用已有的压缩感知算法构造符合时间门控延迟采样原理的测量矩阵；
    所述测量矩阵为随机伯努利测量矩阵或稀疏随机测量矩阵，其中，所述稀疏随机测量矩阵的生成方法为：先生成一个全零元素M×N矩阵Φ，然后在所述矩阵的每一列随机选取d个位置的元素置1，得到一个稀疏随机测量矩阵；其中，d为任意大于0小于N的自然数。
  3. 如权利要求1或2所述的荧光寿命的测量方法，其特征在于，所述将当前采样模式下的稀疏信号通道的光子数累加在一起获得一个压缩感知测量值y i，包括：
    选择所述测量矩阵Φ第i行数值为1的元素所对应的稀疏信号通道进行顺序曝光并累加构成正采样，得到第一光子数累计，然后对数值为-1的元素所对应的稀疏信号通道进行顺序曝光并累加构成负采样，得到第二光子数累计，利用所述第一光子数累计和所述第二光子数累计相减得到一个压缩感知测量值 yi。
  4. 如权利要求1所述的荧光寿命的测量方法，其特征在于，所述压缩采样模型为模型A或模型B；
    所述模型A为：
    Figure PCTCN2018079924-appb-100003
    其中，y为压缩感知测量值，A为传感矩阵，
    Figure PCTCN2018079924-appb-100004
    Φ为测量矩阵，s为稀疏系数，λ为拉格朗日因子；
    所述模型B为：
    Figure PCTCN2018079924-appb-100005
    其中，y为压缩感知测量值，A为传感矩阵，
    Figure PCTCN2018079924-appb-100006
    h为仪器响应函数，Φ为测量矩阵，s为稀疏系数，λ为拉格朗日因子。
  5. 一种荧光寿命的测量装置，其特征在于，所述装置包括：
    采集模块，用于以预置的测量矩阵的每一行作为一个采样模式，每一个所述采样模式下的非零值位置作为一个时间门控延迟采样的稀疏信号通道，通过时间门控硬件在每个采样模式下对样品进行延迟采样，将当前采样模式下的稀疏信号通道的光子数累加在一起获得一个压缩感知测量值y i，重复各采样模式获取系列压缩感知测量值y＝{y i},i＝1,2,...,M；
    求解模块，用于利用所述压缩感知测量值并结合由所述测量矩阵Φ M×N与稀疏变换矩阵的逆变换
    Figure PCTCN2018079924-appb-100007
    构成的传感矩阵A在l 1范数最优化算法下求解压缩采样模型，得到稀疏系数s＝{a k},k＝1,2,...,N；
    重构模块，用于通过已知的稀疏变换矩阵的逆变换作用于所述稀疏系数，进行信号重构
    Figure PCTCN2018079924-appb-100008
    得到荧光寿命衰减曲线I(t)＝{x j},j＝1,2,...,N，以实现荧光寿命的测量。
  6. 如权利要求5所述的荧光寿命的测量装置，其特征在于，所述采集模块包括测量矩阵构造子模块，所述测量矩阵构造子模块具体用于：利用已有的压缩感知算法构造符合时间门控延迟采样原理的测量矩阵；
    所述测量矩阵为随机伯努利测量矩阵或稀疏随机测量矩阵；
    所述测量矩阵构造子模块包括：稀疏随机测量矩阵构造子模块，所述稀疏随机测量矩阵构造子模块具体用于：生成一个全零元素M×N矩阵Φ，并在所述矩阵的每一列随机选取d个位置的元素置1，得到一个稀疏随机测量矩阵；其中，d为任意大于0小于N的自然数。
  7. 如权利要求5或6所述的荧光寿命的测量装置，其特征在于，所述采集模块包括：压缩感知测量值获取子模块，所述压缩感知测量值获取子模块具体用于：选择所述测量矩阵Φ第i行数值为1的元素所对应的稀疏信号通道进行顺序曝光并累加构成正采样，得到第一光子数累计，然后对数值为-1的元素所对应的稀疏信号通道进行顺序曝光并累加构成负采样，得到第二光子数累计，利用所述第一光子数累计和所述第二光子数累计相减得到一个压缩感知测量值yi。
  8. 如权利要求5所述的荧光寿命的测量装置，其特征在于，所述压缩采样模型为模型A或模型B；
    所述模型A为：
    Figure PCTCN2018079924-appb-100009
    其中，y为压缩感知测量值，A为传感矩阵，
    Figure PCTCN2018079924-appb-100010
    Φ为测量矩阵，s为稀疏系数，λ为拉格朗日因子；
    所述模型B为：
    Figure PCTCN2018079924-appb-100011
    其中，y为压缩感知测量值，A为传感矩阵，
    Figure PCTCN2018079924-appb-100012
    h为仪器响应函数，Φ为测量矩阵，s为稀疏系数，λ为拉格朗日因子。
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