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CN117974525B - Laser speckle contrast blood flow imaging method based on second-order autocorrelation function calculation - Google Patents

Laser speckle contrast blood flow imaging method based on second-order autocorrelation function calculation Download PDF

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CN117974525B
CN117974525B CN202410370762.4A CN202410370762A CN117974525B CN 117974525 B CN117974525 B CN 117974525B CN 202410370762 A CN202410370762 A CN 202410370762A CN 117974525 B CN117974525 B CN 117974525B
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翟林君
杜永兆
李毅
傅玉青
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Abstract

A laser speckle contrast blood flow imaging method based on second-order autocorrelation function calculation relates to the field of biological tissue medical imaging, and comprises the following steps: collecting a plurality of frames of continuous time sequence speckle images, and calculating a second-order autocorrelation function of the continuous time sequence speckle images; calculating a second-order light intensity signal of the time-series speckle images based on the second-order autocorrelation function; a contrast value is calculated based on the second order light intensity signal and the contrast value is used to reconstruct a two-dimensional blood flow image. The invention innovates the imaging theory and calculation method of laser speckle, and can effectively improve imaging contrast, imaging dynamic range, blood flow estimation accuracy and sensitivity.

Description

Laser speckle contrast blood flow imaging method based on second-order autocorrelation function calculation
Technical Field
The invention relates to the field of biomedical imaging, in particular to a laser speckle contrast blood flow imaging method based on second-order autocorrelation function calculation.
Background
The laser speckle Contrast blood flow Imaging (LASER SPECKLE Contrast Imaging, LSCI) is a living whole-field optical Imaging technology, has the advantages of simple equipment, non-invasiveness, high resolution, long-time continuous measurement and the like, and has important application value in the research fields of clinical diagnosis, life science and the like.
The statistics of speckle include the standard deviation and average value of the speckle intensity, and the ratio of the standard deviation and average value. One important parameter in the first-order statistical properties of speckle is the average intensity of the speckle image, which is the average of all pixel intensity values in the speckle image. An important parameter in the second order statistical properties of speckle is the contrast of the speckle image. Contrast is a measure of the degree of variation in intensity in a speckle image. Mathematically, contrast is generally defined as the ratio of standard deviation to average. For a speckle image, the contrast can be calculated by the following formula:
in the formula (1) Representing the standard deviation of the light intensity of all pixels of the whole speckle image.Representing the average value of the light intensity of all pixels of the whole speckle image.
The current laser speckle contrast blood flow imaging method is mainly based on the calculation of a first-order autocorrelation function of speckle, according to Boas, the light scattered by the movement of scattering particles changes the current of a camera so as to change the intensity of an electric field and further cause the intensity fluctuation of a speckle image, so that the intensity change in a dynamic speckle image sequence can be analyzed through the first-order autocorrelation function (electric field autocorrelation function) shown in the formula (2) to obtain information about blood flow velocity and blood flow dynamics:
In the formula, As a first-order autocorrelation function,Indicating the strength of the electric field,The delay time is indicated as such,Representing the complex conjugate of the electric field,Mean values are indicated. However, the electric field autocorrelation function is difficult to directly measure, the light intensity is easy to obtain, and a mapping relation exists between the current and the light intensity of the camera, so that the electric field autocorrelation function can be indirectly calculated according to the Siegert relation (4) by combining the second-order autocorrelation function formula (3), and further, a contrast value calculated based on the first-order autocorrelation function is obtained, as shown in the formula (5).
In the above-mentioned description of the invention,Is a second-order autocorrelation function which is a function of the autocorrelation,As a first-order autocorrelation function,Indicating the intensity of the light,The delay time is indicated as such,The average value is represented by a value of,K is a contrast value, which is a system factor related to system parameters such as speckle size, polarization, light source coherence, etc.
Existing classical laser speckle contrast blood flow imaging methods such as LSCI techniques based on spatial contrast analysis (LASER SPECKLE SPATIAL contrast analysis, LSSCA), temporal contrast analysis (LASER SPECKLE temporal contrast analysis, LSTCA), and spatio-temporal joint contrast analysis (spatiotemporal LASER SPECKLE contrast analysis, stLASCA) as proposed in the literature (J. D. Briers and S. Webster, "Laser speckle contrast analysis (LASCA): a nonscanning, full-field technique for monitoring capillary blood flow," Journal of biomedical optics 1(2), 174-179 (1996).), , (H. Y. Cheng, Q. M. Luo, S. Q. Zeng, S. B. Chen, J. Cen, and H. Gong, "Modified laser speckle imaging method with improved spatial resolution," Journal of Biomedical Optics 8(3), 559-564 (2003).) and (D. D. Duncan and S. J. Kirkpatrick, "Spatio-temporal algorithms for processing laser speckle imaging data," Proc. SPIE 6858,7-12 (2008)), respectively. Spatial contrast analysis (LASER SPECKLE SPATIAL contrast analysis, LSSCA) achieves higher temporal resolution and significant noise attenuation at the expense of spatial resolution, but does not facilitate blood flow detection of small blood vessels; the spatio-temporal joint contrast analysis (spatiotemporal LASER SPECKLE contrast analysis, stLASCA) achieves higher signal-to-noise ratio and statistical accuracy by balancing the contradiction between temporal resolution, spatial resolution and statistical accuracy.
However, due to the use of the spatiotemporal window stLASCA, the blood flow signal is smoothed at the same time as the noise averaging, resulting in the loss of the blood flow signal in the microvasculature. Whereas time contrast analysis (LASER SPECKLE temporal contrast analysis, LSTCA), while having a higher spatial resolution, is at the expense of time resolution and signal-to-noise ratio. In general, the classical laser speckle contrast blood flow imaging method uses a time-space rectangular window to perform local filtering average to obtain first-order statistical characteristics of speckles, and then calculates contrast values by using the first-order statistical characteristics, wherein the local filtering average respectively reduces the space-time resolution of imaging in the space-time dimension.
Classical laser speckle contrast blood flow imaging methods all perform contrast value calculation based on a first-order autocorrelation function, and speckle fluctuation in space-time is analyzed through electric field correlation. Since the first order autocorrelation function typically analyzes the first moment of intensity, this may result in insufficient sensitivity to capture of certain flow dynamics. In addition, the first-order autocorrelation function mainly considers the mean value of signals, and the smoothing effect of the mean value can cause certain defects in calculation accuracy, and is not sensitive to the dynamic characteristics of high-speed blood flow; on the other hand, in practical applications, the optical imaging process is inevitably affected by the background light, and the first-order autocorrelation function mainly focuses on the mean value of the signal instead of the variation of the signal intensity, so that the imaging result is affected by the non-uniform background light.
Disclosure of Invention
The invention aims to overcome the defects in the prior art, and provides a laser speckle contrast ratio blood flow imaging method based on second-order autocorrelation function calculation, which innovates an imaging theory and a calculation method of laser speckle and can effectively improve imaging contrast, imaging dynamic range, blood flow estimation accuracy and sensitivity.
The invention adopts the following technical scheme:
The laser speckle contrast blood flow imaging method based on second-order autocorrelation function calculation comprises the following steps:
Collecting a plurality of frames of continuous time sequence speckle images, and calculating a second-order autocorrelation function of the continuous time sequence speckle images;
calculating a second-order light intensity signal of the time-series speckle images based on the second-order autocorrelation function;
A contrast value is calculated based on the second order light intensity signal and the contrast value is used to reconstruct a two-dimensional blood flow image.
The time-series speckle images have a size ofWhereinRepresenting the resolution of the time-series speckle images in the horizontal direction,Representing the resolution of the temporal sequential speckle images in the vertical direction,Representing the number of frames of the original speckle image sequence.
By calculating the position of a single pixel point in the time sequence speckle images of a plurality of framesIs to be used for the adjacent delay time of (a)The light intensity autocorrelation among them forms a three-dimensional matrix form of a second-order autocorrelation function:
wherein, In the time-series speckle image representing any time or t-th frame, inThe light intensity at this pixel location,Representing delay timeOn the time-series speckle images captured by the rear cameraThe light intensity at this pixel location; Representing multiple successive frames of said time-series speckle images The average value of the light intensity at this pixel position.
The light intensity average value calculation formula is as follows:
Wherein the method comprises the steps of Representing the position coordinates of the pixel points; representing the position of the time-series speckle images over time; representing the number of frames of the time-series speckle image.
The second order light intensity signal is calculated as follows:
where A is the original time series speckle image, For the second order intensity signal of the time series of speckle images,Is a second order autocorrelation function.
Calculating a contrast ratio value based on the second-order light intensity signal, specifically as follows:
In the middle of Representing the amplitude of the second order light intensity signal,Mean taking the average.
As can be seen from the above description of the present invention, compared with the prior art, the present invention has the following advantages:
Compared with a laser speckle contrast blood flow imaging method based on first-order autocorrelation function calculation, the invention provides a new imaging theory, signal addition in the speckle signal forming process is changed into signal multiplication to analyze the interference process, the correlation of fields in the first-order autocorrelation function is changed into the intensity correlation in the second-order autocorrelation function, the method is more sensitive to the change of signal intensity, and the method is favorable for capturing the change of dynamic blood flow, in particular to the blood flow information flowing at high speed.
The first-order autocorrelation function mainly considers the mean value of signals, the smoothing effect of the mean value can introduce an interference error of non-uniform background light on a calculation result, so that the calculation accuracy of the method is deficient, and the second-order autocorrelation function mainly considers the change of the signal intensity, so that the method provided by the invention has an advantage in the calculation accuracy.
The method calculates the second-order autocorrelation function of the speckle image with adjacent delay time based on a single pixel point, and further constructs a second-order light intensity signal, and has the following advantages: on the one hand, the single-point calculation can obtain higher spatial resolution, and secondly, the fluctuation of the variation between adjacent delay times can reflect the detail variation, so compared with the traditional LSCI technology based on space (LSSCA) or space-time window average (stLASCA), the method has obvious advantages in identifying blood flow signals in micro blood vessels and space-time resolution.
The method constructs the second-order light intensity signal of the time sequence speckle image based on the second-order autocorrelation function, then calculates the contrast value based on the second-order light intensity signal, and the second-order autocorrelation function mainly considers the change of the signal intensity, calculates the change rate instead of the mean value, so that the method has a larger dynamic range. Furthermore, due to the local filtering averaging effect of the space-time rectangular window, the laser speckle contrast blood flow imaging method calculated based on the first-order autocorrelation function may not be quantitatively measured for fast flowing blood flow information with variance smaller than the camera noise/lens noise variance, and the present invention can avoid this problem.
Drawings
FIG. 1 is a flow chart of the present invention;
fig. 2 is a schematic diagram of a three-dimensional matrix of the second-order autocorrelation function of the present invention.
The invention is further described in detail below with reference to the drawings and the specific examples.
Detailed Description
The invention is further described below by means of specific embodiments.
Referring to fig. 1, the laser speckle contrast blood flow imaging method based on second-order autocorrelation function calculation of the present invention includes the following steps:
1) A plurality of frames of continuous time series speckle images are acquired, and a second order autocorrelation function of the continuous time series speckle images is calculated.
The time-series speckle images are of the size ofWhereinRepresenting the resolution of the time-series speckle images in the horizontal direction,Representing the resolution of the temporal sequential speckle images in the vertical direction,The number of frames representing the time-series speckle image sequence.
According to a second-order autocorrelation functionCalculating the position of a single pixel point in a plurality of frames of continuous time sequence speckle imagesIs to be used for the adjacent delay time of (a)The light intensity autocorrelation between them, thus forming a three-dimensional matrix form of the second-order autocorrelation function:
wherein, In the speckle image representing the time sequence of any time or t-th frameThe light intensity at this pixel location,Representing delay timeOn time-series speckle images captured by a rear cameraThe light intensity at this pixel location; Representing multiple successive time-series speckle images in a multi-frame The average value of the light intensity at this pixel position.
For the followingThe light intensity average value calculation formula is as follows:
Wherein the method comprises the steps of Representing the position coordinates of the pixel points; Representing the position of the time-series speckle image over time; the number of frames representing the time-series speckle image.
Finally, the size isThree-dimensional matrix of (2)Form a second-order autocorrelation functionAs shown in fig. 1.
2) Calculating a second-order light intensity signal of the time-series speckle image based on the second-order autocorrelation function;
the invention calculates the contrast value based on the first-order autocorrelation function according to Siegert relation, and the relation is as follows:
based on this, the second order intensity signal defining the time-series speckle images is calculated as follows:
where A is the original time series speckle image, For the second order intensity signal of the time series of speckle images,Is a second order autocorrelation function.
Thereby establishing a contrast valueAnd a mapping relationship between the second order light intensity signals.
3) Contrast values are calculated based on the second order intensity signals and used to reconstruct a two-dimensional blood flow image.
The contrast ratio is calculated based on the second-order light intensity signal, and is specifically as follows:
In the middle of Representing the amplitude of the second order light intensity signal,Mean taking the average.
The method of the invention analyzes the fluctuation of speckle image in time and space based on the second-order autocorrelation function, thus constructing the second-order light intensity signal of time sequence speckle image, and then calculates contrast value based on the second-order light intensity signalThereby realizing imaging of blood flow of biological tissues and measuring of blood flow velocity. Compared with the traditional laser speckle blood flow imaging algorithm, the method innovates the imaging theory and the calculation method of the laser speckle, and the method can effectively improve imaging contrast, imaging dynamic range, blood flow estimation accuracy and sensitivity.
The foregoing is merely illustrative of specific embodiments of the present invention, but the design concept of the present invention is not limited thereto, and any insubstantial modification of the present invention by using the design concept shall fall within the scope of the present invention.

Claims (3)

1.基于二阶自相关函数计算的激光散斑衬比血流成像方法,其特征在于,包括如下:1. A laser speckle contrast blood flow imaging method based on second-order autocorrelation function calculation, characterized by comprising the following: 采集若干帧连续的时间序列散斑图像,计算连续的所述时间序列散斑图像的二阶自相关函数,通过计算若干帧连续的所述时间序列散斑图像中单个像素点位置(i,j)的相邻延迟时间τ之间的光强自相关性,构成二阶自相关函数的三维矩阵形式:Collect several frames of continuous time series speckle images, calculate the second-order autocorrelation function of the continuous time series speckle images, and construct a three-dimensional matrix form of the second-order autocorrelation function by calculating the light intensity autocorrelation between adjacent delay times τ of a single pixel position (i, j) in several frames of continuous time series speckle images: gτ (2)(i,j)=<It(i,j)It+τ(i,j)>/<I(i,j)>2 g τ (2) (i, j)=<I t (i, j)I t+τ (i, j)>/<I (i, j)> 2 其中,It(i,j)表示任意时刻或第t帧的所述时间序列散斑图像中,在(i,j)这个像素点位置的光强,It+τ(i,j)表示延迟时间τ后相机所捕获到的所述时间序列散斑图像上(i,j)这个像素点位置的光强;<I(i,j)>表示多帧连续的所述时间序列散斑图像在(i,j)这个像素点位置的光强均值;Wherein, It (i,j) represents the light intensity at the pixel position (i,j) in the time series speckle image at any time or the t-th frame, It (i,j) represents the light intensity at the pixel position (i,j) on the time series speckle image captured by the camera after a delay time τ; <I(i,j)> represents the average light intensity at the pixel position (i,j) of multiple frames of continuous time series speckle images; 基于所述二阶自相关函数计算所述时间序列散斑图像的二阶光强信号,所述二阶光强信号计算如下:The second-order light intensity signal of the time series speckle image is calculated based on the second-order autocorrelation function. The second-order light intensity signal is calculated as follows: I(2)=A2·(gτ (2)(i,j)-1);I (2) =A 2 ·(g τ (2) (i,j)-1); 式中,A为原始时间序列散斑图像,I(2)为时间序列散斑图像的二阶光强信号,gτ (2)(i,j)为二阶自相关函数的三维矩阵形式;Where A is the original time series speckle image, I (2) is the second-order light intensity signal of the time series speckle image, and g τ (2) (i, j) is the three-dimensional matrix form of the second-order autocorrelation function; 基于所述二阶光强信号计算衬比值,并使用所述衬比值来重构二维血流图像,基于所述二阶光强信号计算衬比值,具体如下:The contrast value is calculated based on the second-order light intensity signal, and the contrast value is used to reconstruct a two-dimensional blood flow image. The contrast value is calculated based on the second-order light intensity signal, specifically as follows: 式中|I(2)|表示二阶光强信号的幅值,<>表示取平均值。Where |I (2) | represents the amplitude of the second-order light intensity signal, and <> means taking the average value. 2.如权利要求1所述的基于二阶自相关函数计算的激光散斑衬比血流成像方法,其特征在于,所述时间序列散斑图像的尺寸为M×N×T,其中M表示所述时间序列散斑图像水平方向的分辨率,N表示所述时间序列散斑图像垂直方向的分辨率,T表示原始散斑图像序列的帧数。2. The laser speckle contrast blood flow imaging method based on second-order autocorrelation function calculation according to claim 1, characterized in that the size of the time series speckle image is M×N×T, wherein M represents the horizontal resolution of the time series speckle image, N represents the vertical resolution of the time series speckle image, and T represents the number of frames of the original speckle image sequence. 3.如权利要求1所述的基于二阶自相关函数计算的激光散斑衬比血流成像方法,其特征在于,所述光强均值计算公式如下:3. The laser speckle contrast blood flow imaging method based on second-order autocorrelation function calculation according to claim 1, characterized in that the light intensity mean value calculation formula is as follows: 其中(i,j)表示像素点的位置坐标;t表示所述时间序列散斑图像在时间序列上的位置;T表示所述时间序列散斑图像的帧数。Wherein (i, j) represents the position coordinates of the pixel point; t represents the position of the time series speckle image in the time series; and T represents the frame number of the time series speckle image.
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