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CN106204434A - A kind of Image Iterative reconstructing method towards large visual field high resolution micro-imaging - Google Patents

A kind of Image Iterative reconstructing method towards large visual field high resolution micro-imaging Download PDF

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CN106204434A
CN106204434A CN201610474881.XA CN201610474881A CN106204434A CN 106204434 A CN106204434 A CN 106204434A CN 201610474881 A CN201610474881 A CN 201610474881A CN 106204434 A CN106204434 A CN 106204434A
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CN106204434B (en
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左超
陈钱
孙佳嵩
顾国华
张玉珍
李加基
张佳琳
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Nanjing University of Science and Technology
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    • G06TIMAGE DATA PROCESSING OR GENERATION, IN GENERAL
    • G06T3/00Geometric image transformations in the plane of the image
    • G06T3/40Scaling of whole images or parts thereof, e.g. expanding or contracting
    • G06T3/4053Scaling of whole images or parts thereof, e.g. expanding or contracting based on super-resolution, i.e. the output image resolution being higher than the sensor resolution
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    • G06COMPUTING; CALCULATING OR COUNTING
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Abstract

本发明公开了一种面向大视场高分辨率显微成像的图像迭代重构方法,首先LED阵列作为显微镜的照明光源,顺次点亮其中每一个LED元素,照射样品后采集相对应的图像;利用LED阵列中位于中心的LED元素照射样品所拍摄到的低分辨率图像来初始化高分辨率图像的振幅与相位;采用增量梯度法将所采集的每一幅图像在频域中逐一进行合成孔径运算;以代价函数值为判据对增量梯度迭代系数进行更新;当增量梯度迭代系数小于一个给定的阈值时,停止迭代。本发明在于其无需复杂的参数调节,并对采集图像中的噪声具有很强的抵御能力,能够非常稳定并且准确地重建出大视场高分辨率图像。

The invention discloses an image iterative reconstruction method for large-field-of-view and high-resolution microscopic imaging. Firstly, an LED array is used as the illumination source of the microscope, and each LED element is sequentially lit, and the corresponding image is collected after irradiating the sample. ; Initialize the amplitude and phase of the high-resolution image from the low-resolution image taken by illuminating the sample with the centrally located LED element in the LED array; use the incremental gradient method to step through each acquired image one by one in the frequency domain Synthetic aperture operation; update the incremental gradient iteration coefficient with the cost function value as the criterion; stop iteration when the incremental gradient iteration coefficient is less than a given threshold. The invention does not require complex parameter adjustment, has strong resistance to noise in the collected images, and can very stably and accurately reconstruct high-resolution images with a large field of view.

Description

一种面向大视场高分辨率显微成像的图像迭代重构方法An Image Iterative Reconstruction Method for Large Field of View and High Resolution Microscopic Imaging

技术领域technical field

本发明属于光学显微成像技术,特别是一种面向大视场高分辨率显微成像的图像迭代重构方法。The invention belongs to optical microscopic imaging technology, in particular to an image iterative reconstruction method for large field of view and high resolution microscopic imaging.

背景技术Background technique

在显微成像领域,更高的分辨率一直是追求的目标,但是在提高分辨率的同时存在一个关键性问题,那就是并没有随分辨率一起提高的显微镜的空间带宽积。从成像系统角度看,为了实现高分辨率,必须增加显微物镜的数值孔径,但空间分辨率的提高与视场的扩大往往是一对难以调和的矛盾。简言之,就是在低倍镜下可以看到被检物体的全貌,换成高倍物镜时,就只能看到被检物体的很小一部份。目前,为了突破分辨率与视场大小难以同时兼顾的矛盾,常见的方法是采用常规显微镜系统配合高精度机械扫描和后期空域图像拼接方法将多个小视场高分辨率图像拼接融合生成一幅大视场高分辨率图像([1]2013205777012,适用于结核杆菌抗酸染色图像拼接的装置)。但是由于引入了机械移动装置,所以系统成像时的稳定性和成像速度又成为一对难以调和的矛盾,提高扫描速度必将影响成像稳定性。所以,想要突破分辨率与视场大小难以同时兼顾的矛盾又不引入了机械移动装置,必须采用近年来提出的计算成像的方法,比如基于合成孔径的成像方法。In the field of microscopic imaging, higher resolution has always been the goal of pursuit, but there is a key problem while improving the resolution, that is, the spatial bandwidth product of the microscope does not increase with the resolution. From the perspective of the imaging system, in order to achieve high resolution, the numerical aperture of the microscope objective lens must be increased, but the improvement of spatial resolution and the expansion of the field of view are often a pair of contradictions that are difficult to reconcile. In short, the whole picture of the inspected object can be seen under the low magnification lens, but only a small part of the inspected object can be seen when it is replaced with a high magnification objective lens. At present, in order to break through the contradiction between the resolution and the size of the field of view, the common method is to use a conventional microscope system with high-precision mechanical scanning and a later spatial image stitching method to stitch and fuse multiple high-resolution images of small fields of view to generate a large image. High-resolution images of the field of view ([1] 2013205777012, a device suitable for stitching images of Mycobacterium tuberculosis acid-fast staining). However, due to the introduction of mechanical moving devices, the imaging stability and imaging speed of the system have become a pair of contradictions that are difficult to reconcile. Improving the scanning speed will definitely affect the imaging stability. Therefore, in order to break through the contradiction between resolution and field of view and not introduce mechanical moving devices, computational imaging methods proposed in recent years must be adopted, such as imaging methods based on synthetic aperture.

基于合成孔径成像原理的扫描成像方法最早是由Hoppe为了研究晶体结构所提出的,并通过研究晶体和非晶体的扫描透射电子衍射显微成像,验证了此方法的有效性。Rodenburg和Faulkner等结合相位恢复算法将此方法多次改进,目前这种成像方法已在可见光域、X射线、电子显微镜等不同波段得到了实验证实,并发展出若干种技术以提高成像质量以及分辨率,该技术显示了在大幅面成像和高分辨成像方面的巨大潜力。传统的合成孔径成像技术是通过移动一个全透的小孔(或待测样品本身)使入射平面波照射到待测样品的不同部位,即由小孔控制照明光束尺寸、几何形状及位置,并利用由此得到的一系列衍射强度图样重构出待测样品的振幅与位相信息([2]王雅丽等人.可见光域叠层成像中照明光束的关键参量研究[J].物理学报,2013,Vol.62,No.6.064206-1-9)。合成孔径成像术的关键在于:每次照射待测样品的一个“子孔径”也就是待测样品的某一部分时,都要和至少一个其他的“子孔径”发生交叠。这样就可建立一种重构算法,在分别重构每“子孔径”的复振幅时也要同时满足其他“子孔径”衍射分布的约束,使得最后的待测样品的整体复振幅信息是所有“子孔径”的共同解,从而由各个“子孔径”拼接合成一幅大视场高分辨率的待测样品的图像。合成孔径成像术可以说是一种稳健而简约的显微成像技术,但其一直缺乏一种稳健的图像重构算法。特别是当所采集的图像信噪比较低时,往往难以得到理想的重构图像,因此如何提高重构质量与信噪比成为了合成孔径成像技术必须克服的一个技术难题。The scanning imaging method based on the principle of synthetic aperture imaging was first proposed by Hoppe to study the crystal structure, and the effectiveness of this method was verified by studying the scanning transmission electron diffraction microscopy imaging of crystals and amorphous materials. Rodenburg and Faulkner combined the phase recovery algorithm to improve this method for many times. At present, this imaging method has been experimentally confirmed in different wavebands such as visible light domain, X-ray, and electron microscope, and several technologies have been developed to improve imaging quality and resolution. rate, the technology shows great potential in large-format imaging and high-resolution imaging. The traditional synthetic aperture imaging technology is to irradiate the incident plane wave to different parts of the sample by moving a fully transparent small hole (or the sample itself), that is, the size, geometry and position of the illumination beam are controlled by the small hole, and use A series of diffraction intensity patterns thus obtained can reconstruct the amplitude and phase information of the sample to be measured ([2] Wang Yali et al. Research on the key parameters of the illumination beam in visible light domain lamination imaging[J]. Acta Physica Sinica, 2013, Vol .62, No. 6.064206-1-9). The key to synthetic aperture imaging is that each time a "sub-aperture" of the sample to be tested is irradiated, that is, a certain part of the sample to be tested, it must overlap with at least one other "sub-aperture". In this way, a reconstruction algorithm can be established to satisfy the constraints of the diffraction distribution of other “sub-apertures” when reconstructing the complex amplitude of each “sub-aperture” respectively, so that the overall complex amplitude information of the final sample to be measured is all The common solution of "sub-apertures", so that each "sub-aperture" is spliced into a large field of view and high-resolution image of the sample to be tested. Synthetic aperture imaging can be said to be a robust and simple microscopic imaging technique, but it lacks a robust image reconstruction algorithm. Especially when the signal-to-noise ratio of the collected image is low, it is often difficult to obtain an ideal reconstructed image. Therefore, how to improve the reconstruction quality and signal-to-noise ratio has become a technical problem that must be overcome in synthetic aperture imaging technology.

发明内容Contents of the invention

本发明的目的在于提供一种面向大视场高分辨率显微成像的图像迭代重构方法,以解决显微系统分辨率与视场大小难以同时兼顾的矛盾,提升显微系统的空间带宽积。The purpose of the present invention is to provide an image iterative reconstruction method for large field of view and high resolution microscopic imaging, so as to solve the contradiction between the resolution of the microscopic system and the size of the field of view, and improve the spatial bandwidth product of the microscopic system .

实现本发明目的的技术解决方案为:一种面向大视场高分辨率显微成像的图像迭代重构方法,步骤如下:The technical solution to realize the purpose of the present invention is: an image iterative reconstruction method for large-field-of-view high-resolution microscopic imaging, the steps are as follows:

步骤一,图像采集:LED阵列作为显微镜的照明光源,顺次点亮其中每一个LED元素,照射样品后采集相对应的图像;Step 1, image acquisition: the LED array is used as the illumination source of the microscope, and each LED element is sequentially lit, and the corresponding image is collected after irradiating the sample;

步骤二,初始化:利用LED阵列中位于中心的LED元素照射样品所拍摄到的低分辨率图像来初始化高分辨率图像的振幅与相位;Step 2, initialization: initialize the amplitude and phase of the high-resolution image by using the low-resolution image captured by the LED element in the center of the LED array to irradiate the sample;

步骤三,迭代重构:采用增量梯度法将所采集的每一幅图像在频域中逐一进行合成孔径运算;Step 3, iterative reconstruction: use the incremental gradient method to perform synthetic aperture operations on each image collected in the frequency domain;

步骤四,增量梯度迭代系数更新:以代价函数值为判据对增量梯度迭代系数进行更新;Step 4, update the incremental gradient iteration coefficient: update the incremental gradient iteration coefficient with the cost function value as the criterion;

步骤五,停止迭代判断:当增量梯度迭代系数小于一个给定的阈值时,停止迭代,此时的高分辨率图像的振幅与相位就是最终得到的大视场高分辨率显微图像。Step 5, stop the iteration judgment: when the incremental gradient iteration coefficient is less than a given threshold, stop the iteration, and the amplitude and phase of the high-resolution image at this time are the finally obtained large-field high-resolution microscopic image.

本发明还可以在步骤一中的照明光源分别为红光、绿光或蓝光的单色光来照明物体,对于每种照明波长分别采用上述五个步骤进行图像重构,将各自重构的三组图像分别作为最终的真彩色图像的红、绿、蓝分量合成得到重构真彩色图像。In the present invention, the illumination sources in step 1 are red light, green light or blue monochromatic light to illuminate the object, and for each illumination wavelength, the above five steps are used to reconstruct the image, and the reconstructed three The group images are respectively synthesized as the red, green and blue components of the final true color image to obtain a reconstructed true color image.

本发明与现有技术相比,其显著优点:(1)利用LED阵列产生不同角度的入射光照射待测样品,再用相机拍摄多幅低分辨率图像,最后采用频域合成孔径技术将多幅大视场低分辨率图像合成一幅大视场高分辨率图像,无需任何机械扫描装置,系统成像稳定性高。与常规显微镜系统的高精度机械扫描和后期空域图像拼接方法相比,大大降低了系统的成本。(2)无需复杂的参数调节,并对采集图像中的噪声具有很强的抵御能力,能够非常稳定并且准确地重建出大视场高分辨率图像。Compared with the prior art, the present invention has significant advantages: (1) The LED array is used to generate incident light at different angles to irradiate the sample to be tested, and then multiple low-resolution images are taken with a camera, and finally the frequency-domain synthetic aperture technology is used to combine multiple A large field of view low resolution image is synthesized into a large field of view high resolution image without any mechanical scanning device, and the system has high imaging stability. Compared with the high-precision mechanical scanning and post-space image stitching methods of conventional microscope systems, the cost of the system is greatly reduced. (2) It does not require complex parameter adjustment, and has a strong resistance to noise in the collected images, and can reconstruct large-field-of-view high-resolution images very stably and accurately.

下面结合附图对本发明作进一步详细描述。The present invention will be described in further detail below in conjunction with the accompanying drawings.

附图说明Description of drawings

图1是基于可编程LED阵列的显微镜光路示意图。Figure 1 is a schematic diagram of the optical path of a microscope based on a programmable LED array.

图2是LED阵列中每个像素点的坐标系示意图。Fig. 2 is a schematic diagram of the coordinate system of each pixel in the LED array.

图3为本发明面向大视场高分辨率显微成像的图像迭代重构方法的流程示意图。FIG. 3 is a schematic flowchart of the image iterative reconstruction method for large-field-of-view and high-resolution microscopic imaging of the present invention.

图4(a)是4倍物镜(数值孔径0.1)下利用LED阵列中位于中心的LED元素照射1951USAF分辨率板样品所拍摄到的低分辨率图像;选取图4(a)方框中的图像直接进行放大,得到图4(b)。从中再选择更小的区域直接进行放大,又得到图4(c)。Figure 4(a) is a low-resolution image captured by using the LED element in the center of the LED array to illuminate the 1951USAF resolution plate sample under a 4x objective lens (numerical aperture 0.1); select the image in the box of Figure 4(a) Directly zoom in and get Figure 4(b). Then choose a smaller area to zoom in directly, and get Figure 4(c).

图5(a)为采用本发明方法对1951USAF分辨率板重构的大视场高分辨率显微图像;选取图5(a)方框中的图像直接放大,得到图5(b)。从中再选择更小的区域进行放大,又得到图5(c)。Figure 5(a) is a large-field high-resolution microscopic image reconstructed on the 1951USAF resolution plate using the method of the present invention; the image in the box in Figure 5(a) is selected to be directly enlarged, and Figure 5(b) is obtained. Then choose a smaller area to zoom in, and get Figure 5(c).

具体实施方式detailed description

本发明面向大视场高分辨率显微成像的图像迭代重构方法所依赖的硬件平台是基于可编程LED阵列的显微镜。结合图1,基于可编程LED阵列的显微镜主要包括显微物镜1、样品2、载物台3、LED阵列4组成。LED阵列4作为显微镜的照明光源,其被直接安置在样品载物台3下方,其距离载物台的上表面距离H一般在20-100mm之间,并且LED阵列4的中心处于显微物镜1的光轴上。LED阵列1中包括若干个LED元素5,它们规则排布形成一个二维阵列。其中单个LED元素均为红绿蓝三色LED,其典型波长为红光635nm、绿光525nm和蓝光475nm。每个LED元素之间中心间距d典型值1-10mm。LED阵列4并不需要进行单独加工,在市场上可直接购置。其包含呈阵列排列的一组多个LED,这些LED通过固定基板实现物理与电路连接,如表1给出了一个市面上可购置的LED阵列的产品参数。在此LED阵列中,LED元素共有32行、32列,一共1024个,单个LED的亮度在2000cd/m2以上。The hardware platform on which the image iterative reconstruction method for large-field-of-view and high-resolution microscopic imaging depends is a microscope based on a programmable LED array. Combined with FIG. 1 , the microscope based on the programmable LED array mainly includes a microscope objective lens 1 , a sample 2 , a stage 3 , and an LED array 4 . The LED array 4 is used as the illumination source of the microscope, which is directly placed under the sample stage 3, and the distance H from the upper surface of the stage is generally between 20-100 mm, and the center of the LED array 4 is located at the microscope objective lens 1 on the optical axis. The LED array 1 includes several LED elements 5 arranged regularly to form a two-dimensional array. Among them, the single LED elements are all red, green and blue three-color LEDs, and their typical wavelengths are red light 635nm, green light 525nm and blue light 475nm. The center distance d between each LED element is typically 1-10mm. The LED array 4 does not need to be processed separately, and can be directly purchased in the market. It includes a group of multiple LEDs arranged in an array, and these LEDs are physically and electrically connected through a fixed substrate. Table 1 shows the product parameters of a commercially available LED array. In this LED array, there are 32 rows and 32 columns of LED elements, a total of 1024, and the brightness of a single LED is above 2000cd/m 2 .

表1 LED阵列的物理参数Table 1 Physical parameters of LED array

LED阵列1中每个LED元素均可通过实现单独点亮,点亮LED元素的具体方法为现有技术,实现电路可以采用(但不限于)单片机、ARM、或者可编程逻辑器件等现有技术即可实现,具体实现方法可参考相关文献,如郭宝增,邓淳苗:基于FPGA的LED显示屏控制系统设计[J].液晶与显示,2010,25(3):424-428。Each LED element in the LED array 1 can be individually lit by realizing that the specific method of lighting the LED element is the prior art, and the implementation circuit can adopt (but not limited to) existing technologies such as single-chip microcomputer, ARM, or programmable logic devices. It can be realized, and the specific implementation method can refer to relevant literature, such as Guo Baozeng, Deng Chunmiao: FPGA-based LED display control system design [J]. Liquid Crystal and Display, 2010,25(3):424-428.

本发明面向大视场高分辨率显微成像的图像迭代重构方法实施之前,首先对LED阵列4中每LED元素所对应的照明光的空间频率进行标记,具体方法如下:结合图2,建立坐标系。其中矩形区域代表LED阵列4有效区域,坐标原点位于成像系统的光轴中央。对于任意一个LED元素P,其位置坐标为(Px,Py),首先计算该LED元素所对应的照明光的空间频率矢量:Before the implementation of the image iterative reconstruction method for large-field-of-view and high-resolution microscopic imaging in the present invention, the spatial frequency of the illumination light corresponding to each LED element in the LED array 4 is first marked, and the specific method is as follows: Combined with FIG. 2, establish Coordinate System. The rectangular area represents the effective area of the LED array 4, and the coordinate origin is located at the center of the optical axis of the imaging system. For any LED element P, whose position coordinates are (P x , P y ), first calculate the spatial frequency vector of the illumination light corresponding to the LED element:

uu ii == (( uu xx ,, uu ythe y )) == 22 ππ λλ (( PP xx PP xx 22 ++ PP ythe y 22 ++ Hh 22 ,, PP ythe y PP xx 22 ++ PP ythe y 22 ++ Hh 22 ))

类似地,针对LED阵列4中每个LED元素,都可以计算得到其相对应的空间频率矢量,记作ui,下标i=1,2,...,N其中N为LED阵列4中LED元素的总个数,λ为单色照明光(红、绿或蓝)的波长。ui为第i个LED的照明光空间频率矢量。Similarly, for each LED element in the LED array 4, its corresponding spatial frequency vector can be calculated, denoted as u i , subscript i=1, 2,..., N where N is the element in the LED array 4 The total number of LED elements, λ is the wavelength of monochromatic illumination light (red, green or blue). u i is the spatial frequency vector of the illumination light of the i-th LED.

结合图3,基于上述技术,本发明面向大视场高分辨率显微成像的图像迭代重构方法,其步骤包括:In conjunction with Fig. 3, based on the above-mentioned technology, the present invention is oriented to an image iterative reconstruction method for large-field-of-view high-resolution microscopic imaging, the steps of which include:

步骤一:图像采集。LED阵列4作为显微镜的照明光源,顺次点亮其中每一个LED像素,照射样品后采集相对应的图像。由于整个LED阵列中共包含N个LED像素,那么共计拍摄N幅低分辨率图像,记作Ii(r),i=1,2,...,N,r为实空间的二维坐标r=(x,y)。理想情况下,这些拍摄到的低分辨率图像Ii(r)可以被表示为Step 1: Image acquisition. The LED array 4 is used as the illumination source of the microscope, sequentially lights up each LED pixel, and collects corresponding images after irradiating the sample. Since the entire LED array contains N LED pixels, a total of N low-resolution images are taken, denoted as I i (r), i=1,2,...,N, r is the two-dimensional coordinate r of the real space =(x,y). Ideally, these captured low-resolution images I i (r) can be expressed as

其中为二维傅里叶变换,u为与r所对应的空间频率坐标,为二维逆傅里叶变换,O(u)为待求的高分辨率物函数的傅里叶变换,即P(u)为显微镜的孔径函数。可以看出,物函数的傅里叶变换首先被第i个LED的照明光空间频率矢量ui所移动,然后受显微镜的孔径函数P(u)限制后,经过傅里叶逆变换后在实空间形成低分辨率图像Ii(r),这也就对应着相机所拍摄到的N幅图像Ii(r),i=1,2,...,N。in is the two-dimensional Fourier transform, u is the spatial frequency coordinate corresponding to r, is the two-dimensional inverse Fourier transform, O(u) is the Fourier transform of the high-resolution object function to be found, namely P(u) is the aperture function of the microscope. It can be seen that the Fourier transform of the object function is firstly moved by the spatial frequency vector u i of the illumination light of the i-th LED, and then limited by the aperture function P(u) of the microscope, after the inverse Fourier transform in the real A low-resolution image I i (r) is formed spatially, which corresponds to N images I i (r) captured by the camera, i=1, 2, . . . , N.

求解高分辨率物函数的傅里叶变换O(u)实质上等价于求解如下的最优化问题Solving the Fourier transform O(u) of the high-resolution object function is essentially equivalent to solving the following optimization problem

ε为代价函数,其衡量所拍摄到的图像与计算得到的图像之间差异的大小。上述公式表明,待求的高分辨率物函数的傅里叶变换O(u)是令代价函数ε最小化的解。以下为了便于叙述,将上述公式与变量全部表示为向量形式:代表将拍摄到的低分辨率图像Ii(r)按像素顺序排布成的列向量,该列向量中元素个数与图像的像素数相等,均为M。Ii为低分辨率图像向量。代表高分辨率物函数的傅里叶变换O(u)按像素顺序排布成的列向量,该列向量中元素个数为L,O为高分辨率物函数的傅里叶变换向量。由于重构图像的分辨率往往远高于原始图像的分辨率,所以L>>M。Pi是一个由孔径函数P(u)所决定的M×L的矩阵,称之为孔径函数矩阵,其作用就是在整个高分辨率物函数的傅里叶变换向量的M个原素中抽取由孔径所限制的L个元素。通过上述向量表示后,代价函数ε可以被表示为ε is a cost function that measures the difference between the captured image and the computed image. The above formula shows that the Fourier transform O(u) of the high-resolution object function to be found is the solution to minimize the cost function ε. In the following, for the convenience of description, all the above formulas and variables are expressed in vector form: Represents a column vector in which the captured low-resolution image I i (r) is arranged in pixel order, and the number of elements in the column vector is equal to the number of pixels in the image, both of which are M. I i is a low-resolution image vector. The Fourier transform O(u) representing the high-resolution object function is a column vector arranged in pixel order, the number of elements in the column vector is L, and O is the Fourier transform vector of the high-resolution object function. Since the resolution of the reconstructed image is often much higher than that of the original image, L>>M. P i is an M×L matrix determined by the aperture function P(u), called the aperture function matrix, and its function is to extract from the M elements of the Fourier transform vector of the entire high-resolution object function L elements bounded by the aperture. After expressed by the above vector, the cost function ε can be expressed as

ϵϵ == ΣΣ ii || || II ii -- || Ff -- 11 PP ii Oo || || || 22 == ΣΣ ii || || II ii -- || gg ii || || || 22

其中||·||代表欧几里得范数,F是离散傅里叶变换的矩阵表达形式,gi≡F-1PiO.根据Parseval定理,代价函数ε可以被化简为where ||·|| represents the Euclidean norm, F is the matrix expression of the discrete Fourier transform, and g i ≡ F -1 P i O. According to Parseval's theorem, the cost function ε can be simplified as

ϵϵ == ΣΣ ii || || ΨΨ ii -- PP ii Oo || || 22

其中in

ΨΨ ii == ΠΠ mm →&Right Arrow; II ii (( PP ii Oo ))

代表更新后的子频谱;代表实空间模投影操作represents the updated sub-spectrum; Represents the real-space modular projection operation

ΠΠ mm →&Right Arrow; II ii (( PP ii Oo )) == Ff DD. ii aa gg (( gg ii || gg ii || -- 11 )) II ii

其代表将gi的幅度部分采用测量值所替换,而保持其相位部分不变。Diag()代表对角矩阵。It represents that the magnitude of gi is partly taken from the measured value replaced, while keeping its phase part unchanged. Diag() represents a diagonal matrix.

步骤二:初始化。利用LED阵列中位于中心的LED元素照射样品所拍摄到的低分辨率图像来初始化高分辨率图像的振幅与相位,如下式所示:Step 2: Initialization. The amplitude and phase of the high-resolution image are initialized by using the low-resolution image captured by the LED element in the center of the LED array to illuminate the sample, as shown in the following formula:

Oo 00 == Ff ↑&Up Arrow; II cc ee nno tt ee rr

式中,Icenter为LED阵列4中位于中心的LED元素照射样品所拍摄到的低分辨率图像向量;↑代表图像上采样,即将图像由原始的M像素插值为L个像素。这里的插值方法可直接采用现有技术,如最邻近插值法、双线性插值法或双三次插值法等等,插值方法的选取并不会影响最终的重构结果。增量梯度迭代系数α0初始化为α0=1,代价函数值ε0初始化为这里O0的下标0代表内循环迭代次数,α0与ε0的上标0代表外循环迭代次数。In the formula, I center is the low-resolution image vector captured by the LED element in the center of the LED array 4 irradiating the sample; ↑ represents image upsampling, that is, the image is interpolated from the original M pixels to L pixels. The interpolation method here can directly adopt the existing technology, such as the nearest neighbor interpolation method, bilinear interpolation method or bicubic interpolation method, etc., and the selection of the interpolation method will not affect the final reconstruction result. The incremental gradient iteration coefficient α 0 is initialized to α 0 =1, and the cost function value ε 0 is initialized to Here the subscript 0 of O 0 represents the number of iterations of the inner loop, and the superscript 0 of α 0 and ε 0 represents the number of iterations of the outer loop.

步骤三:迭代重构。采用增量梯度法将所采集的每一幅图像在频域中逐一进行合成孔径运算。为了最小化代价函数ε,将代价函数写为增量形式,即:Step 3: Iterative reconstruction. The incremental gradient method is used to perform synthetic aperture operation on each acquired image one by one in the frequency domain. In order to minimize the cost function ε, the cost function is written in incremental form, namely:

εi=||Ψi-PiO||2 ε i =||Ψ i -P i O|| 2

因此,代价函数的增量梯度可以表示为Therefore, the incremental gradient of the cost function can be expressed as

▿▿ ϵϵ ii == -- PP ii ** (( ΨΨ ii -- PP ii Oo ))

然后采用增量梯度法对高分辨率物函数的傅里叶变换向量进行更新,这里主要可细分为三个子步骤:Then, the incremental gradient method is used to update the Fourier transform vector of the high-resolution object function, which can be subdivided into three sub-steps:

第一步,采用增量梯度法对高分辨率物函数的傅里叶变换向量进行如下更新:In the first step, the Fourier transform vector of the high-resolution object function is updated using the incremental gradient method as follows:

Oo ii ++ 11 kk == Oo ii kk ++ αα kk WW ii ▿▿ ϵϵ ii kk == Oo ii kk -- αα kk WW ii PP ii ** (( ΨΨ ii kk -- PP ii Oo ii kk ))

其中,αk为增量梯度迭代系数;代表被Ii更新后的子频谱Among them, α k is the incremental gradient iteration coefficient; Represents the sub-spectrum updated by I i

ΨΨ ii kk == ΠΠ mm →&Right Arrow; II ii (( PP ii Oo ii kk ))

上面的公式中的下标i代表内循环迭代次数,上标k代表外循环迭代次数。Wi为权重矩阵The subscript i in the above formula represents the number of iterations of the inner loop, and the superscript k represents the number of iterations of the outer loop. W i is the weight matrix

WW ii == DD. ii aa gg (( || PP mm ,, ii || mm aa xx -- 22 ))

Diag()代表对角矩阵,其对角线元素依次为|Pm,i|max代表孔径函数模的最大值。Wi的作用是对孔径函数内部的频率成分进行加权,并排除孔径函数外部的频率成分。Diag() represents a diagonal matrix, and its diagonal elements are in order |P m,i | max represents the maximum value of the aperture function modulus. The function of W i is to weight the frequency components inside the aperture function and exclude the frequency components outside the aperture function.

第二步,高分辨率物函数的傅里叶变换向量更新完毕之后,内循环迭代次数加1,即i←i+1,切换到下一幅低分辨率图像向量Ii,i=1,2,...,N,重复第一步。In the second step, the Fourier transform vector of the high-resolution object function After the update is completed, the number of iterations of the inner loop is increased by 1, that is, i←i+1, switch to the next low-resolution image vector I i , i=1,2,...,N, and repeat the first step.

第三步,当所有图像遍历过一次后,即每幅低分辨率图像向量Ii,i=1,2,...,N均参与迭代运算直到i=N,步骤三完成。In the third step, after all the images have been traversed once, that is, each low-resolution image vector I i , i=1, 2, .

步骤四:增量梯度迭代系数更新,分为三个子步骤:Step 4: Incremental gradient iteration coefficient update, divided into three sub-steps:

1、计算当前高分辨率物函数的傅里叶变换向量所对应的代价函数值εk所对应的误差函数:1. Calculate the Fourier transform vector of the current high-resolution object function The error function corresponding to the corresponding cost function value ε k :

ϵϵ kk == ΣΣ ii || || II ii -- || Ff -- 11 PP ii Oo NN kk || || || 22

2、以代价函数值εk为判据对增量梯度迭代系数进行更新,更新公式如下:2. Use the cost function value ε k as the criterion to update the incremental gradient iteration coefficient. The update formula is as follows:

上述公式表明,增量梯度迭代系数αk在代价函数值εk不再减少时就减小到原来的一半。这样可以保证算法的自适应收敛,并有效提高算法对噪声的鲁棒性。The above formula shows that the incremental gradient iteration coefficient α k is reduced to half of the original value when the cost function value ε k no longer decreases. This can ensure the adaptive convergence of the algorithm and effectively improve the robustness of the algorithm to noise.

3、外循环迭代次数加1,即k←k+1,内循环迭代次数清0,即i←0。3. The number of iterations of the outer loop is increased by 1, that is, k←k+1, and the number of iterations of the inner loop is cleared to 0, that is, i←0.

这里的核心在于增量梯度迭代系数αk的趋势在于逐步减小以保证算法的稳定收敛。The core here is that the incremental gradient iteration coefficient α k tends to decrease gradually to ensure the stable convergence of the algorithm.

步骤五:停止迭代判断。当增量梯度迭代系数αk小于一个给定的阈值时(建议值为0.001),停止迭代。此时对迭代得到的高分辨率物函数的傅里叶变换向量进行逆傅里叶变换变换到空域中Step 5: Stop iterative judgment. When the incremental gradient iteration coefficient α k is less than a given threshold (the recommended value is 0.001), the iteration is stopped. At this time, the Fourier transform vector of the high-resolution object function obtained by iteration Perform an inverse Fourier transform into the spatial domain

Oo rr ee sthe s uu ll tt == Ff -- 11 Oo NN kk

即得到了待测样品大视场高分辨率的振幅分布|Oresult|和相位分布angle(Oresult),其中angle()代表取复数的幅角。如果停止条件不满足,则返回步骤三,重新进行一次内循环,直到满足停止条件为止。That is, the amplitude distribution |O result | and the phase distribution angle(O result ) of the large field of view and high resolution of the sample to be tested are obtained, where angle() represents the argument of a complex number. If the stop condition is not met, go back to step 3 and perform an inner loop again until the stop condition is met.

本发明物体焦面自动确定方法为:在一种面向大视场高分辨率显微成像的图像迭代重构方法的步骤一:图像采集之前。必须保证载物台3的高度正确,即样品2能够准确的位于显微物镜1的焦面上,对于显微物镜1是无穷远物镜,即保证物体严格位于显微物镜1的前焦面上,此时显微物镜1可以对样品2进行清晰成像。为了保证载物台3的高度正确,按照以下步骤进行载物台高度的调节:The method for automatically determining the focal plane of an object in the present invention is as follows: before step 1 of an image iterative reconstruction method for large-field-of-view and high-resolution microscopic imaging: before image acquisition. It is necessary to ensure that the height of the stage 3 is correct, that is, the sample 2 can be accurately located on the focal plane of the microscopic objective lens 1, and for the microscopic objective lens 1, it is an infinity objective lens, that is, to ensure that the object is strictly located on the front focal plane of the microscopic objective lens 1 , at this moment, the microscope objective lens 1 can image the sample 2 clearly. In order to ensure that the height of the stage 3 is correct, follow the steps below to adjust the height of the stage:

①LED阵列4作为显微镜的照明光源,点亮其中所有LED像素。①The LED array 4 is used as the illumination source of the microscope to light up all the LED pixels therein.

②将载物台3的高度调节到最小值z0,采集相对应的图像 ② Adjust the height of the stage 3 to the minimum value z 0 , and collect the corresponding images

③按如下公式求解所对应的离焦测度函数值 ③ Solve according to the following formula Corresponding defocus measurement function value

LaplaceLaplace zz 00 (( xx ,, ythe y )) == || 22 II zz 00 (( xx ,, ythe y )) -- II zz 00 (( xx -- sthe s tt ee pp ,, ythe y )) -- II zz 00 (( xx ++ sthe s tt ee pp ,, ythe y )) || ++ || 22 II zz 00 (( xx ,, ythe y )) -- II zz 00 (( xx ,, ythe y -- sthe s tt ee pp )) -- II zz 00 (( xx ,, ythe y ++ sthe s tt ee pp )) ||

LL zz 00 == ΣΣLaplaceΣΣLaplace zz 00 (( xx ,, ythe y )) ,, forΣΣLaplaceforΣΣLaplace zz 00 (( xx ,, ythe y )) >> TT

其中step为梯度求解步长,一般取1-5像素。T为梯度阈值,一般取图像最大灰度值的3%。Where step is the gradient solution step size, generally 1-5 pixels. T is the gradient threshold, generally taken as 3% of the maximum gray value of the image.

④将载物台3的高度提高到z1,采集相对应的图像 ④ Raise the height of stage 3 to z 1 and collect corresponding images

⑤类似地,求解所对应的离焦测度函数 ⑤Similarly, solve The corresponding defocus measurement function

⑥重复上述过程,直至找到所有范围内最小的离焦测度函数值此时所对应的载物台3的高度即是正确值。此时可保证显微物镜1对样品2进行清晰成像。⑥Repeat the above process until the minimum defocus measurement function value in all ranges is found At this time, the corresponding height of the stage 3 is the correct value. At this time, it can be ensured that the microscope objective lens 1 can clearly image the sample 2 .

本发明的步骤三中迭代重构的图像顺序选择:这里有两种备选方案,一种是LED从最中央(光轴上)到外围(远离光轴)顺次进行更新。还有一种是按图像的强度值||Ii||降序进行更新。两种更新顺序都可以得到良好的重构效果。Image sequence selection for iterative reconstruction in Step 3 of the present invention: There are two alternatives here, one is that the LEDs are updated sequentially from the center (on the optical axis) to the periphery (away from the optical axis). Another is to update in descending order according to the intensity value ||I i || of the image. Both update orders can get good refactoring results.

上述步骤仅仅针对单色照明的情况(如红、绿、蓝等),若想重构真彩色图像。则每个LED元素需分别采用红光、绿光、蓝光来照明物体,然后对于每种照明波长分别采用上述五个步骤进行图像重构,重构的三组图像分别作为最终的真彩色图像的红、绿、蓝分量合成即可。The above steps are only for monochromatic lighting (such as red, green, blue, etc.), if you want to reconstruct a true color image. Then each LED element needs to use red light, green light, and blue light to illuminate the object, and then use the above five steps for image reconstruction for each illumination wavelength, and the three reconstructed images are respectively used as the final true color image The red, green and blue components can be synthesized.

为了测试大视场高分辨率显微成像的图像迭代重构方法,我们选取了1951USAF分辨能力测试板进行了成像测试。实验中,使用的LED阵列包含21行21列共441个LED,并利用其产生225个不同角度的照明光,LED之间间距为2.5mm,发出的红光波长为632.8nm。系统所采用的显微物镜的数值孔径为0.1,放大倍率为4x。利用LED阵列中位于中心的LED元素照射样品所拍摄到的低分辨率图像如图4所示。选取图4(a)方框中的图像直接进行放大,得到图4(b)。从中再选择更小的区域直接进行放大,又得到图4(c)。如图可见,最小可分辨的特征为第七组第三个元素,根据1951USAF分辨能力测试板的物理参数(见表2)可知成像系统的原始成像分辨率约为6.2μm/线对。这与成像系统的瑞利衍射极限公式推断的结果吻合良好。而采用本发明重构后的高分辨率图像如图5所示,选取图5(a)方框中的图像直接进行放大,得到图5(b)。从中再选择更小的区域直接进行放大,又得到图5(c)。分辨率板中最小的特征均可以分辨(第九组第三个元素)。通过表2可知,经过合成后的成像系统的分辨率优于1.56μm/线对,即分辨率高于1000um/(645*2)=0.775um。对比其中图5(c)和图4(c)可以明显看出本发明方法能够在低数值孔径大视场情况下实现大视场高分辨率成像,且重构图像具有良好的信噪比。In order to test the image iterative reconstruction method of large-field-of-view high-resolution microscopic imaging, we selected the 1951USAF resolution test board for imaging testing. In the experiment, the LED array used contains a total of 441 LEDs in 21 rows and 21 columns, and it is used to generate 225 different angles of illumination light. The spacing between the LEDs is 2.5mm, and the emitted red light has a wavelength of 632.8nm. The numerical aperture of the microscope objective used in the system is 0.1, and the magnification is 4x. A low-resolution image taken of the sample illuminated by the centrally located LED element of the LED array is shown in Figure 4. Select the image in the box in Figure 4(a) and directly zoom in to get Figure 4(b). Then choose a smaller area to zoom in directly, and get Figure 4(c). As can be seen from the figure, the smallest resolvable feature is the third element of the seventh group. According to the physical parameters of the 1951USAF resolution test board (see Table 2), the original imaging resolution of the imaging system is about 6.2 μm/line pair. This is in good agreement with the results inferred from the Rayleigh diffraction limit formula for imaging systems. However, the high-resolution image reconstructed by the present invention is shown in FIG. 5 , and the image in the box in FIG. 5( a ) is selected and directly enlarged to obtain FIG. 5( b ). Then choose a smaller area to zoom in directly, and get Figure 5(c). The smallest feature in the resolution board can be resolved (third element of the ninth group). It can be seen from Table 2 that the resolution of the combined imaging system is better than 1.56 μm/line pair, that is, the resolution is higher than 1000 um/(645*2)=0.775 um. Comparing Fig. 5(c) and Fig. 4(c), it can be clearly seen that the method of the present invention can realize large-field-of-view high-resolution imaging in the case of low numerical aperture and large field of view, and the reconstructed image has a good signal-to-noise ratio.

表2 1951USAF分辨能力测试板的物理参数Table 2 Physical parameters of 1951USAF resolution test board

Claims (10)

1. the Image Iterative reconstructing method towards large visual field high resolution micro-imaging, it is characterised in that step is as follows:
Step one, image acquisition: LED array, as microscopical lighting source, sequentially lights each of which LED element, shine Corresponding image is gathered after penetrating sample;
Step 2, initializes: utilize the LED element being positioned at center in LED array to irradiate the low resolution figure taken by sample As initializing amplitude and the phase place of high-definition picture;
Step 3, iterative reconstruction: use incremental gradient method to carry out the every piece image gathered the most one by one synthesizing hole Footpath computing;
Step 4, incremental gradient iteration coefficient updates: be updated incremental gradient iteration coefficient with cost function value for criterion;
Step 5, stops iteration and judges: when incremental gradient iteration coefficient is less than a given threshold value, stops iteration, now Amplitude and the phase place of high-definition picture be exactly the large visual field high resolution micro-image finally given.
2. the Image Iterative reconstructing method towards large visual field high resolution micro-imaging, it is characterised in that step is as follows:
Step one, image acquisition: LED array, as microscopical lighting source, sequentially lights each of which LED element, shine Corresponding image is gathered after penetrating sample;
Step 2, initializes: utilize the LED element being positioned at center in LED array to irradiate the low resolution figure taken by sample As initializing amplitude and the phase place of high-definition picture;
Step 3, iterative reconstruction: use incremental gradient method to carry out the every piece image gathered the most one by one synthesizing hole Footpath computing;
Step 4, incremental gradient iteration coefficient updates: be updated incremental gradient iteration coefficient with cost function value for criterion;
Step 5, stops iteration and judges: when incremental gradient iteration coefficient is less than a given threshold value, stops iteration, now Amplitude and the phase place of high-definition picture be exactly the large visual field high resolution micro-image finally given;
Step 6, the respectively HONGGUANG of the lighting source in step one, green glow, the monochromatic light of blue light illuminate object, for often Kind illumination wavelengths is respectively adopted above-mentioned five steps and carries out image reconstruction, using three groups of images of each via Self-reconfiguration as final The red, green, blue component synthesis of true color image obtains reconstructing true color image.
Image Iterative reconstructing method towards large visual field high resolution micro-imaging the most according to claim 1 and 2, it is special Levy before being that iterative reconstruction is implemented, first the spatial frequency of the illumination light corresponding to LED element every in LED array is marked Note, concrete grammar is as follows: set up coordinate system, and wherein rectangular area represents the effective coverage of LED array (4), and zero is positioned at The optical axis central authorities of imaging system;For any one LED element P, its position coordinates is (Px,Py), first calculate this LED element The spatial frequency vector of corresponding illumination light:
u i = ( u x , u y ) = 2 π λ ( P x P x 2 + P y 2 + H 2 , P y P x 2 + P y 2 + H 2 )
It is calculated its corresponding spatial frequency vector for LED element each in LED array 4, is denoted as ui, subscript i=1, 2 ..., N, total number of LED element during wherein N is LED array 4, λ is the wavelength of illumination light, uiIllumination light for i-th LED Spatial frequency vector.
Image Iterative reconstructing method towards large visual field high resolution micro-imaging the most according to claim 1 and 2, it is special Levying and be in step one, the enforcement step of image acquisition is: LED array (4), as microscopical lighting source, sequentially lights it In each LED pixel, irradiate after sample and gather corresponding image;Owing to whole LED array comprising N number of LED pixel altogether, Amount to shooting N width low-resolution image, be denoted as Ii(r), i=1,2 ..., N, r be the real space two-dimensional coordinate r=(x, y), will The low-resolution image I photographediR () column vector that according to pixels order is arranged into, obtains low-resolution image vector Ii
Image Iterative reconstructing method towards large visual field high resolution micro-imaging the most according to claim 1 and 2, it is special Levy and be in step 2, initialized enforcement step by: utilize LED array is positioned at center LED element irradiate sample clapped The low-resolution image taken the photograph is to initialize amplitude and the phase place of high-definition picture, i.e.
O 0 = F ↑ I c e n t e r
In formula, IcenterFor LED array 4 is positioned at the LED element at center irradiate low-resolution image taken by sample to Amount;↑ representative image up-samples, and will image is M pixel by original L picture element interpolation;Incremental gradient iteration coefficient α0Initially Turn to α0=1, cost function value ε0It is initialized asO0Subscript 0 represent interior loop iteration number of times, α0With ε0Upper Mark 0 represents outer circulation iterations.
Image Iterative reconstructing method towards large visual field high resolution micro-imaging the most according to claim 1 and 2, it is special Levying and be in step 3, iterative reconstruction is divided into three sub-steps:
The first step, uses incremental gradient method to update the Fourier Transform vector of high-resolution thing function as follows:
O i + 1 k = O i k + α k W i ▿ ϵ i k = O i k - α k W i P i * ( Ψ i k - P i O i k )
Wherein, αkFor incremental gradient iteration coefficient;Represent by IiSub-frequency spectrum after renewal:
Ψ i k = Π m → I i ( P i O i k )
Subscript i in above formula represents interior loop iteration number of times, and subscript k represents outer circulation iterations;WiFor weight square Battle array:
W i = D i a g ( | P m , i | m a x - 2 )
Diag () represents diagonal matrix, and its diagonal entry is followed successively by|PM, i|maxRepresent the maximum of aperture function mould Value;
Second step, the Fourier Transform vector of high-resolution thing functionUpdate complete after, interior loop iteration number of times adds 1, i.e. I ← i+1, is switched to next width low-resolution image vector Ii, i=1,2 ..., N, repeats the first step;
3rd step, after all image traversal are crossed once, the most every width low-resolution image vector Ii, i=1,2 ..., N both participates in Interative computation is until i=N, and step 3 completes.
Image Iterative reconstructing method towards large visual field high resolution micro-imaging the most according to claim 1 and 2, it is special Levying and be in step 4, incremental gradient iteration coefficient updates and is divided into three sub-steps:
The first step, calculates the Fourier Transform vector of Current high resolution thing functionCorresponding cost function value εkCorresponding Error function:
ϵ k = Σ i | | I i - | F - 1 P i O N k | | | 2
Second step, with cost function value εkBeing updated incremental gradient iteration coefficient for criterion, more new formula is as follows:
3rd step, outer circulation iterations adds 1, i.e. k ← k+1, interior loop iteration number of times clear 0, i.e. i ← 0.
Image Iterative reconstructing method towards large visual field high resolution micro-imaging the most according to claim 1 and 2, it is special Levying and be in step 5, the implementation process stopping iteration judgement is: as incremental gradient iteration coefficient αkThe threshold given less than one During value, stop iteration, the Fourier Transform vector of the high-resolution thing function now iteration obtainedCarry out inverse Fourier to become Transformation is changed in spatial domain
O r e s u l t = F - 1 O N k
I.e. obtain the distribution of amplitudes of testing sample large visual field high resolution | Oresult| and PHASE DISTRIBUTION angle (Oresult), its Middle angle () represents and takes argument of complex number;If stop condition is unsatisfactory for, then return step 3, re-start circulation in once, Until meeting stop condition.
Image Iterative reconstructing method towards large visual field high resolution micro-imaging the most according to claim 1 and 2, it is special Levy and be before the image acquisition of step one, it is ensured that the height of object stage (3) is correct, carries out object stage height according to the following steps Regulation:
1. LED array (4) is as microscopical lighting source, lights the most all LED pixel;
2. by the altitude mixture control of object stage (3) to minima z0, gather corresponding image
Solve the most as followsCorresponding out of focus measure function value
Laplace z 0 ( x , y ) = | 2 I z 0 ( x , y ) - I z 0 ( x - s t e p , y ) - I z 0 ( x + s t e p , y ) | + | 2 I z 0 ( x , y ) - I z 0 ( x , y - s t e p ) - I z 0 ( x , y + s t e p ) |
L z 0 = ΣΣLaplace z 0 ( x , y ) , forΣΣLaplace z 0 ( x , y ) > T
Wherein step is that gradient solves step-length, and T is Grads threshold;
4. the height of object stage (3) is brought up to z1, gather corresponding image
5. according to step 3. in formula, solveCorresponding out of focus measure function
6. repeat said process, until find all in the range of minimum out of focus measure function valueNow corresponding loading The height of platform (3) is i.e. right value, now ensures that microcobjective 1 carries out blur-free imaging to sample 2.
Image Iterative reconstructing method towards large visual field high resolution micro-imaging the most according to claim 1 and 2, its The image sequence selection mode being characterised by iterative reconstruction in step 3 is: LED from the most central optical axis to periphery away from light Axle is sequentially updated;Or press the intensity level of image | | Ii| | descending is updated.
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