WO2015101060A1 - 单臂x射线血管造影图像多运动参数分解估计方法 - Google Patents

单臂x射线血管造影图像多运动参数分解估计方法 Download PDF

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WO2015101060A1
WO2015101060A1 PCT/CN2014/085727 CN2014085727W WO2015101060A1 WO 2015101060 A1 WO2015101060 A1 WO 2015101060A1 CN 2014085727 W CN2014085727 W CN 2014085727W WO 2015101060 A1 WO2015101060 A1 WO 2015101060A1
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motion
sequence
decomposition
signal
emd
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张天序
黄正华
黄怡宁
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华中科技大学
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    • A61—MEDICAL OR VETERINARY SCIENCE; HYGIENE
    • A61B—DIAGNOSIS; SURGERY; IDENTIFICATION
    • A61B6/00—Apparatus or devices for radiation diagnosis; Apparatus or devices for radiation diagnosis combined with radiation therapy equipment
    • A61B6/52—Devices using data or image processing specially adapted for radiation diagnosis
    • A61B6/5258—Devices using data or image processing specially adapted for radiation diagnosis involving detection or reduction of artifacts or noise
    • A61B6/5264—Devices using data or image processing specially adapted for radiation diagnosis involving detection or reduction of artifacts or noise due to motion
    • A—HUMAN NECESSITIES
    • A61—MEDICAL OR VETERINARY SCIENCE; HYGIENE
    • A61B—DIAGNOSIS; SURGERY; IDENTIFICATION
    • A61B6/00—Apparatus or devices for radiation diagnosis; Apparatus or devices for radiation diagnosis combined with radiation therapy equipment
    • A61B6/50—Apparatus or devices for radiation diagnosis; Apparatus or devices for radiation diagnosis combined with radiation therapy equipment specially adapted for specific body parts; specially adapted for specific clinical applications
    • A61B6/504—Apparatus or devices for radiation diagnosis; Apparatus or devices for radiation diagnosis combined with radiation therapy equipment specially adapted for specific body parts; specially adapted for specific clinical applications for diagnosis of blood vessels, e.g. by angiography
    • G—PHYSICS
    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06T—IMAGE DATA PROCESSING OR GENERATION, IN GENERAL
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    • G06T7/20—Analysis of motion
    • G06T7/246—Analysis of motion using feature-based methods, e.g. the tracking of corners or segments
    • A—HUMAN NECESSITIES
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    • A61B6/481—Diagnostic techniques involving the use of contrast agents
    • G—PHYSICS
    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06T—IMAGE DATA PROCESSING OR GENERATION, IN GENERAL
    • G06T2207/00—Indexing scheme for image analysis or image enhancement
    • G06T2207/10—Image acquisition modality
    • G06T2207/10116—X-ray image
    • G06T2207/10121—Fluoroscopy
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    • G06T2207/30—Subject of image; Context of image processing
    • G06T2207/30004—Biomedical image processing
    • G06T2207/30101—Blood vessel; Artery; Vein; Vascular

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  • the invention belongs to the field of digital signal processing and medical imaging crossover technology, and particularly relates to a multi-motion parameter decomposition estimation method for single-arm x-ray angiography images.
  • the thoracic rhythm is enlarged and reduced to complete inhalation and exhalation. This is the breathing movement.
  • the regular pulsation of the heart itself (heart movement), the movement of capillaries (high-frequency movement), the movement of the breathing, and the movement of the person or the shaking of the bed (translational movement) can cause the overall translational movement of the human heart in three-dimensional space.
  • a two-dimensional translational motion occurs on the contrast surface of the coronary arteries.
  • the coronary angiography image records on the one hand the projection of the motion of the heart on a two-dimensional plane, and also superimposes the two-dimensional translational motion of the coronary artery on the contrast surface caused by the respiratory motion, high-frequency motion and translational motion of the human body.
  • the multiple motions are separately extracted separately, and one method of extracting the respiratory motion is to perform sequence tracking on the human body by extracting the marker points in advance.
  • one method of extracting the respiratory motion is to perform sequence tracking on the human body by extracting the marker points in advance.
  • people will move other organs in the body together when breathing. It is generally believed that these organs will translate in three dimensions with the movement of the lungs, and their movements are synchronized. Therefore, it is assumed that the motion of the heart caused by the respiratory motion and the motion of the organ adjacent thereto are also coincident in the plane of the contrast image, and some feature points on other tissues outside the heart can be found in the contrast map as the marker points.
  • the present invention aims to propose a multi-motion parameter decomposition estimation method for single-arm x-ray angiography images, which forms a data sequence by tracking structural feature points, and automatically extracts by using empirical mode decomposition (EMD) method.
  • EMD empirical mode decomposition
  • a method for estimating a multi-motion parameter decomposition of a single-arm x-ray angiography image sequence comprising the following steps:
  • the present invention has the following beneficial effects:
  • the present invention has higher safety and operability than the method of directly setting the marker point near the heart and then tracking by the relevant imaging means. This is because the markers added to tissues in the body are generally invasive, causing more or less damage to the human body itself, and the process of adding, imaging, eliminating, and extracting respiratory movements of the markers is complicated. Inevitable troubles and errors in actual operation;
  • the feature points selected by the method of the present invention involve the blood vessels of the left and right coronary vessels, and comprehensively take into account the motion information of the left and right coronary vessels, thereby having better reliability and accuracy.
  • Figure 1 is a flow chart of a preferred embodiment of the present invention
  • 2(a) and 2(b) are respectively a angiogram selected in the embodiment of the present invention and a vascular structure diagram corresponding to the angiogram, and the corresponding projection angle is (-26.5°, -20.9°);
  • 3(a), 3(b), 3(c), 3(d), 3(e), 3(f), 3(g), 3(h), and 3(i), 3(j) are plots of the left-sequence original signal, the high-frequency signal, the cardiac signal, the respiratory signal, and the translational signal on the X-axis and the Y-axis, respectively;
  • 4(a) and 4(b) are respectively a contrast image selected in the embodiment of the present invention and the contrast image
  • the corresponding vascular structure diagram, the corresponding projection angle is (42.3 °, 26.8 °);
  • Figure 5 (a), 5 (b), Figure 5 (c), 5 (d), Figure 5 (e), 5 (f), Figure 5 (g), 5 (h), Figure 5 (i), 5(j) is a plot of the original sequence of the right sequence, the high frequency signal, the heart signal, the respiratory signal, and the translation signal on the X-axis and the Y-axis, respectively.
  • the method of the present invention utilizes the EMD method to automatically extract heart, breath, translation, and other motions. As shown in Figure 1, the following steps are included:
  • the marked feature points need to be able to comprehensively reflect the motion information of the whole blood vessel. Therefore, the selected special points include the starting point and ending point of each blood vessel segment, and each part between the blood vessel segments. Inflection point. Moreover, in the sequence of contrast images at two different projection angles, all the feature points are numbered, and the corresponding feature points have the same number. As shown in Fig. 2 and Fig. 4, in the pair of contrast images with projection angles of (-26.5°, -20.9°) and (42.3°, 26.8°), there are five numbered points (Fig. The white dots in the middle), their relationship is one-to-one correspondence by numbers.
  • EMD Empirical mode decomposition
  • Both the heart and the human respiratory movement are periodic movements, but the frequency of respiratory movements is much smaller than that of the heart movement.
  • the frequency of normal heart movement is 60-100 beats/min, and the period is 0.6. -1.0s, while the cycle of breathing is much longer, usually 3-6s, and may be longer when quiet.
  • the heart movement is more intense, and the magnitude of the breathing movement is smaller, that is, the generated displacement is smaller, which is a relatively stable process.
  • the period is less than 0.6 s and the amplitude variation range is small.
  • the biggest feature of translational motion is that it is aperiodic motion, as opposed to Periodic movements are easy to discern.
  • EMD empirical mode decomposition
  • the first iterative step of the screening process is to repeat steps (1)-(5) for the detail signal d(t) until the mean of d(t) is 0. , or satisfy some sort of stopping criterion to stop iteration.
  • the detail signal d(t) at this time is called the Intrinsic Mode Function (IMF), and the d(t) corresponding residual signal is calculated in the fifth step.
  • IMF Intrinsic Mode Function
  • s(n) c(n)+r(n)+h(n)+L(n)
  • r(n) (x r (n), y r (n)) indicates motion caused by respiratory motion
  • h(n) (x h (n), y h (n)) indicates The motion produced by tremor or the beating of the blood vessel itself is generally regarded as a high frequency component
  • L(n) (x L (n), y L (n)) represents the translational motion (including the movement of the body during the angiography) , as well as the movement of contrast equipment, etc.).
  • s(n) is used to indicate the coordinate curve of the extracted blood vessel point along the x-axis and the y-axis
  • c(n) represents the coordinate curve of the blood vessel point along the x-axis and the y-axis caused by the cardiac motion
  • r(n) represents the coordinate curve of the blood vessel point along the x-axis and the y-axis caused by the respiratory motion
  • h(n) represents the coordinate curve of the blood vessel point along the x-axis and the y-axis caused by the high-frequency motion
  • L(n) represents The coordinate curve of the translational motion along the x-axis and the y-axis.
  • the operation on s(n) is the operation on x(n) and y(n) respectively
  • the operation on c(n) is the operation on x c (n) and y c (n) respectively, on r
  • the operation of (n) is the operation of x r (n) and y r (n) respectively.
  • the operation of h(n) is the operation of x h (n) and y h (n) respectively, for L(n)
  • the operation is to operate on x L (n) and y L (n) respectively.
  • Step1 Automatically track the vascular structural feature points selected in (1) throughout the angiographic sequence
  • Step3 Will Decomposed into motion x(n) in the x direction and motion y(n) in the y direction, and then EMD decomposition is performed on x(n) and y(n), respectively, to obtain independent motion signals after EMD decomposition;
  • Step4 According to the prior physiological knowledge, the independent signals are classified accordingly.

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Abstract

一种单臂X射线血管造影图像序列多运动参数分解估计方法，包括以下步骤：（1）自动选取稳定的血管结构特征点；（2）对选取的血管结构特征点在整个造影图序列中进行自动跟踪；（3）在点的跟踪序列中选取长度为n s=k*N 1（k>1）的序列ŝ（n）（N 1为心脏运动的周期）；（4）将ŝ（n）分解为在x方向的运动x（n）和在y方向上的运动y（n），再分别对x（n）和y（n）进行EMD分解，得到EMD分解后的各独立运动信号；（5）根据先验生理知识对各独立信号进行相应的归类。所述方法具有广泛的适用性和灵活性，更高的安全性和可操作性，以及更好的可靠性和准确性。

Description

单臂x射线血管造影图像多运动参数分解估计方法 [技术领域]
本发明属于数字信号处理与医学成像交叉技术领域，具体涉及一种单臂x射线血管造影图像多运动参数分解估计方法。
[背景技术]
胸廓有节律的扩大和缩小，从而完成吸气与呼气，这就是呼吸运动。心脏本身有规律的博动(心脏运动)、毛细血管的运动(高频运动)、呼吸运动以及人的移动或者是病床的摇动(平移运动)等都会造成人体心脏在三维空间中整体的平移运动。在X射线造影***中，由于上述运动的综合影响，冠状动脉血管在造影面上会发生二维平移运动。因此，冠脉造影图像一方面记录有心脏的运动在二维平面上的投影，同时也叠加有人体的呼吸运动、高频运动和平移运动造成的冠状动脉在造影面上的二维平移运动。
要得到更接近真实情况下的二维血管造影图并用于血管三维重建，则需将这些运动进行自动分离。现有技术一般是将多运动分别独立进行提取，提取呼吸运动的一种做法是在提取人体上述运动时通过预先设置标记点，对它们进行序列跟踪。根据呼吸运动的特点，人在进行呼吸的时候会带动体内的其他器官一起运动。一般认为，这些器官会随着肺的运动进行三维空间的平移，且它们的运动都是同步的。所以，假设呼吸运动引起的心脏的运动和与它相邻的器官的运动在造影图平面上也是一致的，可以在造影图中找到心脏外的其他组织上的一些特征点作为标记点。在整个序列中跟踪这些标记点，得到这些标记点的运动情况，然后将这些标记点的运动近似为此二维投影面上的呼吸运动。另一种做法同样利用这些不会跟随心脏一起运动的结构特征点，所不同的是，后者是在造影的同时记录这些标记点的运动。因此，要求在造影前就对各个特征点进行选取和标记。很显然， 这两种方案都是有缺陷的。前者的适用性很差，因为并不能保证每一帧造影图中都存在符合这种条件的标记点(心脏外的其他组织上的一些特征点)，而且找这种点也需要经验(需要对人体解剖结构比较了解)。当造影图中不存在以上特征点时，呼吸运动是很难被提取出来的。后者的实现则需要大量实验控制，对一般的临床应用不合适。此外，在上述两种方法中，人体在进行生理活动时是否存在其他的运动并不能有效地表现出来，而且要进行其他运动的分析提取给病人会带来二次伤害。
此外，还有一种方法是在双臂x射线造影条件下实现的，其分离心脏运动与呼吸运动的思想是：取同一时刻不同投影角度的两幅造影图，对其中相对应的冠脉血管进行三维重建，获得该时刻的血管三维空间分布。那么，对一个呼吸周期中的所有造影图对进行匹配和重建后，得到一组三维结构序列，它们间的空间位移矢量便是呼吸运动。相对来说，通过该方法能得到比较可靠的呼吸运动估计结果，但是由于双臂x射线造影条件的约束，不能广泛的应用在实践中，并且，此方法也不能提取出除了心脏信号和呼吸信号之外的运动信号。
[发明内容]
针对现有技术的不足，本发明的目的在于提出一种单臂x射线血管造影图像多运动参数分解估计方法，通过跟踪结构特征点形成数据序列，并利用经验模式分解(EMD)的方法自动提取人体的心脏、呼吸、高频以及平移运动。
为实现以上发明目的，本发明采用以下技术方案：
一种单臂x射线血管造影图像序列多运动参数分解估计方法，包括以下步骤：
(1)选取血管结构特征点；
(2)对选取的血管结构特征点在整个造影图序列中进行自动跟踪；
(3)在点的跟踪序列s(n)中选取长度为ns＝k*N1(k>1)的序列
Figure PCTCN2014085727-appb-000001
(4)将
Figure PCTCN2014085727-appb-000002
分解为在x方向的运动x(n)和y方向上的运动y(n)，再分别对x(n)和y(n)进行EMD分解，得到EMD分解后的各独立运动信号；
(5)根据先验生理知识对各独立信号进行相应的归类。
与现有技术相比，本发明具有以下有益效果：
(1)相较于单纯的手动跟踪，自动选取血管结构特征点和EMD相结合的途径来自动提取各周期运动和非周期运动具有更广泛的适用性和灵活性，几乎可适用于所有造影序列图；
(2)同时，相较于直接在心脏附近组织设置标识点再通过相关成像手段进行跟踪的方法，本发明拥有更高安全性和可操作性。这是因为在体内组织添加的标记物一般是可侵入性的，会对人体自身产生或多或少的损害，并且其标记物的添加、成像、排除、呼吸运动提取整个过程都是繁杂的，为实际操作中带来不可避免的麻烦与误差；
(3)本发明方法选取的特征点涉及到左右冠脉的各级血管，综合考虑到了左右冠脉的运动信息，从而具有更好的可靠性和准确性。
[附图说明]
参照下面的说明，结合附图，可以对本发明有最佳的理解。在附图中，相同的部分可由相同的标号表示。
图1是本发明较佳实施例的流程图；
图2(a)和图2(b)分别是本发明实施例中选取的造影图和该造影图所对应的血管结构图，对应的投影角度为(-26.5°，-20.9°)；
图3(a)，3(b)、图3(c)，3(d)、图3(e)，3(f)、图3(g)，3(h)、图3(i)，3(j)分别为一左序列原始信号、高频信号、心脏信号、呼吸信号和平移信号在X轴和Y轴的曲线图；
图4(a)和图4(b)分别是本发明实施例中选取的造影图和该造影图所对 应的血管结构图，对应的投影角度为(42.3°，26.8°)；
图5(a)，5(b)、图5(c)，5(d)、图5(e)，5(f)、图5(g)，5(h)、图5(i)，5(j)分别为一右序列原始信号、高频信号、心脏信号、呼吸信号和平移信号在X轴和Y轴的曲线图。
[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，以下结合附图及示例性实施例，对本发明进行进一步详细说明。应当理解，此处所描述的示例性实施例仅用以解释本发明，并不用于限定本发明的适用范围。
本发明方法是利用EMD方法来自动提取心脏、呼吸、平移以及其他运动的。如图1所示，包括以下步骤：
(1)选取血管结构特征点
根据生理学和解剖学等知识的指导，标记的特征点需要能够综合反映出血管整体的运动信息，因此，所选的形殊点包括各血管段的起始点和终止点，以及血管段间的各个拐点。并且，在两不同投影角度下的造影图像序列中，对所有特征点编号，相互对应的特征点拥有相同的编号。如图2和图4所示，在投影角分别为(-26.5°，-20.9°)和(42.3°，26.8°)的一对造影图中，存在着5个编号后的形殊点(图中的白色点)，它们的关系是按照数字命名一一对应的。
(2)分离多运动的经验模式分解(EMD)方法
心脏与人体呼吸运动都是周期性的运动，但是呼吸运动的频率相比心脏运动来说却要小得多，一般来说，心脏正常运动的频率为60～100次/分钟，其周期为0.6-1.0s，而呼吸运动的周期则长得多，一般为3-6s，安静的时候可能更长。另一方面，心脏运动比较剧烈，而呼吸运动的幅度较小，即产生的位移较小，是一个相对平稳的过程。对于毛细血管的自身的震动，相比于心脏运动和呼吸运动，其更加剧烈，周期更短，一般认为其周期小于0.6s，幅度变化范围小。而平移运动最大的特征是其为非周期运动，相对于 周期运动易于辨别。
根据造影图中上述各运动信号的这些特点，可以通过经验模式分解(EMD)的方法对心脏、呼吸、平移以及高频运动进行自动分离。下面介绍一下EMD方法。
1)EMD方法
EMD的出发点是把信号内的震荡看作是局部的。实际上，如果要看评估信号x(t)的2个相邻极值点之间的变化(2个极小值，分别在t-和t+处)，需要定义一个(局部)高频成分{d(t),t-≤t≤t+}(局部细节)，这个高频成分与震荡相对应，震荡在2个极小值之间并且通过了极大值(肯定出现在2极小值之间)。为了完整这个图形，还需要定义一个(局部)低频成分m(t)(局部趋势)，这样x(t)＝m(t)+d(t),(t-≤t≤t+)。对于整个信号的所有震动成分，如果能够找到合适的方法进行此类分解，这个过程可以应用于所有的局部趋势的残余成分，因此一个信号的构成成分能够通过迭代的方式被抽离出来。
对于一个待分解的信号x(t)，进行有效的EMD分解步骤如下：
(1)找出x(t)的所有极值点；
(2)用插值法对极小值点形成下包络emin(t)，对极大值形成上包络emax(t)；
(3)计算均值m(t)＝(emin(t)+emax(t))/2；
(4)抽离细节信号d(t)＝x(t)-m(t)；
(5)对残余的m(t)，令x(t)＝m(t)，重复步骤(1)-(5)，直到d(t)的均值为0，或者满足停止准则为止。
在实际中，上述过程需要通过一个筛选过程进行重定义，筛选过程的第一个迭代步骤是对细节信号d(t)重复(1)-(5)步，直到d(t)的均值是0，或者满足某种停止准则才停止迭代。
一旦满足停止准则，此时的细节信号d(t)就被称为本征模函数(Intrinsic Mode Function，简称IMF)，d(t)对应残量信号用第5步计算。通过以上过程，极值点的数量伴随着残量信号的产生而越来越少，整个分解过程会产生有限个IMF，这有限个IMF就是所需要的独立的信号。
2)分离算法
假设造影图序列中冠脉血管上某点p(x,y)的x轴坐标的运动曲线为x(n)(n为造影帧的帧数)，y轴坐标的运动曲线为y(n)，令s(n)＝(x(n),y(n))，可将s(n)分解成下面的式子：
s(n)＝c(n)+r(n)+h(n)+L(n)其中c(n)＝(xc(n),yc(n))表示心脏的运动引起的血管点的运动；r(n)＝(xr(n),yr(n))表示呼吸运动引起的运动；h(n)＝(xh(n),yh(n))表示因人体震颤或者血管自身的跳动产生的运动，一般将其视为高频成分；L(n)＝(xL(n),yL(n))表示平移运动(包括人在造影过程中身体的移动，以及造影器材的移动等)。为方便表示，后面都用s(n)来表示提取的血管点沿x轴、y轴的坐标变化曲线，c(n)表示心脏运动引起的血管点沿x轴、y轴的坐标变化曲线，r(n)表示呼吸运动引起的血管点沿x轴、y轴的坐标变化曲线，h(n)表示高频运动引起的血管点沿x轴、y轴的坐标变化曲线，L(n)表示平移运动沿x轴、y轴的坐标变化曲线。因此，对s(n)的操作就是分别对x(n)和y(n)的操作，对c(n)的操作就是分别对xc(n)和yc(n)的操作，对r(n)的操作就是分别对xr(n)和yr(n)的操作，对h(n)的操作就是分别对xh(n)和yh(n)的操作，对L(n)的操作就是分别对xL(n)和yL(n)的操作。
具体算法如下：
Step1：对(1)中选取的血管结构特征点在整个造影图序列中进行自动跟踪；
Step2：在点的跟踪序列s(n)中选取长度为ns＝k*N1(k>1)的序列
Figure PCTCN2014085727-appb-000003
若 原始序列s(n)的长度为n，则选取序列长度为ns＝n-n％N1，也即，使ns是N1的整数倍，其中N1为心脏运动的周期，％为取余符号。
Step3：将
Figure PCTCN2014085727-appb-000004
分解为在x方向的运动x(n)和y方向上的运动y(n)，再分别对x(n)和y(n)进行EMD分解，得到EMD分解后的各独立运动信号；
Step4：根据先验生理知识对各独立信号进行相应的归类。
通过先验生理知识结合EMD方法分解出的各运动信号进行分析，可以确定容易确认各运动信息的成分，具体见图3(a)-3(j)和图5(a)-5(j)，其中，心脏信号曲线图、呼吸信号曲线图和高频信号曲线图分别为跟踪前面5个特征点所得到的曲线图，平移信号的虚线表示手动跟踪的骨骼肌的运动，而实线表示的是由EMD方法提取出的曲线图。
从图3(a)-3(j)和图5(a)-5(j)中分离出的各运动信号可以看出，各特征点的心脏信号和呼吸信号具有明显的规律性；高频信号由于多种因素的影响(例如血管自身震颤和人的震颤等)而参差不齐，但是其都在生理知识的范围之外，所以将其都归为高频信号；而由EMD方法自动提取出的平移信号与手动跟踪骨骼肌所提取出的平移信号基本吻合，因而具有很强的实用性。
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 (4)

  1. 一种单臂x射线血管造影图像序列多运动参数分解估计方法，包括以下步骤：
    (1)选取稳定的血管结构特征点；
    (2)对选取的血管结构特征点在整个造影图序列中进行自动跟踪；
    (3)在点的跟踪序列s(n)中选取长度为ns＝k*N1(k>1)的序列
    Figure PCTCN2014085727-appb-100001
    (4)将
    Figure PCTCN2014085727-appb-100002
    分解为在x方向的运动x(n)和y方向上的运动y(n)，再分别对x(n)和y(n)进行经验模式分解(EMD)分解，得到EMD分解后的各独立运动信号；
    (5)对各独立信号进行相应的归类。
  2. 根据权利要求1所述的方法，步骤(1)中，所述结构特征点包括各血管段的起始点和终止点，以及血管段间的各个拐点。
  3. 根据权利要求1所述的方法，步骤(3)中，若原始序列s(n)的长度为n，则选取序列长度为ns＝n-n％N1(N1为心脏运动的周期)，也即，使ns是N1的整数倍，其中％为取余符号。
  4. 根据权利要求1所述的方法，步骤(4)中，对于一个待分解信号x(n)，所述EMD分解具体为：
    (4-1)找出x(n)的所有极值点；
    (4-2)用插值法对极小值点形成下包络emin(n)，对极大值形成上包络emax(n)；
    (4-3)计算均值m(n)＝(emin(n)+emax(n))/2；
    (4-4)抽离细节信号d(n)＝x(n)-m(n)；
    (4-5)对残余的m(n)，令x(n)＝m(n)，重复步骤(4-1)至(4-5)，直到d(n)的均值为0，或者满足停止准则为止。
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