CN102890286A  Radioactivity energy spectrum smoothing method  Google Patents
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 CN102890286A CN102890286A CN2011101995189A CN201110199518A CN102890286A CN 102890286 A CN102890286 A CN 102890286A CN 2011101995189 A CN2011101995189 A CN 2011101995189A CN 201110199518 A CN201110199518 A CN 201110199518A CN 102890286 A CN102890286 A CN 102890286A
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Abstract
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一种放射性能谱平滑方法 A radioactive spectrum smoothing method
技术领域 FIELD
[0001] 本发明涉及一种放射性能谱平滑方法。 [0001] The present invention relates to a radioactive spectrum smoothing method.
背景技术 Background technique
[0002] 在进行放射性测量中，测得的谱线带有统计涨落性，特别是当含放射性核素种类多、放射性活度微弱时，测得的放射性能谱不仅复杂，而且较弱的谱峰又容易被强峰或本底及其统计涨落所掩盖。 [0002] When carrying out the radioactivity measurement, the measured spectra with statistical fluctuations, particularly when many kinds of radionuclidecontaining, weakly radioactivity, radioactivity measured spectrum is not only complicated, but also weak peak and easy to be overshadowed by strong peaks or background and statistical fluctuation. 为了可靠地进行定性和定量分析，就必须对原始谱进行有效平滑滤波。 In order to reliably perform qualitative and quantitative analysis, it must be effectively smoothing the raw spectrum. 国内外对放射性能谱的平滑滤波已经进行了多年的研究，传统的方法为：平均移动法、重心法、多项式最小二乘拟和法，这些方法采用逐次分段进行拟和以达到光滑的目的，虽能部份消除能谱数据的统计涨落，但容易引起较大的谱形畸变。 At home and abroad smoothing radioactive energy spectrum has been studied for many years, as the traditional methods: moving average method, the center of gravity, polynomial leastsquares fitting method, and the methods employed to achieve the intended purpose of a smooth segment sequentially performed , although able to eliminate most of the statistical fluctuation spectroscopy data, but likely to cause large spectral shape distortion. 小波分析是时间窗和频率窗都可以改变的时频局域化分析方法，在低频部分有较高的频率分辨率且在高频部分具有较高的时间分辨率，它在1980年首次被引入到地震学研究后并取得了很好的检测效果。 Wavelet analysis is a frequency when the localized time window analysis and frequency window can be changed with a high frequency resolution and has a high time resolution in the high frequency portion, which was first introduced in 1980 in the low frequency portion after seismological studies and achieved good detection results. 小波分析已经广泛应用于信号处理、图象处理等领域，并在20世纪90年代末引入到Y谱数据的平滑中，取得了较好的效果，但计算量较大，不适于实时和大量数据处理的场合。 Wavelet analysis has been widely used in signal processing, image processing, etc., and is introduced in the late 1990s to the smoothing of the spectral data Y, and achieved good results, but the large amount of calculation, and is not suitable for large volumes of data in realtime applications processed. 本文结合放射性能谱通常所具有的高斯统计涨落特性，并将一般的高斯滤波方法与小波理论、多分辨率理论相结合，提升到通过尺度的伸缩来适应滤波的精度与速度，同时又给出了简便的算法，结果表明该平滑方法是一种有效的方法。 Bound radioactivity spectra herein generally have statistical fluctuations Gaussian characteristic, and the general method of Gaussian filter and wavelet theory, multiresolution theory, raised to the scale by stretching to accommodate the filtering accuracy and speed, the same time gave a simple algorithm, results show that the smoothing method is an effective method.
发明内容 SUMMARY
[0003] 本发明的目的在于公开一种放射性能谱平滑方法。 [0003] The object of the present invention is to disclose a radiation spectrum smoothing method. 该方法克服了目前放射性能谱平滑方法的不足。 The method overcomes the shortcomings of the current radiation spectrum smoothing method.
[0004] 本发明是通过以下技术方案实现的，本发明的具体步骤如下：①选择合适的高斯母函数；②选择合适的尺度；③构造由高斯函数构成的函数空间将能谱在该函数空间内进行多次投影，在投影中调整高斯函数的权重以实现能谱平滑滤波。 [0004] The present invention is achieved by the following technical solutions of the present invention, the specific steps as follows: ① select the appropriate master Gaussian function; ② select the appropriate scale; ③ a function of spatial structure consisting of a Gaussian function in the function space spectrum the multiple projectors, adjustment of the Gaussian function in the projection spectra weights to achieve smoothing.
[0005] 步骤①中合适的高斯母函数是指根据能谱的统计涨落、平滑速度及平滑后的精度要求选择合适的标准方差σ。 [0005] Step ① Suitable generating function is a Gaussian energy spectrum means the statistical fluctuations, and the smoothing of the smoothed velocity accuracy to select the appropriate standard deviation σ.
[0006] 步骤②中合适的尺度是指根据能谱的统计涨落、平滑速度及平滑后的精度要求选择合适的尺度J'，J'取整数。 [0006] Suitable Step ② The scale refers to statistical fluctuation spectrum, smoothing the smoothed speed and accuracy requirements select the appropriate scale J ', J' rounded.
[0007] 步骤③中函数空间是指将步骤①所求取的高斯母函数按步骤②选择的尺度J进行伸缩并进行系列平移，再由这些平移后的高斯函数组成的线性函数空间。 [0007] Step ③ a function space is ascertained in step ① the step ② of the Gaussian generating function according to the selected scale and J series telescopic translation space defined by a linear function of the Gaussian function after translation of these components again.
[0008] 步骤④中投影是指将欲平滑处理的能谱用步骤③中的函数空间近似地线性表示，每次投影完成一次统计涨落的去除。 [0008] Step ④ spectrum to the projection means to be processed by the smoothing function space in the step ③ is approximately linear representation, every time the projector is removed to complete a statistical fluctuation.
[0009] 本发明的有益效果是：在平滑中，可灵活地选择标准方差σ和尺度空间Vj.,以适应平滑精度和处理速度的要求。 [0009] Advantageous effects of the present invention is that: in the smoothing may be flexibly selected, and the standard deviation σ Vj of scale space, in order to meet the requirements of accuracy and the processing speed smoothing. 选取的标准方差σ和尺度J较小时，每次用高斯尺度方法平滑后峰位保持不变，峰高降低较小，半高宽（FWHM)增大较小，峰形畸变小；对于在高本底谱中分辨重峰和识别弱峰的情况，尽量选取零尺度空间Ktl和较小的标准方差σ进行精细平滑。 When the selected standard deviation σ and J smaller scale, each scale unchanged After Gaussian smoothing method of peak position, peak height reduction is small, half width (FWHM) is small increases, the peak shape distortion is small; for high background spectrum in the case resolved doublet and identify weak peaks, try to select zero and smaller scale space Ktl standard deviation σ fine smooth. 选取的标准方差O和尺度J较大时，用本平滑方法可使统计涨落得到较大抑制，并使谱峰成形加快，这对于统计涨落较大且谱峰较强较明显的能谱是一种有效方法。 O and standard deviation of the selected J large scale, the present smoothing method using the statistical fluctuation can be greatly suppressed, and accelerated shaped peak, for which the statistical fluctuation is large and strong peaks obvious spectrum It is an effective method. 分析表明，该平滑方法具有灵活、性能良好、计算简便和快捷等特点。 Analysis shows that the flexible smoothing method, good performance, and so fast and simple calculation.
附图说明 BRIEF DESCRIPTION
[0010] 图I为本发明方法的流程图。 [0010] Figure I a flow chart of a method of the present invention.
具体实施方式 Detailed ways
[0011] 下面结合附图对本发明的实施例作详细说明：本实施例在以本发明技术方案为前提下进行实施，给出了详细的实施方式和过程，但本发明的保护范围不限于下述的实施例。 [0011] The following embodiments in conjunction with the accompanying drawings of embodiments of the present invention will be described in detail: In the present embodiments of the present invention is a technical premise, gives a detailed embodiments and processes, although the scope of the present invention is not limited to the Example embodiments described below.
[0012] 本实施例设原始能谱为/㈤(《 = 1…AT),其中#为总道址数，总计数为#t(rtal，平滑时所投影次数为K,采用本方法对其进行平滑的具体步骤如下。 [0012] The present embodiment is provided original spectrum / v ( "= 1 ... AT), where # is the total number of access channels, the total number of #t (rtal, smoothing the projected number of times K, the present method thereof smoothing the following specific steps.
[0013] 步骤①根据能谱的统计涨落、平滑速度及平滑后的精度要求选择合适的标准方差σ，构造高斯母函数。 [0013] Step ① The spectrum of statistical fluctuations, and the smoothing of the smoothed velocity accuracy to select the appropriate standard deviation [sigma], A Gaussian generating function. 对于在高本底能谱中分辨重峰和识别弱峰的情况，选取较小的标准方差σ (σ =0.2、. 6)进行精细平滑；对于统计涨落较大且谱峰较强较明显的能谱，选取较大的标准方差σ ( σ =0. 6"Ί)0当标准方差σ选定后,构造的高斯母函数为： For the case of resolving and identifying a weak peak doublet in high background energy spectrum, select a smaller standard deviation σ (σ = 0.2 ,. 6) fine smooth; for statistical fluctuation is large and strong peaks obvious energy spectrum, selecting the larger the standard deviation σ (σ = 0 6 "Ί.) 0 when the standard deviation [sigma] is selected, the configuration of the parent Gaussian function:
[0014] 步骤②根据能谱的统计涨落、平滑速度及平滑后的精度要求选择合适的尺度 [0014] Step ② The spectrum of statistical fluctuations, and the smoothing of the smoothed velocity accuracy to select the appropriate scale
取整数。 Rounded. 对于在高本底能谱中分辨重峰和识别弱峰的情况，尽量选取零尺度空间Ktl进行精细平滑；对于统计涨落较大且谱峰较强较明显的能谱，选取较大的尺度(户1，2，3…）。 For the case of resolving and identifying weak doublet peak in the high energy spectrum in the background, try to select a zero smoothing fine scale space Ktl; for statistical fluctuation is large and strong peaks obvious spectrum, selecting a larger scale (households 1,2,3 ...).
[0015] 步骤③构造由高斯函数构成的函数空间。 [0015] Step ③ function space structure composed of a Gaussian function. 根据步骤①和步骤②所选取的标准方差σ和尺度J对高斯母函数#¢)进行伸缩和系列平移，得到如下函数序列 σ step according to standard procedures ① and ② and the variance of the selected scale and J series telescopic translation generating function Gaussian # ¢), to give the following sequence of functions
由（2)式中高斯函数的线性组合构成的函数空间即为所求的函数空间。 The function space (2), wherein a linear combination of Gaussian function configuration is also desired function space. 在本步骤，为了验证函数空间的可靠性，须考虑内积 In this step, in order to verify the reliability of the function space, the inner product to be considered
当的为小于10_4数量级时,可视其为零;另外，由(I)式和(2)式可知〈Κή，洛Jt(Z)I ;故结合(3)式后可认为以下关系成立： When 10_4 is less than the number of stages, depending on their zero; Further, by the formula (I) and (2) shows that <Κή, Los Jt (Z) I; after so binding (3) may be considered the relationship is established:
〈ίζΆ)> Φβ (ij/ = 3(k — k) (4) <ΊζΆ)> Φβ (ij / = 3 (k  k) (4)
(4)式中5(H：f) = 0(1：其, S(kkf) 1φ = k1);可认为此时多典(0满足理想正交关 (4) In the formula 5 (H: f) = 0 (1: which, S (kkf)  1φ = k1); MultiCode can be considered at this time (0 orthogonal to meet off over
系，并将ΦβΜ、张成的空间匕二ψΜΦβΧί)} (λ*€ τ)称为j尺度高斯函数空间，_可视为 System, and ΦβΜ, the space spanned by two dagger ψΜΦβΧί)} (λ * € τ) j called scale Gaussian function space, can be considered _
j·尺度下的正交基，该函数空间对已知能谱的表示较为精确。 In group j · orthogonal dimensions, more precise spatial representation of the function of the known spectra. 当的为大于 When the is more than
ιο_4数量级时，Φ0)的正交关系变差，该函数空间对已知能谱的表示精度也变差。 When ιο_4 magnitude, Phi] 0) of the orthogonal relationship deteriorated, the function representing the spatial spectrum of the known accuracy is deteriorated. 在本步骤 In this step,
中可以重新调整标准方差ο的值，以调整&w的正交关系，通常将限定为小于10_2数量级。 Can readjust the value of the standard deviation ο to adjust a quadrature relationship & w, typically limited to less than 10_ magnitude.
[0016] 步骤④将能谱在构造的函数空间内进行多次投影，在投影中调整高斯函数的权重以实现能谱平滑滤波。 [0016] Step ④ The spectrum multiple projection configuration in function space, the Gaussian function to adjust the weights in the projection spectra to achieve smoothing. 用/^/(ί)表示函数/(ί)在以'¢)为正交基的高斯函数空间Vj上的投影，则有： With / ^ / (ί) denotes a function / (ί) projected on the spatial Gaussian function to Vj '¢) of the orthogonal basis, there are:
在放射性测量中，能谱信号/fc)可视为连续函数/(ί)的离散值。 Radioactivity measurement, the spectrum signal / fc) can be regarded as a continuous function / (ί) discrete values.
[0017] 当##)视为满足理想正交关系时，此时设/⑴e K7.，则/⑴在Ky上的二次投影PAPjfit))可按下式化简： [0017] When ##) considered as meeting over an orthogonal relationship, this time provided / ⑴e K7, the / ⑴ PAPjfit second projection on the Ky)) may be simplified by the following formula:
可见，将/(i)在高斯函数空间进行多次投影后，可认为投影并不发生变化。 Visible, a / (i) a plurality of times after the projection Gaussian function space, the projection does not change may be considered.
[0018] 随着σ值的增大，'⑷的正交关系变差，亦即，当σ取稍大值时，不再满足 [0018] With the increase of the value of σ 'orthogonal relationship ⑷ deteriorated, i.e., when σ takes the value slightly larger, no longer satisfied
理想正交关系，（7)式不严格成立。 Ideal orthogonal relationship, (7) is not strictly true. 但存在极为重要的近似关系乂PfiXU影Pfif)含有比更多的高频信号，换言之，信号/(ί)每经过一次投影就滤出一部分高频信号。 But there are very important the approximate relationship qe PfiXU Movies Pfif) containing more than high frequency signals, in other words, the signal / (ί) is projected through the highfrequency signal to filter out a portion of each.
[0019] 本步骤即步骤④的投影平滑方法概括为：将欲处理的信号/(ί)在高斯函数空间Ky上进行投影/y(i)，随后将/y(i)在F7.上进行投影4(/y(i))，再将4(/y(i))在K7.上进行投影如此反复投影，最终实现的平滑滤波。 [0019] In this step, i.e., the projection smoothing method step ④ are summarized as follows: the signal / (ί) to be treated is projected / y (i) in the Gaussian function of space Ky, followed by / y (i) in F7 on. projection 4 (/ y (i)), then 4 (/ y (i)) projected in K7. projector on and so forth, ultimately smoothing filter. 本步骤即步骤④的投影平滑方法具体按如下A、B、C三个环节实现： I.e., the smoothing method of the projection step follows the step ④ of the specific A, B, C to realize three aspects:
A、将原始能谱/fc)视为一连续函数/(ί)，设选取的高斯函数空间为Fy，通常选取彡O，求得/(ί)在Ky上的第一次投影： A, the original spectrum / fc) considered as a continuous function / (ί), provided space for the selected Gaussian function Fy, is typically chosen San O, determined / (ί) first projected on the Ky:
由（6)式可知^>=</ω為4)>,为简便起见： From (6) shows that ^> = </ ω 4)>, for simplicity:
参数』与（I)式中』相同，/(2D可取为ί=24处局部区域的平均值；在实际计算中##¢)取ί=24道址处局部区域数个或数十个离散值，使（9)式的计算量大大减小；初始化滤波次数即迭代次数i=l ; Parameter "with formula (I) in the" same, / (2D taken as the average of the local region at ί 24 =; ## ¢ In the actual calculation) ί = taking several or several local area access 24 at ten discrete value to make the calculation (9) formula is greatly reduced; initializations i.e. filtering iterations i = l;
B、将信号再次在Ky上投影，并得到平滑后的信号： B, and the signal again on Ky projection, and smoothed signal obtained:
与（9)式类似： And (9) similar to the formula:
C、若平滑滤波次数ί二K,则按下式计算并取整求得滤波后的能谱/(»)： C, if the smoothing filter ί two times K, the spectra obtained by the following formula and rounding / ( ») filtered:
否则，令i=i+l，以便从第i步递推到i+Ι步，返回到A步继续作投影处理。 Otherwise, let i = i + l, so from the recursion step i to step i + Ι, returns to step A for the projection process continues.
[0020] 通过以上步骤①〜④步即完成能谱/fc)的平滑处理。 [0020] ①~④ step is completed spectroscopy / fc) of the smoothing process by the above steps.
[0021] 本方法通过选取合适的σ值和尺度^将欲处理的信号/(ί)在高斯函数空间Vj上进行投影/^./(ί)，随后将/y⑴在匕上进行投影⑴），再将4(/y(i))在匕上进行投影如此反复投影，最终实现m的平滑滤波。 [0021] The method of the present signal by selecting the appropriate values and scales σ ^ to be treated / (ί) projecting on the Gaussian function /^./(ί space Vj), followed / y⑴ ⑴ projected on a dagger) , then 4 (/ y (i)) are projected on a projection dagger so forth, ultimately smoothing of m. σ或尺度j取值越 or more scale values σ j
Pj(P/it))与卩禪越相近，每次投影平滑滤波越精细，但整个平滑过程变慢，这适合于需要精细平滑的场合，如对弱峰的平滑处理；反之，σ或尺度取值越大，/^(/^/(ί))与P/(t)相差越大，每次投影平滑滤波精度变差，但整个平滑过程加快，这适合于需要快速平滑的场合，如对统计涨落较大的较强谱峰的平滑处理。 Pj more similar (P / it)) and Jie Chan, each projection finer filtering, but the whole process slow smooth, which is suitable for the case requires fine smooth, such as a weak peak smoothing process; the other hand, [sigma], or scale the larger the value, / ^ (/ ^ / (ί)) and P / (t) the greater the difference, each projection smoothing deterioration in accuracy, but the whole process is accelerated smooth, which is suitable for applications requiring fast smoother, such as statistical fluctuation smoothing large strong spectral peaks. 在平滑中，可灵活地选择标准方差σ和尺度空间Vj.,以适应平滑精度和处理速度的要求，对于存在弱峰的能谱，尽量选取零尺度空间V0和较小的标准方差O Ca=O. 2^0. 6)进行精细平滑，以保持较好的峰形参数并让弱峰较好地显露出来；对于统计涨落较大且谱峰较强较明显的能谱，可选取稍大的标准方差σ (σ=0. 6^1)甚至大尺度空间进行平滑，使统计涨落得到较大抑制，并使谱峰成形加快。 In smoothing, can be flexibly selected, and the standard deviation σ scale space Vj., To meet the requirements of accuracy and the processing speed smoothing, spectrum for the presence of weak peaks, try to select zero and smaller scale space V0 O Ca = standard deviation . O. 2 ^ 0 6) fine smooth, to maintain a better peak shape parameters and make better revealed a weak peak; for statistical fluctuation is large and strong peaks obvious spectrum can be selected slightly the large standard deviation σ (σ = 0. 6 ^ 1) is smoothed even large spaces, so the statistical fluctuation is greatly suppressed, and accelerated shaped peaks. 分析表明，该平滑方法具有灵活、性能良好、计算简便快捷等特点。 Analysis shows that the flexible smoothing method, good performance, and so simple and quick calculation.
[0022] 在上述本发明的实施例中，对能谱的平滑进行了详细说明，但需说明的是，以上所述仅为本发明的一个实施例而已，本发明同样可对各种射线的全谱或局部谱段进行平滑，凡在本发明的精神和原则之内，所作的任何修改、等同替换、改进等，均应包含在本发明的保护范围之内。 [0022] In an embodiment of the present invention, the smoothing of the spectrum will be described in detail, it should be noted that the abovedescribed embodiment is merely one embodiment of the present invention, but the invention is equally to various radiation full spectrum or partial spectral smoothing, any modifications within the spirit and principle of the present invention, the, equivalent substitutions, improvements should be included within the scope of the present invention.
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