CN107589441B  Pulse pileup modification method based on Kalman filter channel  Google Patents
Pulse pileup modification method based on Kalman filter channel Download PDFInfo
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 CN107589441B CN107589441B CN201710798404.3A CN201710798404A CN107589441B CN 107589441 B CN107589441 B CN 107589441B CN 201710798404 A CN201710798404 A CN 201710798404A CN 107589441 B CN107589441 B CN 107589441B
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Abstract
Description
Technical field
The present invention relates to the fields such as nuclear radiation detection, nuclear electronics technology, Digital Signal Processing, are based especially on Kalman The pulse pileup modification method of filter channel.
Background technique
Pileup events are that X (γ) is counted and the critical issue of spectroscopic system, especially there are parameter Xray and positive electrons Under the high density source of emission computed tomography (PET).As one of two uncertain sources, accumulation is by particle micro Caused by the internal factor reached in second rank time interval, so that detector cannot be eliminated accurately from previous radiation event The successor of response, to generate a signal in single pulse overlapping part.Pulse pileup causes handling capacity reduction, extremely Area's time extends, and energy resolution reduces, and leads to radiation detection system reduced performance.
As digital processing unit (ADC) and DSP (FPGA) continue to develop, using the number of the nuclear radiation detection data of processor Word processing executes complicated algorithm to solve pileup pulse, generally comprises: data fitting method, accumulation exclusive method, filtering, transformation approach With it is miscellaneous.But custom design is needed using the electronic module that processor carries out accumulation processing, by use environment factor and electricity Gas characteristic limitation, moreover, electronic module processing pileup events processing cost is higher.
Data fitting method is the fitting based on digit pulse reshaper to detector signal, even if in the composition close phase of signal Also it can restore pileup events when adjacent with high precision, meanwhile, it needs largely to be calculated, wirelessly be approached using nonlinear equation The mode of waveform obtains, and amount of calculation is big.It accumulates exclusive method identification and abandons the data of damage, to reduce to the maximum extent The influence to the calculating stress on energy spectrum and processor is accumulated, still, the method is disadvantageous in that, extends dead detector zones The case where time causes energy spectrum distortion, is not suitable for high radioactivity.Currently, filter method is that most common processing is accumulated in real time Mode, such as the homogeneous Poisson process with known strength still need to eliminate Noise Algorithm before feeding filtering.Conversion Method is signal to be converted to the domain that other original bulk events do not show overlapping from time domain, but converting system needs are appropriate online It calculates and optimal separate design.These methods all realize highprecision to sacrifice calculating source.
Therefore, it is necessary to provide the accumulation modification method that a kind of calculating is easy, power spectrum distortion rate is low.
Summary of the invention
The purpose of the present invention is to provide a kind of pulse pileup modification methods based on Kalman filter channel, main to solve Certainly calculating existing in the prior art it is complicated, can spectrum distortion the problems such as.
To achieve the goals above, The technical solution adopted by the invention is as follows:
Pulse pileup modification method based on Kalman filter channel, comprising the following steps:
The first step generates core pulse signal S using pulse shaper_{n}, obtain core pulse signal S_{n}Afterwards, by core pulse signal S_{n}Parameter carries out Initialize installation, that is, chooses the core pulse signal S of output_{n}Amplitude X_{0}For 0 initial point.
Second step, to the core pulse signal S_{n}It is purged weak signal processing, obtains the core pulse signal S of accumulation_{1n}, tool Body is as follows:
(1) Kalman filter number of channels is set as n, and in Fixed Time Interval, the maximum quantity of pileup events is N, core pulse signal S_{n}Obtain at least one transmission channel, wherein n is the integer greater than 0.
(2) determine core pulse signal S_{n}Weak signal,For in t_{k}In moment, ith^{th}The amplitude of a core pulse signal. The definition of availability isWhen state.IfWhen,Then it is determined as weak signal, wherein eps is tolerance,And the weak signal is inhibited to pass through transmission channel.
Step 3: building core pulse signal S_{1n}The state equation of pileup events, and differentiate and extract the core arteries and veins of the accumulation Rush signal S_{1n}。
The amplitude features of (1) first core pulse signal and extraction, i.e., and if only if the amplitude z of the first core pulse signal_{k1}Greatly In 3 times of measurement noise δ_{ω}When, the amplitude of the core pulse signal of extractionAnd the 4th step is allowed access into, otherwise will It is eliminated.
(2) amplitude features of other core pulse signals and extraction, and if only if survey of the deviation greater than 3 times of prediction measured value Measure noise δ_{ω}When, i.e. current measurement value z_{k2}Subtract residual errorGreater than 3 δ_{ω}When, the amplitude of the core pulse signal of extractionAnd the 4th step is allowed access into, otherwise it will be eliminated.The core pulse signal S of extraction is obtained as a result,_{1n}。
Step 4: building Kalman filter, and by the core pulse signal S of extraction_{1n}Core arteries and veins is obtained through Kalman filter Rush signal S_{2n}。
(1) core pulse signal S is established_{1n}The state equation of pileup events, in time t_{k}It is interior, ith^{th}The table of the amplitude of a pulse Show formula are as follows:
Wherein,For in t_{0}Moment ith^{th}The amplitude of a pulse, τ are attenuation constant；
In time t_{k+1}It is interior, ith^{th}The amplitude expression of a pulse are as follows:
Wherein,For in t_{0}Moment ith^{th}The amplitude of a pulse, τ are attenuation constant；
Expression (12) is acquired divided by expression formula (11) in t_{k+1}In moment, ith^{th}The amplitude of a pulse, expression formula Are as follows:
Wherein,For in t_{0}Moment ith^{th}The amplitude of a pulse, Δ τ indicate t_{k+1}With t_{k}Time difference, τ is that decaying is normal Number；
Metrical information t is established using expression formula (13)_{k}The state matrix X at moment_{k}, and obtain the core arteries and veins that accumulation quantity is n Rush signal t_{k+1}The state matrix equation X at moment_{k+1}, expression formula are as follows:
X_{k+1}=FX_{k}+Q_{k} (14)
Wherein, F is statetransition matrix, Q_{k}For with measurement noise δ_{ω}The statenoise δ unrelated with statetransition matrix F_{y}'s Variance, X_{k}For t_{k}The state matrix at moment；
(2) core pulse signal S is established_{1n}The measurement equation of pileup events, at the signal terminal of detector, metrical information t_{k+1}The state matrix X at moment_{k+1}And be Z_{k+1}, expression formula are as follows:
Z_{k+1}=HX_{k+1}+R_{k+1} (15)
Wherein, H is observing matrix, X_{k+1}For t_{k+1}The state matrix at moment, R_{k+1}To measure noise δ_{ω}Variance；
(3) state matrix equation (14) is utilized, establishes predicted state equation, expression formula are as follows:
Wherein, F is statetransition matrix,For in t_{k+1}The state estimation at moment,For in t_{k}The state at moment is estimated Meter；
White noise K in pileup events is acquired by expression formula (16)_{F}, it is indicated with its covariance, establishes predictive estimation association Variance matrix, expression formula are as follows:
P_{k+1k}=FP_{kk}F^{T}+Q_{k} (17)
Wherein, F is statetransition matrix, Q_{k}For with measurement noise δ_{ω}The statenoise δ unrelated with statetransition matrix F_{y}'s Variance, P_{k+1k}For priori covariance, P_{kk}For Posterior estimator error covariance matrix, F^{T}For the transposition of statetransition matrix；
Using expression formula (17) predictive estimation covariance matrix, residual error, expression formula are calculated are as follows:
Wherein, H is observing matrix,For the deviation of current measurement value and prediction measured value, z_{k+1}For current measurement value,For true value x_{k+1k}And predicted valueDeviation；
Expression formula (15) (16) is brought into (18), calculating acquires residual covariance S_{k+1}, expression formula are as follows:
S_{k+1}=HP_{k+1k}H^{T}+R_{k+1} (19)
Wherein, H is observing matrix, P_{k+1k}For priori covariance, H^{T}For the transposition of observing matrix, R_{k+1}To measure noise δ_{ω} Variance；
Optimal kalman gain processing, Kalman's COEFFICIENT K are carried out to residual covariance expression formula (19)_{k+1}Expression formula are as follows:
Wherein, H^{T}For the transposition of observing matrix, P_{k+1k}For priori covariance, S_{k+1}For residual covariance；
State estimation, preevaluation value are updated to expression formula (16)Its expression formula are as follows:
Wherein,For status assessmentOptimal estimation, K_{k+1}For kalman gain,For current measurement value and in advance Survey the deviation of measured value；
Estimate covariance is updated to expression formula (17), and obtains required Kalman filter, expression formula are as follows:
Wherein, P_{k+1k+1}For Posterior estimator error covariance matrix；P_{k+1k}For priori covariance, K_{k+1}For kalman gain, S_{k+1}For residual covariance,For the transposition of kalman gain；
Step 5: to the core pulse signal S_{2n}Attenuation processing is carried out, and determines whether to meet removing standard, if so, Into second step, otherwise enters the 4th step and continue to filter.
Compared with prior art, the invention has the following advantages:
(1) core pulse signal is carried out initializing set by the present invention, in order to postprocessing, determines the mode of initial value It is relatively simple.Also, introduce weak signal gives up differentiation, and data run amount is reduced by way of filtering out weak signal, is removed from The calculating time of weak signal improves operation efficiency to reduce amount of calculation.Moreover, by Kalman filter The setting in channel guarantees at least one transmission channel of core pulse signal, in this way, which the inhibition energy of weak signal can be improved Power.
(2) in addition, the present invention is when carrying out core pulse signal differentiation and extracting, ingenious setting measurement noise and signal amplitude Differentiate, be effectively prevented from interference of the noisemeasuring noise to core pulse signal, in turn, realizes good under different noise conditions Antinoise ability.
(3) moreover, the present invention measures equation and state matrix by establishing core pulse signal, carries out status assessment, And kalman gain is combined to handle, the recursion filter of Timevarying Linear Systems when acquisition, and then realize the pulse generated to Xray detector The power spectrum distortion rate of separating piled event, pileup events separation is low, is effectively guaranteed filter effect.
(4) present invention detects output signal at the signal terminal of detector, introduces state matrix equation, and optimize and obtain Kalman filter is obtained, filtering is realized by the correction of state, filter capacity is obviously improved.
Detailed description of the invention
Fig. 1 is that flow chart is corrected in the pulse pileup based on Kalman filter channel.
Fig. 2 is 15 timing charts containing pileup events.
Fig. 3 is core pulse signal through 1 pileup pulse discrete state figure of Kalman filter channel.
Fig. 4 is core pulse signal through 2 pileup pulse discrete state figure of Kalman filter channel.
Fig. 5 is core pulse signal through 3 pileup pulse discrete state figure of Kalman filter channel.
Fig. 6 is core pulse signal through 4 pileup pulse discrete state figure of Kalman filter channel.
Fig. 7 is variance δ_{ω}=0.005 pileup events discrete state figure.
Fig. 8 is variance δ_{ω}=0.001 pileup events discrete state figure.
Fig. 9 is variance δ_{ω}=0.05 pileup events discrete state figure.
Figure 10 is variance δ_{ω}=0.01 pileup events discrete state figure.
Figure 11 is the waveform diagram that Xray tube issues.
Figure 12 is that Xray tube issues waveform through 1 pileup pulse discrete state figure of Kalman filter channel.
Figure 13 is that Xray tube issues waveform through 2 pileup pulse discrete state figure of Kalman filter channel.
Figure 14 is that Xray tube issues waveform through 3 pileup pulse discrete state figure of Kalman filter channel.
Figure 15 is that Xray tube issues waveform through 4 pileup pulse discrete state figure of Kalman filter channel.
Specific embodiment
Present invention will be further explained below with reference to the attached drawings and examples, and embodiments of the present invention include but is not limited to The following example.
The present invention provides arithmetic speed height, antinoise abilities by force, the energy accumulation that spectrum distortion is low, pulse separation accuracy is high amendment Method has implementation as follows:
The accumulation time is that X (γ) is counted and critical issue, especially computed tomography present in spectroscopic system (PET) there are when parameter Xray and positron emission for high density source.As one of two uncertain sources, pulse is generated The reason of accumulation is that particle reaches in very short time interval, prevents detector from eliminating response from previous radiation event Successor, to generate a signal in single pulse lap.
As shown in Figure 1, pulse pileup modification method the following steps are included:
The first step generates core pulse signal S using pulse shaper_{n}, obtain core pulse signal S_{n}Afterwards, by core pulse signal S_{n}Parameter carries out Initialize installation, that is, chooses the core pulse signal S of output_{n}Amplitude X_{0}For 0 initial point.
Second step, to the core pulse signal S_{n}It is purged weak signal processing, obtains the core pulse signal S of accumulation_{1n}, tool Body is as follows:
(1) Kalman filter number of channels is set as n, and in Fixed Time Interval, the maximum quantity of pileup events is N, core pulse signal S_{n}Obtain at least one transmission channel, wherein n is the integer greater than 0.
(2) determine core pulse signal S_{n}Weak signal, and the weak signal is inhibited to pass through transmission channel.
Step 3: differentiating and extracting the core pulse signal S of accumulation_{1n}, specifically comprise the following steps:
The amplitude features of (1) first core pulse signal are greater than 3 times of survey and if only if the amplitude of the first core pulse signal When measuring noise, the first signal enters the 4th step, is otherwise eliminated.
(2) the amplitude features of other signals are greater than 3 times of measurement noise and if only if the difference of measured value and estimated value When, then enter the 4th step, is otherwise eliminated.
Step 4: building kalman filter state and measurement equation, and by the core pulse signal S of extraction_{1n}Through Kalman Filter obtains core pulse signal S_{2n}, specifically comprise the following steps:
(1) state matrix equation is established.
(2) state matrix equation is utilized, establishes predicted state, and obtain predictive estimation covariance matrix；
(3) predictive estimation covariance matrix is utilized, calculates residual covariance, and carry out optimal kalman gain processing, more New estimation covariance, Kalman filter needed for obtaining.
Step 5: to the core pulse signal S_{2n}Attenuation processing is carried out, and determines whether to meet removing standard, if so, Into second step, otherwise enters the 4th step and continue to filter.
Embodiment 1
As shown in Fig. 2, the present embodiment only produces 15 core pulse waveform S with pulse shaper_{1}As basic data into Row explanation, the implementation of other situations is identical, repeats no more below.Due to core pulse signal be it is random, it is initial in core pulse signal When change, the amplitude of initial point need to be only set as 0.
Inhibit core pulse waveform S_{1}Weak signal, core pulse waveform S_{1}Differentiated and extracted, Fig. 3 to Fig. 6 is to filter through Kalman Wave device obtains waveform S after being filtered_{2}Result.By comparison it is found that the feelings of 4 core pulses accumulation can be applicable in well Condition.
Since noise also has a great impact in the separation process of pileup pulse, by the way that not homoscedastic Gauss white noise is added The pileup events of sound, and use variance δ_{ω}Emulate the excellent effect to illustrate of the invention, true value and estimated value it is square Error amount is as shown in table 1:
Noise is studied to pileup pulse separating property by the way that double pileup events of not homoscedastic white Gaussian noise are added Influence.And proposed method is quantified to the robustness of noise level using mean square error (MSE).The discrete state of acquisition As shown in Figure 7 to 10, it can thus be seen that the present invention can be effectively prevented from noisemeasuring noise does to core pulse signal It disturbs, there is good antinoise ability under different noise conditions.
Embodiment 2
The Xray from spherical Xray tube is detected by Xray detector, the detected waveform of detection card is as schemed Shown in 11, the waveform is after pulse pileup amendment of the invention, and the discrete state of acquisition is as shown in Figure 12 to Figure 15, by right Than it is found that there is the present invention Xray pulse to accumulate separating capacity.
To sum up, the present invention dexterously uses Kalman filter, the method for proposing to solve pulse pileup event, can not only Pulse pileup separation is effectively performed, and is also equipped with good antinoise ability, reduces Xray energy spectrum distortion rate.Through applicant Validation trial, the present invention have many advantages, such as that arithmetic speed is high, antinoise ability is strong, energy spectrum distortion is low, pulse separation accuracy is high, It can be said that compared with prior art, there is substantive distinguishing features outstanding and significant progress, in nuclear radiation detection, nuclear electronics Technology, digital processing field have wide advance and promotional value.
Abovedescribed embodiment is merely a preferred embodiment of the present invention, and it is not intended to limit the protection scope of the present invention, as long as using Design principle of the invention, and the noncreative variation worked and made is carried out on this basis, it should belong to of the invention Within protection scope.
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CN103454671A (en) *  20130821  20131218  中国人民解放军第二炮兵工程大学  Nuclear radiation pulse accumulation judging and correcting method based on highspeed digital sampling 
CN103940447A (en) *  20140411  20140723  哈尔滨工程大学  Mooring state initial aligning method based on selfadaptive digital filter 
CN104848862A (en) *  20150605  20150819  武汉大学  Precise and synchronous positioning and timekeeping method and system of Mars orbiting detector 
CN106814090A (en) *  20170224  20170609  山东省科学院海洋仪器仪表研究所  A kind of soil K element content measuring method and device 

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CN102426373A (en) *  20110901  20120425  中国航空工业第六一八研究所  Open and closed loop mixing correction method of inertia/satellite combination navigation system 
CN103454671A (en) *  20130821  20131218  中国人民解放军第二炮兵工程大学  Nuclear radiation pulse accumulation judging and correcting method based on highspeed digital sampling 
CN103940447A (en) *  20140411  20140723  哈尔滨工程大学  Mooring state initial aligning method based on selfadaptive digital filter 
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