CN106529126B - A kind of on-line monitor guards the processing method that image information is inherited after interrupting - Google Patents
A kind of on-line monitor guards the processing method that image information is inherited after interrupting Download PDFInfo
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- 238000003672 processing method Methods 0.000 title claims abstract description 11
- 238000012544 monitoring process Methods 0.000 claims abstract description 47
- 238000005259 measurement Methods 0.000 claims abstract description 46
- 238000003384 imaging method Methods 0.000 claims abstract description 39
- 239000011159 matrix material Substances 0.000 claims abstract description 38
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- 210000003128 head Anatomy 0.000 description 6
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- G—PHYSICS
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Abstract
The processing method that image information is inherited is guarded after being interrupted the invention discloses a kind of cranium brain dynamic electric impedance imaging on-line monitor, for the monitoring image information for recovering to lose after cranium brain dynamic electric impedance imaging clinic on-line monitor interrupts.Measurement data before and after this method interrupts on-line monitor is analyzed, measurement data is handled first by the method for batten difference fitting, suppress image artifacts caused by the inconsistent caused measurement data baseline change of electrode contact condition before and after on-line monitor interrupts, then augmentation processing is carried out to image reconstruction matrix, the prior information of electrode displacement is introduced into reconstruction matrix, electrode is because of the inconsistent influence to guarding image of riding position before and after reducing monitoring interruption.After tested, this method can effectively suppress image artifacts caused by electrode contact condition and riding position change before and after monitoring is interrupted, and recover normal monitoring target, improve the Clinical practicability of electrical impedance imaging monitoring.
Description
Technical field
The invention belongs to dynamic electric impedance technical field of imaging, and in particular to a kind of cranium brain dynamic electric impedance imaging is continuously supervised
Shield guards the processing method that image information is inherited after interrupting.
Background technology
Cranium brain dynamic electric impedance tomography technology is by being evenly distributed on surrounding's electrode on head, real-time continuously to cranium
Brain applies safe current excitation and Measured Boundary voltage, using two data at different moments, with the data at wherein more early moment
For reference frame, the data at another moment are prospect frame, after two frame data difference, with reference to certain imaging method, are rebuild
Go out inside the cranium in the two impedance variations at different moments.Therefore, the gathered data of continuous-stable is that system is normally moved
The most important condition of state impedance imaging.
During clinical practice use, the situation for having to temporarily interrupt monitoring often occurs.For example patient needs
The imageological examination such as CT is carried out, it is necessary to remove the electrode that ring is attached to head, inspection finish it is follow-up it is continuous guarded if need
Re-posted electrode.After re-posted electrode, compared with initially starting the state of monitoring, the position of electrode and contact condition are likely to send out
Raw to change, this change can directly affect gathered data.Restart monitoring when, if still using initially start monitoring when
Reference frame, then since the change of electrode-scalp contact condition and electrode position may produce artifact in reconstruction image, fall into oblivion
Normal impedance variations information.Data when if selection restarts monitoring are as frame is referred to, although electrode-head can be eliminated
Influence caused by skin contact condition and electrode position change, but the image information restarted before monitoring can not be reflected directly in newly
Monitoring image on, impedance variations information before causing is lost.The interruption of on-line monitor seriously affect observation to the state of an illness and
Diagnosis, is unfavorable for clinical expansion and the application of dynamic cranium brain electrical impedance imaging.
Therefore, in order to eliminate the influence of electrode position and contact condition change to image, and the image monitoring of early period is retained
Information, there is an urgent need for a kind of method that can be handled the data after on-line monitor interruption.
The content of the invention
Image information is guarded after being interrupted it is an object of the invention to provide a kind of cranium brain dynamic electric impedance imaging on-line monitor
The processing method of succession, this method can effectively suppress electrode position and electrode-reconstruction figure caused by the change of scalp contact condition
As artifact, and retain effective image monitoring information, improve the clinical applicability of dynamic electric impedance imaging.
The present invention is to be achieved through the following technical solutions：
A kind of cranium brain dynamic electric impedance imaging on-line monitor guards the processing method that image information is inherited, the processing after interrupting
Measurement data before and after method interrupts on-line monitor is analyzed：First, the method being fitted using batten difference handles measurement
Data, it is pseudo- to suppress image caused by the inconsistent caused measurement data baseline change of electrode contact condition before and after on-line monitor interrupts
Shadow；Then, augmentation processing is carried out to image reconstruction algorithm, the prior information of electrode displacement is introduced into reconstruction matrix, reduces monitoring
Electrode is because of the inconsistent influence to guarding image of riding position before and after interruption.
Above-mentioned processing method specifically includes following steps：
1) the Baseline wander value of measurement data is obtained
Last n frame data and the preceding n frame data for restarting monitoring before selected on-line monitor interruption, data connection is existed
Together, it is data x (l), to i-th of valid data channel data xi(l) Spline-Fitting is used, obtains fitting sequence
Wherein, i ∈ N, N are Measurement channel sum；
It is then detected thatThe maximum of uplifted side at baseline transitionWith the minimum for declining side
Calculate Baseline wander value
2) Baseline wander is measured to the data for restarting monitoring
To restarting the ith measurement channel data sequence y after guardingi(l), useTo yi(l) baseline is carried out
Correction, compared with the data before monitoring is interrupted, if yi(l) the elevated side of baseline is in, then after correctingIf yi(l) side in baseline decline, then after correcting
3) augmentation processing is carried out to Gauss-Newton image reconstruction formula
To Δ ρ=- [JtJ+λR]-1Jz, Δ ρ be at different moments between electrical impedance change profile vector, z is at different moments
Boundary voltage difference vector；
By Jacobin matrixExpand toBy constraint matrixExtension
ForAnd determine coefficient lambda and constraint matrix R using prior informationaugUnit item；
4) impedance variations of target field domain are rebuild using the data after correction and the reconstruction formula of augmentation
I.e.WhereinFor the measurement voltage data at t1 moment,For the t2 moment
Measurement voltage data.
In step 1), to i-th of valid data channel data xi(l) Spline-Fitting is used, is specifically carried out as the following formula：
Wherein, S (x) is data sequence xi(l) spline-fit function, asks the value that S (x) makes L to get minimum；Wherein, p ∈
[0,1] degree of closeness of fitting function and measured data is reflected；S (x) is segmentation batten fitting function, is write as general type：
Sj(l)=aj(l-lj)3+bj(l-lj)2+cj(l-lj)+dj；
Add each piecewise fitting function coefficients that boundary condition solves S (l) using least square method.Obtained S (l) tools
After body expression formula, fitting reconfiguration sequence is soughtDetectionThe maximum of uplifted side at baseline transitionAnd decline
The minimum of sideCalculate Baseline wander value
Step 3) concrete operations are：
Gauss -- Newtonian image reconstruction formula such as following formula：
Δ ρ=- [JtJ+λR]-1Jz；
Wherein, J is Jacobin matrix, and λ R are regularization constraint item, Δ ρ be at different moments between electrical impedance change profile to
Amount, z are boundary voltage difference vector at different moments；
Change influence on RT to suppress electrode position, augmentation processing is carried out to the matrix in reconstruction formula：It is right
In Jacobin matrixExpand tonmeasThe measurement voltage number included for a frame data,
nelemTo be imaged the finite element model unit number that reconstruct used uses, ndimTo be imaged dimension, two-dimensional imaging, institute are usually carried out
To take ndim=2, neFor number of electrodes, the expansion of Jacobin matrix is filled with due to the disturbance of measuring electrode change in location,
I.e.：
Wherein, A is current excitation vector, and H is positive calculating matrix,It is electrode position on x or y directions
The positive calculating matrix recalculated after change, the displacement are usually uniformly arranged to a priori constant；
Then, augmentation processing is carried out to constraint matrix R：
WillExpand toThe noise that expansion is filled with reconstruct data is first
Test estimation and reconstruct the prior estimate of conductivity variations, i.e.,：
Wherein, RextraFor a Laplace filter, according to the prior information of imaging field domain determine regularization parameter λ and
RextraLaplce's template, then have：
Wherein, avenoiseAverage priori amplitude for noise relative to measurement data, aveconductFor conductivity variations phase
For the average priori amplitude of initial conductivity distribution, avemoveTo be averaged priori width relative to the electrode displacement of field domain radius
Value,For Laplace operator.
Compared with prior art, the present invention has technique effect beneficial below：
Cranium brain dynamic electric impedance imaging on-line monitor disclosed by the invention guards the processing side that image information is inherited after interrupting
Method, for the monitoring image information for recovering to lose after cranium brain dynamic electric impedance imaging clinic on-line monitor interrupts.This method is to even
Measurement data before and after continuous monitoring is interrupted is analyzed, and is handled measurement data first by the method for batten difference fitting, is suppressed
Image artifacts caused by measurement data baseline change caused by electrode contact condition is inconsistent before and after on-line monitor interrupts, it is then right
Image reconstruction matrix carries out augmentation processing, and the prior information of electrode displacement is introduced reconstruction matrix, reduces electricity before and after monitoring is interrupted
Pole is because of the inconsistent influence to guarding image of riding position.After tested, electrode connects before and after this method can effectively suppress monitoring interruption
Image artifacts caused by the state of touching and riding position change, recover normal monitoring target, improve electrical impedance imaging monitoring
Clinical practicability.
Brief description of the drawings
Fig. 1 is the method flow schematic diagram of the present invention；
Fig. 2 is the reconstructed image that on-line monitor interrupts previous moment.
Fig. 3 is that the method for the present invention processing is not used, and on-line monitor is interrupted data for the previous period and restarts to supervise
One-dimensional data curve (a) after one piece of data connects after shield, and reselect reference frame (c) and do not reselect ginseng
Examine the Two-Dimensional Reconstruction image in the case of frame (b)；
Fig. 4 is the one-dimensional data curve (a) used after this method rectification step, and innovatory algorithm (b) is not used and uses
This method improves the Two-Dimensional Reconstruction image (c) of imaging algorithm.
Embodiment
With reference to specific embodiment, the present invention is described in further detail, it is described be explanation of the invention and
It is not to limit.
A kind of cranium brain dynamic electric impedance imaging on-line monitor of the present invention guards the processing side that image information is inherited after interrupting
Method, comprises the following steps：
(1) the Baseline wander value of measurement data is obtained.Select the last n frame data before on-line monitor interrupts and restart
The preceding n frame data of monitoring, are data x (l) together by data connection, a effectively to i-th (i ∈ N, N are Measurement channel sum)
Data channel data xi(l) Spline-Fitting is used：
Wherein S (x) is data sequence xi(l) spline-fit function, S (x) make the value of L get minimum.Wherein p ∈ [0,
1] degree of closeness of fitting function and measured data is reflected.S (x) is segmentation batten fitting function, can be write as general shape
Formula：
Sj(l)=aj(l-lj)3+bj(l-lj)2+cj(l-lj)+dj
Add each piecewise fitting function coefficients that boundary condition solves S (l) using least square method.Obtained S (l) is specific
After expression formula, fitting reconfiguration sequence is soughtDetectionThe maximum of uplifted side at baseline transitionWith decline side
MinimumCalculate Baseline wander value
(2) Baseline wander is measured to the data for restarting monitoring.Lead to restarting the ith measurement after guarding
Track data sequences yi(l), useTo yi(l) Baseline wander is carried out, compared with the data before monitoring is interrupted, if yi(l) place
In the elevated side of baseline, then after correctingIf yi(l) in the side that baseline declines, then correct
Afterwards
Repeat step (1) (2), above processing is carried out to all Measurement channels,.
(3) imaging algorithm is improved, augmentation processing is carried out to Gauss-Newton image reconstruction formula.It is imaged for Gauss-Newton
Algorithmic formula：
Δ ρ=- [JtJ+λR]-1Jz
Wherein it is J restructuring matrixes, λ R are regularization constraint item, and z is boundary voltage difference vector at different moments, and Δ ρ is not
Electrical impedance change profile vector between in the same time.
In order to suppress electrode position change influence on RT, then the matrix in reconstruction formula is carried out at augmentation
Reason.For Jacobin matrixExpand tonmeasThe measurement electricity included for a frame data
Press number, nelemTo be imaged the finite element model unit number that reconstruct used uses, ndimFor be imaged dimension, usually carry out two dimension into
Picture, so taking ndim=2, neFor number of electrodes, the expansion of Jacobin matrix is filled with due to measuring electrode change in location
Disturbance, i.e.,
Wherein
A is current excitation vector, and H is positive calculating matrix,After changing in an x or y direction for electrode position
The positive calculating matrix recalculated, the displacement are usually uniformly arranged to a priori constant.
Then augmentation processing is carried out to constraint matrix R, willExpand toExpand
Exhibition is partially filled with the noise prior estimate to reconstruct data and the prior estimate of reconstruct conductivity variations, i.e.,
Wherein RextraFor a Laplace filter.According to imaging field domain prior information determine regularization parameter λ and
RextraLaplce's template, have
Wherein avenoiseAverage priori amplitude for noise relative to measurement data, aveconductIt is opposite for conductivity variations
In the average priori amplitude of initial conductivity distribution, avemoveTo be averaged priori amplitude relative to the electrode displacement of field domain radius.
(4) impedance variations of target field domain are rebuild using the data after correction and the reconstruction formula of augmentation.I.e.WhereinTo restart the reference frame voltage data after monitoring,To restart
Prospect frame voltage data after monitoring, and Δ ρ=S can be abbreviated asaugz。
Embodiment is as follows：
The impedance bioelectrical measurement electrode for all coating conductive paste is posted in subject's head, and head is wound to fix with bandage
Electrode, after the contact of all electrodes is normal, proceeds by data acquisition and image monitoring.Image such as Fig. 2 of normal on-line monitor
It is shown, obvious impedance variations target is included on image.In order to simulate monitoring interrupt situation, by whole measuring electrodes from by
Examination person head removes, after the region wiped clean that subject's head is pasted to electrode with gauze, re-posted whole impedance bioelectrical measurement electrode.
Limited by operation actual conditions, the electrode of re-posted compared with original state, distributing position and with the contact impedance of scalp all
It can change, influence boundary voltage so that it is inconsistent to restart to guard front and rear measurement data baseline, such as Fig. 3 (a) institutes
Show.If without any processing, the reference frame before still being interrupted using monitoring, then can be shown strong on monitoring image
Strong artifact, falls into oblivion original target, as shown in Fig. 3 (b)；If it is background frames to choose the data after restarting monitoring, scheme
As the upper then target information without before, as shown in Fig. 3 (c).Therefore certain processing method is needed, is not reselecting imaging
In the case of reference frame, suppress image artifacts and recover original target information on image.
The flow according to Fig. 1, when restarting monitoring, is according to the following steps handled data and imaging algorithm：
Step 1：Obtain the inconsistent caused measurement data baseline change of electrode tip skin contact condition.Monitoring is read to interrupt
The last n frame data of preceding monitoring process, and the preceding n frame data of the monitoring restarted, are combined into measurement data sequence x
(l), the composition of data sequence is expressed in matrix as：
xmeas(l) represent the measurement data of the meas Measurement channel of l frame data, and have l=2n.Surveyed in EIT
Measurement channel number is related with number of electrodes and excitation-measurement pattern of use in amount system.It is per treatment to choose single measurement
The data sequence x of passagei(l), using spline function according to the following formula to xi(l) it is fitted, seeks fitting function S (l)：
Fitting function S (l) is a segmental cubic polynomials, the general type that can be written as：
Sj(l)=aj(l-lj)3+bj(l-lj)2+cj(l-lj)+dj
Add natural boundary conditions b0=bl=0, and each section boundaries condition and the derivative condition of continuity are substituted into, obtain matrix
Equation：
hi=xi+1-xi, qi=2 (hi-1+hi),
And obtain coefficient aj,cjOn bj,djExpression formula：
L'=0 is made, tries to achieve corresponding cubic polynomial coefficient.After obtaining the expression formula of spline-fit function S (l), calculate
The fitting value sequence of correspondence positionDetectionThe maximum of uplifted side at baseline transitionWith the pole for declining side
Small valueCalculate Baseline wander value
Step 2：Correct the measurement data baseline of change.To the ith measurement channel data sequence y of monitoring process 2i
(l), useTo yi(l) Baseline wander is carried out.As shown in Fig. 3 (a), compared with the data before monitoring is interrupted, yi(l) place
In the elevated side of baseline, then after correctingShown in correction result such as Fig. 4 (a).Such as Fig. 4 (b) institutes
Show, if be directly imaged, occur on monitoring image and guard image artifacts caused by electrode position changes, influence
The identification for guarding target is judged, it is necessary to carry out suppression processing to image artifacts.
Step 3：Make imaging algorithm into, suppress image artifacts caused by electrode position change.To used in dynamic imaging
Gauss-Newton image reconstruction formula carries out augmentation processing.There is Gauss-Newton imaging algorithm formula：
Δ ρ=- [JtJ+λR]-1Jz
Wherein it is J restructuring matrixes, λ R are regularization constraint item, and z is boundary voltage difference vector at different moments, and Δ ρ is not
Electrical impedance change profile vector between in the same time.
For Jacobin matrixExpand tonmeasThe survey included for a frame data
Measure voltage number, nelemTo be imaged the finite element model unit number that reconstruct used uses, neFor measuring electrode quantity, Jacobi square
The expansion of battle array is filled with the priori disturbance compensation value of measuring electrode change in location, i.e.,：
In order to try to achieve filling element therein, the positive calculation formula of electrical impedance imaging is utilized
Z=HA
Wherein A is current excitation vector, and H is positive calculating matrix, z related with the finite element model coordinate for imaging
For boundary voltage vector.CalculateOne priori amount θ is first set, changes the x-axis direction coordinate u of No. 1 electrodexFor ux
=ux+ θ, recalculates positive reconstruction matrix, obtains new boundary voltage vector：
zmove=HmoveA
Then have
Similarly calculate other electrodes and the J matrix augmentation elements in the case that y-axis coordinate is subjected to displacement, priori amount all use
θ。
Then augmentation processing is carried out to constraint matrix R, willExpand toExtension
The noise prior estimate to reconstruct data and the prior estimate of reconstruct conductivity variations are partially filled with, i.e.,
Wherein RextraFor discrete Laplace filter form, can be write as：
Specific element is：Ri,j|(extra)=2.1 δ2, Ri,j|(extra)=-1 δ2(i units and j units are adjacent), it is other
Element is 0.WhereinaveconductThe ratio system being distributed for target conductivity change relative to initial conductivity
Number, avemoveProportionality coefficient for electrode average displacement relative to field domain radius.
Constraint factor λ is：
Wherein, avenoiseProportionality coefficient for noise signal relative to measurement data.
Shown in imaging results such as Fig. 4 (c) after correction.With without algorithm process, reselecting the imaging of imaging reference frame
As a result compare, the imaging results after processing can effectively reflect the imageable target before monitoring interruption.With without algorithm process, not weighing
New to be chosen to as the imaging results of reference frame are compared, the imaging results after processing can effectively suppress the baseline change of DATA REASONING
Caused image artifacts.By the Baseline wander of the algorithm compensation changed to electrode position, and measurement data, compared with Fig. 2, warp
Imaging results after this paper algorithm process effectively reduce original image information, the color range bar on the right side of reference picture, it is ensured that also
Former image result is consistent with original image in numeric distribution.Therefore, the monitoring image information inherit the processing method of processing can be with
Successfully manage and restart the situation that original monitoring-information is lost after guarding after cranium brain dynamic electric impedance imaging on-line monitor interrupts.
Claims (2)
1. a kind of cranium brain dynamic electric impedance imaging on-line monitor guards the processing method that image information is inherited after interrupting, its feature exists
In the measurement data before and after the processing method interrupts on-line monitor is analyzed：First, the method being fitted using batten difference
Measurement data is handled, suppresses the inconsistent caused measurement data baseline change of electrode contact condition before and after on-line monitor interrupts and causes
Image artifacts；Then, augmentation processing is carried out to image reconstruction algorithm, the prior information of electrode displacement is introduced into reconstruction matrix,
Electrode is because of the inconsistent influence to guarding image of riding position before and after reducing monitoring interruption；
Concrete operations are as follows：
1) the Baseline wander value of measurement data is obtained
Select the last n frame data before on-line monitor interrupts and restart the preceding n frame data of monitoring, by data connection one
Rise, be data x (l), to i-th of valid data channel data xi(l) Spline-Fitting is used, obtains fitting sequence
Wherein, i ∈ N, N are Measurement channel sum；
It is then detected thatThe maximum of uplifted side at baseline transitionWith the minimum for declining sideCalculate base
Line correction value
2) Baseline wander is measured to the data for restarting monitoring
To restarting the ith measurement channel data sequence y after guardingi(l), useTo yi(l) Baseline wander is carried out,
Compared with the data before monitoring is interrupted, if yi(l) the elevated side of baseline is in, then after correcting
If yi(l) side in baseline decline, then after correcting
3) augmentation processing is carried out to Gauss-Newton image reconstruction formula
To Gauss -- Newtonian image reconstruction formula：Δ ρ=- [JtJ+λR]-1Jz, wherein, J is Jacobin matrix, and λ R are regularization
Bound term, Δ ρ be at different moments between electrical impedance change profile vector, z is boundary voltage difference vector at different moments；
Change influence on RT to suppress electrode position, augmentation processing is carried out to the matrix in reconstruction formula：Will be refined each
Compare matrixExpand toBy constraint matrixExpand toAnd determine coefficient lambda and constraint matrix R using prior informationaugUnit item；
Wherein, nmeasThe measurement voltage number included for a frame data, nelemTo be imaged the finite element model list that reconstruct used uses
First number, ndimTo be imaged dimension；Two-dimensional imaging is carried out, so taking ndim=2, neFor number of electrodes, the extension of Jacobin matrix
Point it is filled with due to the disturbance of measuring electrode change in location, i.e.,：
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Wherein, A is current excitation vector, and H is positive calculating matrix,After changing in an x or y direction for electrode position
The positive calculating matrix recalculated, the displacement are uniformly arranged to a priori constant；
Then, augmentation processing is carried out to constraint matrix R：
WillExpand toExpansion is filled with the noise prior estimate of reconstruct data
With reconstruct conductivity variations prior estimate, i.e.,：
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Wherein, RextraFor a Laplace filter, regularization parameter λ and R are determined according to the prior information of imaging field domainextra
Laplce's template, then have：
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</msub>
</mrow>
</mfrac>
<mo>,</mo>
<msub>
<mi>R</mi>
<mrow>
<mi>e</mi>
<mi>x</mi>
<mi>t</mi>
<mi>r</mi>
<mi>a</mi>
</mrow>
</msub>
<mo>=</mo>
<msup>
<mrow>
<mo>(</mo>
<mfrac>
<mrow>
<msub>
<mi>ave</mi>
<mrow>
<mi>c</mi>
<mi>o</mi>
<mi>n</mi>
<mi>d</mi>
<mi>u</mi>
<mi>c</mi>
<mi>t</mi>
</mrow>
</msub>
</mrow>
<mrow>
<msub>
<mi>ave</mi>
<mrow>
<mi>m</mi>
<mi>o</mi>
<mi>v</mi>
<mi>e</mi>
</mrow>
</msub>
</mrow>
</mfrac>
<mo>)</mo>
</mrow>
<mn>2</mn>
</msup>
<msup>
<mo>&dtri;</mo>
<mn>2</mn>
</msup>
<mo>;</mo>
</mrow>
Wherein, avenoiseAverage priori amplitude for noise relative to measurement data, aveconductFor conductivity variations relative to
The average priori amplitude of initial conductivity distribution, avemoveTo be averaged priori amplitude relative to the electrode displacement of field domain radius,
For Laplace operator；
4) impedance variations of target field domain are rebuild using the data after correction and the reconstruction formula of augmentation
I.e.WhereinFor the measurement voltage data at t1 moment,For the measurement at t2 moment
Voltage data.
2. cranium brain dynamic electric impedance imaging on-line monitor according to claim 1 guards the place that image information is inherited after interrupting
Reason method, it is characterised in that in step 1), to i-th of valid data channel data xi(l) Spline-Fitting is used, specifically
Carry out as the following formula：
<mrow>
<mi>L</mi>
<mo>=</mo>
<mi>p</mi>
<munderover>
<mo>&Sigma;</mo>
<mrow>
<mi>j</mi>
<mo>=</mo>
<mn>0</mn>
</mrow>
<mi>n</mi>
</munderover>
<msup>
<mrow>
<mo>(</mo>
<msub>
<mi>x</mi>
<mrow>
<mi>i</mi>
<mo>,</mo>
<mi>j</mi>
</mrow>
</msub>
<mo>-</mo>
<mi>S</mi>
<mo>(</mo>
<msub>
<mi>l</mi>
<mi>j</mi>
</msub>
<mo>)</mo>
<mo>)</mo>
</mrow>
<mn>2</mn>
</msup>
<mo>+</mo>
<mrow>
<mo>(</mo>
<mn>1</mn>
<mo>-</mo>
<mi>p</mi>
<mo>)</mo>
</mrow>
<msubsup>
<mo>&Integral;</mo>
<mi>m</mi>
<mi>n</mi>
</msubsup>
<msup>
<mrow>
<mo>(</mo>
<msup>
<mi>S</mi>
<mrow>
<mo>&prime;</mo>
<mo>&prime;</mo>
</mrow>
</msup>
<mo>(</mo>
<mi>l</mi>
<mo>)</mo>
<mo>)</mo>
</mrow>
<mn>2</mn>
</msup>
<mi>d</mi>
<mi>l</mi>
<mo>;</mo>
</mrow>
Wherein, S (x) is data sequence xi(l) spline-fit function, asks the value that S (x) makes L to get minimum；Wherein, p ∈ [0,1]
Reflect the degree of closeness of fitting function and measured data；S (x) is segmentation batten fitting function, is write as general type：
Sj(l)=aj(l-lj)3+bj(l-lj)2+cj(l-lj)+dj；
Each piecewise fitting function coefficients that boundary condition solves S (l) using least square method are added, obtain S (l) expressions
Afterwards, fitting reconfiguration sequence is soughtDetectionThe maximum of uplifted side at baseline transitionWith decline side it is minimum
ValueCalculate Baseline wander value
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