CN103116148A - Inversion method of nuclear magnetic resonance two-dimensional spectrum - Google Patents
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Abstract
The invention relates to an inversion method of nuclear magnetic resonance two-dimensional spectrum. The method includes firstly, extracting and estimating noise, namely extracting noise in CPMG (Carr-Purcell-Meiboom-Gill) echo string of acquired data and estimating standard deviation of the noise; secondly, compressing data, namely generating an inversion kernel and performing truncated singular value decomposition and reconstruction by sequence of a nuclear matrix to complete data compression; and thirdly, fitting the data, namely subjecting fitting problem of the compressed data to regularization, performing iterative solution to regularization factors and inversion spectrum by newton method with non-exact one-dimensional search so as to obtain the inversion spectrum. Execution efficiency of two-dimensional inversion algorithm and resolution of two-dimensional spectrum are increased greatly, and the inversion method is well robust.
Description
Technical field
The present invention relates in a kind of nuclear magnetic resonance field signal and process, particularly a kind of method of Inversion of Two-dimensional NMR Map.
Background technology
Nuclear magnetic resonance technique is widely applied in the energy exploration field.NMR well logging can be fast, nondestructively provide information accurately for each step in the conventional logging workflows such as fluid identification of reservoir, physical properties of rock evaluation and production prediction.Compare the classic methods such as electrical log, acoustic logging, the NMR well logging method is a kind of only method that Fluid Flow in A is identified with regard to energy convection cell type.All there is significantly deficiency in solution based on one dimension well logging experiment on efficient and precision, two-dimentional NMR logging technology is arisen at the historic moment.Use D-T2(diffusion-transverse relaxation) two-dimensional spectrum can be distinguished water, wet goods heterogeneity quickly and intuitively, by calculating T1/T2(longitudinal relaxation/transverse relaxation) this ratio can also be exactly judges the type of hydrocarbon, two-dimentional NMR logging method has advantageous advantage in qualitative and quantitative analysis.The range of application of conventional NMR test experience has also been widened in the realization of two dimension NMR detection method, for the fields such as food, agricultural, biomaterial provide more accurate, reliable solution.
The data of NMR detection method collection can not directly be used, and " spectrum " informational needs that really needs is undertaken just obtaining after inverting by these experimental datas.Only has in the world at present the two-dimentional logging equipment of the capable production of only a few NMR logging equipment manufacturer, and these Zoomlions only provide instrument lease and paid explanation service to various countries energy company, do not sell equipment and Inversion Software, the two dimensional inversion algorithm is close to and is in by the monopolization state.On the other hand, the data volume that the two dimension experiment gathers is tested much larger than one dimension, and traditional one-dimensional inversion method can not satisfy the two dimensional inversion requirement.Laplace Inversion method is a kind of two-dimensional inversion method based on BRD method and deviation principle fast, and this method is devoted to error of fitting is limited to the data error level (deviation) of estimation, can be finally inversed by rational result from low SNR data.But if data SNR is higher, in the situation that do not add other restrictive condition, this method possibly can't restrain.The most popular inversion method that is based on truncated singular value decomposition (Truncated Singular Value Decomposition, TSVD) of domestic researcher, the TSVD method accesses gratifying result at SNR very Gao Shineng.But because TSVD is very responsive to noise, use the method can't obtain result accurately when SNR is low.Maximum entropy method (MEM) can access the two-dimensional spectrum of the most random (the most probable), but excessive as method operand in solution procedure of penalty function with entropy (logarithmic term), and execution speed is excessively slow on ordinary PC.Can reduce the calculated amount of inverting by introducing basis function, but use the prerequisite that Basis Function Method is processed to be, the known distribution of waiting to ask the spectrum intermediate value satisfies that certain is linear.Other if you would the Te Kaluo class methods etc. probability of use control the method for evolution direction, only theoretical feasible in this big data quantity problem of two dimensional inversion, large-scale population can cause evolutionary rate excessively slow.
Summary of the invention
The present invention be directed to the problem that present two dimensional inversion exists, proposed a kind of method of Inversion of Two-dimensional NMR Map, can under the prerequisite that guarantees inverting spectrum accuracy, improve the resolution of inverting spectrum, efficient and the robustness of inversion algorithm.
Technical scheme of the present invention is: a kind of method of Inversion of Two-dimensional NMR Map comprises the steps:
1) noise extracts and estimates: use wavelet transformation that the noise in image data CPMG echo string is extracted and estimate its standard deviation;
2) data compression: generate inverting core, and utilize the nuclear moment rank of matrix to carry out truncated singular value decomposition and data compression is completed in reconstruct;
3) data fitting: the fitting problems of compressing rear data is carried out Regularization, and carry out the iterative of the regularization factor and inverting spectrum with the Newton method that combines non-accurate linear search, obtain the inverting spectrum.
Use the method for Wavelet Denoising Method to carry out denoising to the CPMG serial data in described step 1), amplitude difference by data before data and filtering after the comparison denoising, carrying out " noise " extracts, at first, use the sym8 wavelet basis to carry out 4 grades of decomposition to raw data, then use global threshold to carry out soft-threshold to wavelet coefficient, carry out at last signal reconstruction, obtain relatively smooth CPMG serial data after filtering; Then calculate the difference of data after raw data and filtering, use the amplitude model of white Gaussian noise to carry out match to difference data, obtain the estimation poor to noise criteria.
At first described step 3) data fitting obtains a new matrix to after each element of kernel matrix square, with new matrix trace (trace) divided by the value of diagonal element number as the initial regularization factor; Secondly for given regular factor, use Newton method (Newton Method) that minimum problem is found the solution, the step-length of using on Newton direction is determined by the non-accurate linear search of Wolfe-Powell.
Described step 3) regularization factor update mode is: calculate the ideal value of the regularization factor according to the deviation principle, if ideal value is greater than original value, so with 1/2 value as the new regularization factor of initial value; Otherwise, directly use ideal value as the new value of the regularization factor.
Described step 3)
The final value condition of the iterative of inverting spectrum is:
The new value of 1. regularization factor next round circulation has been not more than a default little value;
The match residual error is not more than the noise level that the first step is estimated.
Beneficial effect of the present invention is: the method for Inversion of Two-dimensional NMR Map of the present invention, significantly improved the execution efficient of two dimensional inversion algorithm and the resolution of two-dimensional spectrum, and also have simultaneously good robustness.
Description of drawings
Fig. 1 is the method flow diagram of Inversion of Two-dimensional NMR Map of the present invention;
Fig. 2 is that in the method for Inversion of Two-dimensional NMR Map of the present invention, noise extracts algorithm flow chart with estimating part;
Fig. 3 is the figure as a result that in the method for Inversion of Two-dimensional NMR Map of the present invention, the noise of a CPMG serial data is extracted;
Fig. 4 is the shutdown criterion schematic diagram that in the method for Inversion of Two-dimensional NMR Map of the present invention, data fitting is partly used;
Fig. 5 is the two-dimentional spectrogram that the method for Inversion of Two-dimensional NMR Map of the present invention is processed for the T1-T2 spectrum of certain brand cottonseed;
Fig. 6 is the two-dimentional spectrogram that the method for Inversion of Two-dimensional NMR Map of the present invention is processed for the D-T2 spectrum of certain full water rock core;
Fig. 7 is the default true spectrogram of the method for Inversion of Two-dimensional NMR Map of the present invention;
Fig. 8 is that the method for Inversion of Two-dimensional NMR Map of the present invention is the figure as a result that 100 emulated data is processed to signal to noise ratio (S/N ratio);
Fig. 9 is that the method for Inversion of Two-dimensional NMR Map of the present invention is the figure as a result that 10 emulated data is processed to signal to noise ratio (S/N ratio);
Figure 10 is that the method for Inversion of Two-dimensional NMR Map of the present invention is the figure as a result that 1 emulated data is processed to signal to noise ratio (S/N ratio).
Embodiment
Fig. 1 is the method flow diagram of Inversion of Two-dimensional NMR Map of the present invention, comprises step: the first step, noise are extracted and are estimated: use wavelet transformation that the noise in image data CPMG echo string is extracted and estimate its standard deviation; Second step, data compression: generate inverting core, and utilize the nuclear moment rank of matrix to carry out truncated singular value decomposition and data compression is completed in reconstruct; The 3rd step, data fitting: the fitting problems of compressing rear data is carried out Regularization, and carry out the iterative of the regularization factor and inverting spectrum with the Newton method that combines non-accurate linear search, obtain the inverting spectrum.
1, noise extracts and estimates:
It is the algorithm flow chart of noise extraction and estimating part as Fig. 2.Introduced wavelet transformation in noise extracts, used the method for Wavelet Denoising Method to carry out denoising to the CPMG serial data, by the amplitude difference of data before data and filtering after the comparison denoising, carried out " noise " and extract.The mode of the Wavelet Denoising Method that the present invention uses is: at first, use the sym8 wavelet basis to carry out 4 grades of decomposition to raw data, then use global threshold to carry out soft-threshold to wavelet coefficient, carry out at last signal reconstruction.Here " noise " refers to affect the composition of flashlight slip, is the consideration for line smoothing, and this does not have directly to use the main cause of data after filtering just in subsequent treatment.For the variance to noise is estimated, need to carry out statistics with histogram to noise amplitude, then use formula (1) to carry out match to histogram.(1) in formula, A and
Be fitting parameter,
Be the variance of Gaussian noise.The figure as a result that Fig. 3 extracts for the noise to a CPMG serial data.
（1）
2, data compression:
To nuclear matrix K, always there is following decomposition:
In formula,
For
Real two-dimensional matrix;
For
The row orthogonal matrix, be called left singular matrix;
For
The row orthogonal matrix, be called right singular matrix;
For
Diagonal matrix, the element value correspondence of diagonal position matrix
Singular value.By matrix S VD computing method, the singular value in S is successively decreased from the upper left corner to the lower right corner.Under many circumstances, front 10% even 1% singular value and just accounted for whole singular value sums more than 99%.We that is to say, before also can use
Large singular value is come the approximate description matrix:
Further the two dimensional inversion problem is analyzed, if inverting nuclear energy enough splits into two individual core (as T1-T2 inverting core), so just drilling rule can be expressed as:
In formula, M is the data of experiment measuring,
Known relation between expression measurement data and spectrum to be asked.
Now two cores being carried out respectively singular value blocks:
, (
The expression disconnect position), so
（5）
Wherein,
,
Obviously, if
, so
Set up sampled data
To significantly reduce, and in this process, spectrum to be asked
Size do not change.(the processing object in subsequent step is the data of using after the method is compressed, for the ease of statement, to not re-use symbol " ~ " distinguishes compressing rear data) Data Reduction to be to lose minimum precision as cost, can accelerate the various computings in subsequent processing steps, improve efficiency of algorithm.
About disconnect position, classic method generally uses SNR or pre-conditioned number to judge, these modes of blocking probably cause some important informations of matrix loss, and the result that follow-up inverting obtains can be also to owe excellent (suboptimal).In fact, if the singular value matrix of two cores is respectively:
So,
Singular value be
, obviously, make data after blocking keep all original features (namely all are greater than 0 singular value), must guarantee disconnect position
With
Just equal rank of matrix.
3, data fitting:
It is a fitting problems (as shown in Equation 6) on the two dimensional inversion question essence.If two cores do not have coupled relation, can directly with tensor product, problem (6) be converted into the form of problem (7) so.At this moment,
,
,
, vect represents two-dimensional matrix is spliced into a column vector by row.If two cores are coupled, can in a certain way two cores be compiled in a core again so, also can change the form of problem (7) into.
（6）
The two dimensional inversion problem is an ill-posed problem, need to use certain additional constraint to obtain only stable solution when finding the solution.In numerous additional constraints, mould or the slickness of separating limited the cognition that meets people, thereby be widely used.With level and smooth of mould as the method for the Tikhonov regularization in standard regularization of penalty as the formula (8).
In formula,
Be a positive number, characterized the weight that mould smoothly occupies in whole minimum problems, be called regular factor.All the other parameter meanings the same (the data before and after compression not being distinguished), 2 interpolation is just in order conveniently to carry out follow-up mathematical operation.If establish
Be easy to problem is converted into the described form of formula (12) by the KKT condition.
For minimum problems (12), due to
At least positive semidefinite,
The permanent establishment so quadratic programming (12) is a convex programming, has only solution, and
Can get arbitrary value.Again due to existence
For given α, can directly find the solution with Newton method and obtain
Yet in practical problems, handled data area is very wide, may produce concussion when directly using Newton method processing section data, can't restrain.In order to address this problem, accelerate simultaneously convergence of algorithm speed, the present invention has introduced Powell Wolfe criterion this non-accurate linear search method determines that iteration is each time advanced on Newton direction step-length.
Above-mentioned treatment step all need to carry out under the prerequisite of known α, but in the practical inversion problem, α and
All unknown.α can determine by L curve or GCV, but these two kinds of methods all need the different value in certain preset range is traveled through, and efficient exists obviously not enough.And in practical problems, a lot of data are not strict " L " shape according to the curve of L Drawing of Curve, thereby can't position the turning.The curve that GCV obtains is often too smooth at root, and the speed of convergence of iteration is excessively slow.The BRD method is a kind of efficient method faster, the mode by iteration pair
When upgrading, reduced to greatest extent unnecessary in certain limit
The calculating of value.But if inaccurate to the estimation of noise, when perhaps the signal to noise ratio (S/N ratio) of data was too high, the BRD method can can't restrain.
The present invention take the BRD method as prototype, has proposed a kind of brand-new iterative manner from efficient.In conjunction with abovementioned steps, the step of data fitting part of the present invention is as follows:
(1) initial value bigger than normal of given α (as
); Set minimum regularization factor Thresh and minimum rate of change TOL;
(2) basis
Ask for
, use
If
, use
Upgrade; If
,
(3) if
, or
, or
, or
No longer change
, shut down; Otherwise, go to step (2).
Fig. 4 is the shutdown criterion schematic diagram that data fitting is partly used, and horizontal ordinate is different
, ordinate represents difference
Corresponding match residual error.Due in advance given
Be a very large value (according to
The words of calculating
Usually be not less than 10
3Magnitude), obtain this moment
It can not be optimum solution.If (the best regular factor of one group of data is very large, and few of real information and actual application value are composed in the inverting that obtains according to these group data so.) if noise estimates accurately, according to formula
Will obtain a regular factor that diminishes, usually through after the iteration below 10 steps
Just no longer change, obtain a solution that just makes the match residual error equal noise level.If it is too small that noise is estimated, when still upgrading according to the method for upper a kind of situation,
Can constantly reduce, and lose gradually the effect of regularization, finally produce one and owe smooth unstable solution.At this moment, be a stable smoothing solution in order to ensure what finally obtain, this paper algorithm is provided with the final value condition
, and
, usually, end condition
More easily reach.If it is excessive that noise is estimated, by
When upgrading regular factor
Concussion back and forth (because be easy to obtain the match residual error less than the solution of data noise, the probability that both just equates is very little), obviously, end condition
Can address this problem, error of fitting is just shut down for the first time less than noise level the time.
Use the iterative algorithm of above-mentioned shutdown criterion can obtain a suitable inverting spectrum, have certain versatility.Fig. 5 is for using method proposed by the invention to process the T1-T2 two-dimensional spectrum of certain the brand cottonseed that obtains, and Fig. 6 is for using method proposed by the invention to process the D-T2 two-dimensional spectrum of certain the full water rock core that obtains.The results showed, when the new method of a kind of Inversion of Two-dimensional NMR Map of employing the present invention is carried out inverting to the experimental data of different field, through just restraining less than algorithm after the iteration of 10 times.When the emulated data of different signal to noise ratio (S/N ratio)s is carried out inverting, can provide to the data of SNR=1 two-dimensional spectrum clearly as Fig. 7～10.
Compared with prior art, the present invention one, the method for utilizing wavelet filtering to carry out the noise extraction can be estimated noise more accurately.When the function model of use white Gaussian noise carried out match to difference, related coefficient illustrated that greater than 99% in document, the noise in the CPMG echoed signal being assumed to be white Gaussian noise is reasonably, has also proved the accuracy of noise Extraction parts in the present invention from the side; Two, in the data compression method that uses, the mode of blocking of singular value, be only a kind of when data are significantly compressed, can guarantee the solution of new problem and the method for former problem equivalent.It is the excellent solution of owing of former problem that other mode of recently blocking according to pre-conditioned number or noise all may cause the optimum solution of new problem.In addition, the data compression mode of the present invention's use need not to think and intervention can adaptively obtain disconnect position; Even three cloth are counted in about 100*100, also can obtain inverting spectrum (take common 32 machines as experiment porch, the concrete concrete data of basis of time and decide) within several minutes even tens of seconds.Cloth is counted and is greatly improved, and the resolution of two-dimensional spectrum is also more meticulous; Four, for the higher data of signal to noise ratio (S/N ratio), algorithm can obtain two-dimensional spectrum very accurately, can be used for quantitative test.For the lower data of signal to noise ratio (S/N ratio), the convergence that algorithm can be very fast also obtains a reliable two-dimensional spectrum, also can be used for quantitative test.Data for the extremely low data of signal to noise ratio (S/N ratio) (SNR＜1), algorithm can be restrained faster, can see clearly the peak Distribution of principal ingredient in the inverting spectrum, but the peak of some small scales or the peak that is separated by very near may be flooded by large peak, in the inverting spectrum, the halfwidth at peak is also wider, can be used for carrying out qualitative analysis this moment.
Claims (5)
1. the method for an Inversion of Two-dimensional NMR Map, is characterized in that, comprises the steps:
1) noise extracts and estimates: use wavelet transformation that the noise in image data CPMG echo string is extracted and estimate its standard deviation;
2) data compression: generate inverting core, and utilize the nuclear moment rank of matrix to carry out truncated singular value decomposition and data compression is completed in reconstruct;
3) data fitting: the fitting problems of compressing rear data is carried out Regularization, and carry out the iterative of the regularization factor and inverting spectrum with the Newton method that combines non-accurate linear search, obtain the inverting spectrum.
2. the method for Inversion of Two-dimensional NMR Map according to claim 1, it is characterized in that, use the method for Wavelet Denoising Method to carry out denoising to the CPMG serial data in described step 1), by the amplitude difference of data before data and filtering after the comparison denoising, carry out " noise " and extract, at first, use the sym8 wavelet basis to carry out 4 grades of decomposition to raw data, then use global threshold to carry out soft-threshold to wavelet coefficient, carry out at last signal reconstruction, obtain relatively smooth CPMG serial data after filtering; Then calculate the difference of data after raw data and filtering, use the amplitude model of white Gaussian noise to carry out match to difference data, obtain the estimation poor to noise criteria.
3. the method for Inversion of Two-dimensional NMR Map according to claim 1, is characterized in that described step 3)
At first data fitting obtains a new matrix to after each element of kernel matrix square, with new matrix trace (trace) divided by the value of diagonal element number as the initial regularization factor; Secondly for given regular factor, use Newton method (Newton Method) that minimum problem is found the solution, the step-length of using on Newton direction is determined by the non-accurate linear search of Wolfe-Powell.
4. the method for according to claim 1 or 3 described Inversion of Two-dimensional NMR Maps, it is characterized in that, described step 3) regularization factor update mode is: the ideal value of calculating the regularization factor according to the deviation principle, if ideal value is greater than original value, so with 1/2 value as the new regularization factor of initial value; Otherwise, directly use ideal value as the new value of the regularization factor.
5. the method for Inversion of Two-dimensional NMR Map according to claim 1, is characterized in that described step 3)
The final value condition of the iterative of inverting spectrum is:
The new value of 1. regularization factor next round circulation has been not more than a default little value;
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