CN110850491A - T2 spectrum inversion method, device and storage medium - Google Patents
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Abstract
The invention provides a T2 spectrum inversion method, a device and a storage medium, wherein the method comprises the following steps: receiving stationing data input by a user; determining an inversion coefficient matrix according to the stationing data and related acquisition parameters; collecting a plurality of groups of echo data, and respectively performing expansion processing on the inversion coefficient matrix according to the plurality of groups of echo data to obtain an expanded inversion coefficient matrix; and according to the expanded inversion coefficient matrix, carrying out non-negative constraint to determine the initial amplitude P of the transverse relaxation component by using a positive and negative scanning operator. The invention realizes the inversion of the T2 spectrum and improves the speed and accuracy of the inversion of the T2 spectrum.
Description
Technical Field
The invention relates to the technical field of logging of geological exploration, in particular to a T2 spectrum inversion method, a T2 spectrum inversion device and a storage medium.
Background
When a Nuclear Magnetic Resonance (NMR) mode is used for logging, each echo signal measured by an actual instrument is the overall effect of multiple relaxation components. This can be expressed as a multi-exponential function:
wherein A (t) is the echo amplitude measured at the time t; t is2iA transverse relaxation time, which is the ith relaxation component, used to characterize pore size; piIs the initial amplitude of the i transverse relaxation component that characterizes the porosity size of a pore of a characteristic relaxation size. Wherein, T2iIn the inversion, a series of values are assumed in advance, after each characteristic relaxation and a characteristic relaxation component i are determined, an overdetermined equation set can be formed by combining echo strings, j is 1, …, k (k is the echo number), and P is obtained through the equation setiThe process is called the inversion of T2 spectrum, and is the key to the nuclear magnetic resonance logging data processing. Inversion of the T2 spectrum is a typical morbidity problem, or ill-posed problem.
In recent years, research on NMR T2 spectrum inversion methods has been greatly advanced, many different inversion algorithms are available at home and abroad, and currently, MAP-II based on singular value decomposition is still a T2 spectrum inversion method widely adopted at present internationally. According to the method, a T2 spectrum inversion linear equation set is constructed, the solution of the linear equation set is solved for an actual problem by using a singular value decomposition method, and finally an inversion T2 spectrum with good continuity is obtained.
However, in the implementation process of the prior art, the number of actually measured echo strings is large, the memory overhead is large, and the inversion speed is slow. In order to improve the signal-to-noise ratio and the inversion speed, the echo train is generally required to be filtered, then a part of data is extracted for inversion, meanwhile, the number of distribution points of T2 is compressed, and finally, the inversion result is interpolated and smoothed, wherein the influence of the middle loop is large, and the efficiency is low.
Disclosure of Invention
The invention provides a method, a device and a storage medium for a T2 spectrum inversion algorithm, which are used for realizing concise and efficient T2 spectrum inversion.
In a first aspect, an embodiment of the present invention provides a T2 spectrum inversion method, including:
receiving stationing data input by a user;
determining an inversion coefficient matrix according to the point distribution data;
collecting a plurality of groups of echo data, and respectively performing expansion processing on the inversion coefficient matrix according to the plurality of groups of echo data to obtain an expanded inversion coefficient matrix;
and determining the initial amplitude P of the transverse relaxation component according to the expanded inversion coefficient matrix.
According to the scheme, the inversion coefficient matrix is determined according to the point distribution data input by a receiving user, the inversion matrix is prevented from being established back and forth according to each processing point in echo parameters, then multiple groups of echo data are collected, the inversion coefficient matrix is respectively subjected to expansion processing according to the multiple groups of echo data, the expanded inversion coefficient matrix is obtained, finally the initial amplitude P of the transverse relaxation component is determined according to the expanded inversion coefficient matrix, the inversion of the T2 spectrum is achieved, and the inversion efficiency of the T2 spectrum is improved by establishing the inversion coefficient matrix.
Optionally, determining an inversion coefficient matrix according to the stationing data includes:
log minimization for receiving user inputValue T2minSum logarithmic maximum T2max；
According to the point distribution data and the logarithm minimum value T2minAnd said logarithmic maximum T2maxDetermining the transverse relaxation time T of the ith relaxation component2i；
According to the T2iAnd determining the inversion coefficient matrix.
Optionally, determining an inversion coefficient matrix according to the stationing data includes:
receiving a user-entered exponential minimum value T2eminAnd exponential step increment Δ T2e；
According to the distribution data and the index minimum value T2eminAnd the exponential step increment Δ T2eDetermining the transverse relaxation time T of the ith relaxation component2i；
According to the T2iAnd determining the inversion coefficient matrix.
Optionally, said is according to said T2iDetermining the matrix of inversion coefficients, comprising:
receiving an echo interval value Te, an echo start sequence number Is and an echo end sequence number Ie, an echo polarization time Tw and a ratio T of longitudinal relaxation time to transverse relaxation time input by a user12R；
Calculating each time point t of the echo according to the echo interval value Te, the echo starting sequence number Is and the end sequence number Isk；
According to the echo polarization time Tw and the ratio T of the longitudinal relaxation time to the transverse relaxation time12RCalculating the polarization correction Pck,i；
According to each time point t of the echokAnd said polarization correction amount Pck,iAnd determining the inversion coefficient matrix.
In the scheme, each time point t of the echo Is calculated according to an echo interval value Te, an echo starting sequence number Is and the termination sequence number Is which are input by a user according to actual conditionskEcho polarization time Tw and ratio T of longitudinal relaxation time to transverse relaxation time inputted by user according to actual situation12RCalculating the polarization correction Pck,i(ii) a Finally, according to each time point t of the echokAnd polarization correction amount Pck,iThe inversion coefficient matrix is determined, and the inversion coefficient matrix is determined in the above mode, so that the inversion matrix is prevented from being established back and forth for each processing point of each group of echoes in the actual measurement process, a large amount of time is saved, and the calculation speed is improved.
Optionally, the performing expansion processing on the inversion coefficient matrix according to the multiple sets of echo parameters to obtain an expanded inversion coefficient matrix includes:
performing matrix transformation on the inversion coefficient matrix to obtain a transformed inversion coefficient matrix;
and according to the multiple groups of echo parameters, performing expansion processing on the transformed inversion coefficient matrix to obtain the expanded inversion coefficient matrix.
In the scheme, the inversion dimension is reduced by matrix transformation of the inversion coefficient matrix, the calculation speed is improved, the storage space is saved, the transformed inversion coefficient matrix is expanded according to a plurality of groups of echo parameters to obtain the expanded inversion coefficient matrix, and the operations of filtering, sampling, artificial dimension reduction and the like are avoided by introducing all measured data, so that the solving efficiency is improved.
Optionally, the determining an initial amplitude P of the transverse relaxation component according to the expanded inversion coefficient matrix includes:
adopting a forward scanning operator to perform forward scanning on all diagonal elements in the expanded inversion coefficient matrix to obtain a forward scanning result;
judging whether a negative solution exists in the positive scanning result;
if the negative solution exists, determining the sequence number of the main diagonal element corresponding to the negative solution;
and determining the initial amplitude P of the transverse relaxation component according to the sequence number of the main diagonal element corresponding to the negative solution.
Optionally, the determining an initial amplitude P of the transverse relaxation component according to the sequence number of the main diagonal element corresponding to the negative solution includes:
step A: according to the sequence number of the main diagonal element corresponding to the first largest negative solution in the negative solutions, performing negative scanning on the element corresponding to the sequence number by using a negative scanning operator to obtain a negative scanning result;
and B: judging whether negative solutions exist in the negative scanning result, if so, determining a second maximum negative solution in the negative scanning result as a new first maximum negative solution, and repeatedly executing the steps A-B until no negative solution exists in the negative scanning result;
and C: and determining the initial amplitude P of the transverse relaxation component according to the negative direction scanning result.
In the scheme, the diagonal elements in the expanded inversion coefficient matrix are positively scanned by adopting a positive scanning operator to obtain all solutions of a matrix equation, including a positive solution, a negative solution and a zero solution, and in the practical problem, because the negative solution has no significance, if the negative solution exists, the sequence number of the main diagonal element corresponding to the maximum negative solution in the negative solution is determined; and performing negative scanning according to the sequence number of the main diagonal element corresponding to the maximum negative solution to obtain a negative scanning result, updating the positive scanning result, then judging whether a negative solution exists in the updated scanning result, if so, determining a second maximum negative solution in the negative scanning result as a new first maximum negative solution, performing negative scanning on the sequence number of the main diagonal element corresponding to the new first maximum negative solution, repeating the steps until no negative solution exists in the negative scanning result, and finally determining the initial amplitude P of the transverse relaxation component according to the negative scanning result.
In a second aspect, an embodiment of the present invention provides a T-spectrum inversion apparatus, including
The receiving module is used for receiving the point distribution data input by the user;
the determining module is used for determining an inversion coefficient matrix according to the stationing data;
the processing module is used for acquiring a plurality of groups of echo data and respectively expanding the inversion coefficient matrix according to the plurality of groups of echo data to obtain an expanded inversion coefficient matrix;
the determining module is further configured to determine an initial amplitude P of the transverse relaxation component according to the extended inversion coefficient matrix.
Optionally, the determining module includes:
a receiving submodule for receiving the logarithm minimum value T input by the user2minSum logarithmic maximum T2max；
A determining submodule for determining the logarithm minimum T according to the point data2minAnd said logarithmic maximum T2maxDetermining the transverse relaxation time T of the ith relaxation component2i；
The determination submodule is further used for determining the T2iAnd determining the inversion coefficient matrix.
Optionally, the determining module includes:
a receiving submodule for receiving the index minimum value T input by the user2eminAnd exponential step increment Δ T2e；
A determining submodule for determining the index minimum value T according to the point data2eminAnd the exponential step increment Δ T2eDetermining the transverse relaxation time T of the ith relaxation component2i；
A determination submodule for further determining a value based on the T2iAnd determining the inversion coefficient matrix.
Optionally, the determining sub-module is specifically configured to:
receiving an echo interval value Te, an echo start sequence number Is and an echo end sequence number Ie, an echo polarization time Tw and a ratio T of longitudinal relaxation time to transverse relaxation time input by a user12R；
Calculating each time point t of the echo according to the echo interval value Te, the echo starting sequence number Is and the end sequence number Isk；
According to the echo polarization time Tw and the ratio T of the longitudinal relaxation time to the transverse relaxation time12RCalculating the polarization correction Pck,i；
According to each time point t of the echokAnd said polarization correction amount Pck,iAnd determining the inversion coefficient matrix.
Optionally, the processing module is specifically configured to:
performing matrix transformation on the inversion coefficient matrix to obtain a transformed inversion coefficient matrix;
and according to the multiple groups of echo parameters, performing expansion processing on the transformed inversion coefficient matrix to obtain the expanded inversion coefficient matrix.
Optionally, the determining module includes:
the scanning submodule is used for carrying out forward scanning on all elements of the diagonal line in the expanded inversion coefficient matrix by adopting a forward scanning operator to obtain a forward scanning result;
the judgment submodule is used for judging whether a negative solution exists in the positive scanning result;
the determining submodule is used for determining the serial number of the main diagonal element corresponding to the negative solution when the judging submodule judges that the negative solution exists;
the determining submodule is further configured to determine an initial amplitude P of the transverse relaxation component according to the sequence number of the main diagonal element corresponding to the negative solution.
Optionally, the determining sub-module is specifically configured to:
step A: according to the sequence number of the main diagonal element corresponding to the first largest negative solution in the negative solutions, performing negative scanning on the element corresponding to the sequence number by using a negative scanning operator to obtain a negative scanning result;
and B: judging whether negative solutions exist in the negative scanning result, if so, determining a second maximum negative solution in the negative scanning result as a new first maximum negative solution, and repeatedly executing the steps A-B until no negative solution exists in the negative scanning result;
and C: and determining the initial amplitude P of the transverse relaxation component according to the negative direction scanning result.
In a third aspect, the present invention provides a server, comprising:
a processor;
a memory; and
a computer program;
wherein the computer program is stored in the memory and configured to be executed by the processor, the computer program comprising instructions for performing the method of the first aspect.
In a fourth aspect, an embodiment of the present invention provides a computer-readable storage medium, where a computer program is stored, and the computer program causes a server to execute the method in the first aspect.
According to the T2 spectrum inversion method, the T2 spectrum inversion device and the storage medium, the inversion coefficient matrix is determined according to the point distribution data input by a user, then, a plurality of groups of echo parameters are collected, the inversion coefficient matrix is subjected to expansion processing according to the plurality of groups of echo parameters, the expanded inversion coefficient matrix is obtained, and finally, the initial amplitude P of the transverse relaxation component is determined according to the expanded inversion coefficient matrix. Because the inversion matrix is prevented from being built back and forth according to each processing point by building the inversion coefficient matrix, the speed of T2 spectrum inversion is improved, and in addition, the inversion coefficient matrix is expanded according to a plurality of groups of echo parameters, the problem of inaccurate inversion result caused by operations such as filtering, sampling, artificial dimension reduction and the like is avoided, and the accuracy of T2 spectrum inversion is improved.
Drawings
In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the drawings needed to be used in the description of the embodiments or the prior art will be briefly introduced below, and it is obvious that the drawings in the following description are some embodiments of the present invention, and for those skilled in the art, other drawings can be obtained according to these drawings without creative efforts.
FIG. 1 is a schematic flow chart of an embodiment of a T2 spectrum inversion algorithm method according to the present invention;
FIG. 2 is a schematic structural diagram of a first embodiment of a T2 spectrum inversion algorithm apparatus according to the present invention;
FIG. 3 is a schematic structural diagram of a second embodiment of a T2 spectrum inversion algorithm apparatus according to the present invention;
FIG. 4 is a schematic structural diagram of a third embodiment of a T2 spectrum inversion algorithm apparatus according to the present invention;
fig. 5 is a schematic structural diagram of a server according to an embodiment of the present invention.
Detailed Description
In order to make the objects, technical solutions and advantages of the embodiments of the present invention clearer, the technical solutions in the embodiments of the present invention will be clearly and completely described below with reference to the drawings in the embodiments of the present invention, and it is obvious that the described embodiments are some, but not all, embodiments of the present invention. All other embodiments, which can be derived by a person skilled in the art from the embodiments given herein without making any creative effort, shall fall within the protection scope of the present invention.
The terms "first," "second," "third," "fourth," and the like in the description and in the claims, as well as in the drawings, if any, are used for distinguishing between similar elements and not necessarily for describing a particular sequential or chronological order. It is to be understood that the data so used is interchangeable under appropriate circumstances such that the embodiments of the invention described herein are, for example, capable of operation in sequences other than those illustrated or otherwise described herein. Furthermore, the terms "comprises," "comprising," and "having," and any variations thereof, are intended to cover a non-exclusive inclusion, such that a process, method, system, article, or apparatus that comprises a list of steps or elements is not necessarily limited to those steps or elements expressly listed, but may include other steps or elements not expressly listed or inherent to such process, method, article, or apparatus.
The following describes the technical solution of the present invention and how to solve the above technical problems with specific examples. The following several specific embodiments may be combined with each other, and details of the same or similar concepts or processes may not be repeated in some embodiments. Embodiments of the present invention will be described below with reference to the accompanying drawings.
Nuclear magnetic resonance logging is the measurement of nuclear magnetic resonance under downhole conditions. One of the cores of the measurement principle is to apply an external magnetic field to the formation to magnetize the hydrogen nuclei. The hydrogen nuclei are magnetic nuclei having a nuclear magnetic moment, and the magnets are placed downhole to generate a magnetic field in the formation surrounding the well, orienting the magnetic moment of the hydrogen nuclei in the direction of the magnetic field, a process called magnetization or polarization, with the time constant of polarization denoted by T1, referred to as longitudinal relaxation time. T1 is related to factors such as the size of the porosity, the size of the diameter of the porosity, the nature of the fluid in the pores, and the lithology of the formation. The second core of the nmr well logging principle is to transmit electromagnetic wave pulses of specific energy, specific frequency and specific time interval to the formation using an antenna system to generate so-called spin echo signals and to receive and collect such echo signals, which is called spin echo. The observed echo train is an exponentially decaying signal, and the decay time constant is represented by T2 and is called transverse relaxation time, and is related to factors such as the size of the formation porosity, the size of the pore diameter, the properties of the fluid in the pores, lithology and acquisition parameters.
However, whether the nmr log is used to calculate porosity, pore size distribution, permeability, etc., or to identify and evaluate fluids and their properties, it is necessary to invert the relaxation time spectrum from the original echo train of the nmr log. The T2 spectrum inversion is to preset a plurality of T2 values, then find the initial amplitudes P of a plurality of transverse relaxation components, and make the initial amplitudes P fit to a real echo string Y, T2iAnd PiThe T2 spectrum is formed, the core of the T2 spectrum is a non-negative constraint linear equation system solving algorithm technology, and therefore, how to design an efficient T2 spectrum inversion algorithm is very important.
Fig. 1 is a schematic flow chart of an embodiment of a T2 spectrum inversion method provided in an embodiment of the present invention, and as shown in fig. 1, the method in the embodiment of the T2 spectrum inversion method provided in the embodiment of the present invention includes the following steps:
In this step, the distribution data includes a distribution number NOC and a logarithmic minimum value T2minSum logarithmic maximum T2maxOr the minimum value T of the index2eminAnd exponential step increment Δ T2e。
The relaxation component T2 is subjected to point distribution, in practice, continuous relaxation components are subjected to discretization point taking, when the number of distributed points is small, an inversion result is too simple, the occurrence condition of fluid in a rock stratum cannot be well reflected, when the number of distributed points of a relaxation time spectrum is large, namely the number of the relaxation components is increased, an inverted matrix model is enlarged, and the calculation speed, the calculation precision and the stability of an equation are also influenced. In the present invention, the number of distribution points of T2 is not limited, and in one possible embodiment, the number of distribution points may be between 30 and 50.
If the point data input by the user comprises the logarithm minimum value T2minSum logarithmic maximum T2maxIf so, the point T2 is distributed in a logarithmic sharing mode; if the point data input by the user comprises T2maxOr the minimum value T of the index2eminAnd exponential step increment Δ T2eThen point T2 is distributed in an exponential averaging fashion.
By receiving the stationing data input by the user, the stationing data of the T2 spectrum can be adjusted according to the actual nuclear magnetic resonance logging condition, so that the T2 stationing is more reasonable.
And 102, determining an inversion coefficient matrix according to the stationing data.
In one possible implementation, determining an inversion coefficient matrix according to the stationing data includes:
first, a logarithmic minimum T input by a user is received2minSum logarithmic maximum T2max。
Wherein, the data input by the user is the logarithm minimum value T2minSum logarithmic maximum T2maxThen, the point distribution mode of T2 adopts a logarithmic mean-square form, specifically, the logarithmic mean increment Δ T is first calculated, and the formula is as follows:
secondly, according to the distribution data and the logarithm minimum value T2minSum logarithmic maximum T2maxDetermining the transverse relaxation time T of the ith relaxation component2i。
Wherein, the minimum value T of the logarithm is firstly input according to the distribution number input by the user2minSum logarithmic maximum T2maxCalculating the obtained logarithmic mean increment delta T, and then calculating the logarithmic mean increment delta T and the logarithmic minimum value T according to the logarithmic mean increment delta T and the logarithmic minimum value T2minEqually dividing the point T2 according to a logarithmic average mode, and calculating the transverse relaxation time T of the ith relaxation component2iThe formula of (1) is as follows:
T2i＝T2min+e(i-1)Δti＝1,...,Noc
the transverse relaxation time T of the ith relaxation component is calculated by the formula2i。
Finally, according to T2iAnd determining an inversion coefficient matrix.
In another possible implementation, determining an inversion coefficient matrix according to the stationing data includes:
firstly, receiving an index minimum value T input by a user2eminAnd exponential step increment Δ T2e。
Secondly, according to the distribution data and the minimum value T of the index2eminAnd exponential step increment Δ T2eDetermining the transverse relaxation time T of the ith relaxation component2i。
Specifically, according to the distribution data and the index minimum value T2eminAnd exponential step increment Δ T2eCalculating the transverse relaxation time T of the i-th relaxation component2iThe formula of (1) is as follows:
finally, according to T2iAnd determining an inversion coefficient matrix.
In the embodiment of the invention, the user can define the average value by the index or the logarithm according to the userDetermining the transverse relaxation time T of the ith relaxation component2i. For more reasonable establishment of the inversion coefficient matrix, in one possible embodiment, the inversion coefficient matrix is based on T2iDetermining an inversion coefficient matrix, comprising:
firstly, receiving an echo interval value Te, an echo start sequence number Is and an echo end sequence number Ie, an echo polarization time Tw and a ratio T of a longitudinal relaxation time to a transverse relaxation time which are input by a user12R。
Secondly, calculating each time point t of the echo according to the echo interval value Te, the echo start sequence number Is and the echo end sequence number Isk. Wherein,
tk＝Te*k k＝Is,...,Ie；
and calculating to obtain each time point of the echo.
Thirdly, according to the echo polarization time Tw and the ratio T of the longitudinal relaxation time to the transverse relaxation time12RCalculating the polarization correction Pck,i. Wherein,
and calculating to obtain a polarization correction value.
Finally, the time points t are determined according to the echokAnd polarization correction amount Pck,iAnd determining an inversion coefficient matrix. Wherein,
in the above embodiment, each time point t of the echo Is calculated by receiving the echo interval value Te, the echo start sequence number Is and the end sequence number Is which are input by the user according to the actual situationkEcho polarization time Tw and ratio T of longitudinal relaxation time to transverse relaxation time inputted by user according to actual situation12RCalculating the polarization correction Pck,i(ii) a Finally according toEcho at each time tkAnd polarization correction amount Pck,iThe inversion coefficient matrix is determined, and the inversion coefficient matrix is determined in the above mode, so that the inversion matrix is prevented from being established back and forth for each processing point of each group of echoes in the actual measurement process, a large amount of time is saved, and the calculation speed is improved.
In this step, in order to introduce the measured data Y, the inversion coefficient matrix X is respectively extended by the collected multiple sets of echo data to obtain an extended inversion coefficient matrix, and a matrix equation XP is established as Y, where P is an initial amplitude P of the transverse relaxation component. Aiming at the processing process of multiple groups of echo data, the inversion coefficient matrix needs to be expanded according to a certain group of echo data respectively, the initial amplitude P of the transverse relaxation component of the group of echo data is obtained through calculation, then the data of other groups are processed in sequence until all the inversion of the echo data of each group is completed, and finally the initial amplitude P of the transverse relaxation component of all the groups of echo data is obtained. Taking a group of echo data as an example, the following describes that the inversion coefficient matrix is expanded according to the group of echo data to obtain an expanded inversion coefficient matrix.
Optionally, the obtaining the expanded inversion coefficient matrix by respectively expanding the inversion coefficient matrix according to the multiple sets of echo data includes:
firstly, matrix transformation is carried out on the inversion coefficient matrix to obtain a transformed inversion coefficient matrix.
In order to improve the calculation speed, matrix transformation is carried out on the established inversion coefficient X matrix, the inversion dimension is reduced, and a matrix A after each group of matrix transformation is calculated, wherein the specific formula is as follows:
A＝XTX
wherein, the matrix XTFor the transposition of matrix X by matrix XTAnd multiplication of matrix X, dimension reduction of matrix X of k rows NOC columns to dimension (Noc ) square matrix.
And then, according to the multiple groups of echo data, performing expansion processing on the transformed inversion coefficient matrix to obtain an expanded inversion coefficient matrix.
By adding measured data, the transformed inversion coefficient matrix A is expanded to a matrix AA, specifically four matrix blocks, and the processing process is as follows:
(1) taking a set of echo data Yk。
Knowing the inversion coefficient matrix X and the echo data Y, the initial amplitude P of the transverse relaxation component is solved according to the matrix equation XP ═ Y. In the formula: p ═ P (P)0,p1,……,pi)；Y＝(y1,y2,……,yk)。
(2) And expanding the matrix AA, namely obtaining the matrix of the upper left block:
AAi,j＝Ai,j；
(3) the expansion matrix AA right column yields:
AAi,Noc+1＝Xk,i×Yk；
(4) the lower row of the extended matrix AA is obtained, and the lower row is symmetric to the right column:
AANoc+1,i＝AAi,Noc+1 T；
(5) the expansion matrix AA bottom right point is found:
AANoc+1,Noc+1＝Yk×Yk；
wherein, i 1., Noc, j 1., Noc.
Xp-Y transposition matrix X with two sides multiplied by X simultaneouslyTObtaining:
XTXP＝XTY
transformed matrix a ═ XTX, after expansion, forming a block matrix, wherein
A11＝XTX；
A12＝XTY；
Wherein, i is 1,2, …, n
In order to remove noise, the mode smoothing processing is carried out on the expanded matrix AA, the resolution of a T2 spectrum is adjusted, the main diagonal of the AA is expanded, and a damping factor α is added.
AAi,i＝Ai,i+αi＝1,...,Noc，j＝1,...,Noc。
The damping factor α can be set according to the echo signal-to-noise ratio of each group, or can be set according to user input parameters, or can be set together with the user input parameters according to the echo signal-to-noise ratio of each group, wherein the larger the signal-to-noise ratio is, the larger the damping factor α is added.
According to the embodiment of the T2 spectrum inversion method provided by the invention, all measured data are introduced, the transformed inversion coefficient matrix is subjected to expansion processing, the expanded inversion coefficient matrix is obtained, the influence of operations such as filtering, sampling and artificial dimension reduction on the processing result is avoided, and the accuracy of T2 spectrum inversion is improved.
And step 104, determining the initial amplitude P of the transverse relaxation component according to the expanded inversion coefficient matrix.
In this step, the initial amplitude P of the transverse relaxation component is determined according to the expanded inversion coefficient matrix, that is, a matrix equation XP ═ Y is solved according to the inversion coefficient matrix X and the actually measured data Y, and finally, the least square solution of the matrix equation XP ═ Y is determined, that is, the initial amplitude P of the transverse relaxation component is determined.
Wherein P has a physical meaning since each value of the P component is non-negativei0 means that some component is not present and presence must be positive, thus requiring the solution of the matrix equation to be non-negative.
Optionally, determining an initial amplitude P of the transverse relaxation component according to the expanded inversion coefficient matrix includes:
firstly, forward scanning is carried out on all diagonal elements in the expanded inversion coefficient matrix by adopting a forward scanning operator to obtain a forward scanning result.
Let AA be a square matrix (a)ij) The kth element a of the diagonalkkNot equal to 0, scanning the matrix AA on the kth element of the diagonal to obtain a new matrix with the same size
The elements are as follows:
wherein i ≠ k, and j ≠ k. The result of the forward scan is an initial amplitude P of the transverse relaxation where a negative solution may exist.
Secondly, whether a negative solution exists in the positive scanning result is judged.
In the process of solving by scanning all diagonal elements of the matrix AA by using the forward scanning operator, negative solutions may exist, and in practical significance, each value of the P component is not negative, and if P is not negative, the P component is meaningfuli0 means that some component is not present, if pi>0, then indicates that some component is present.
For the block matrix AA, if in arbitrary order, in the sub-square matrix A11Is scanned, i.e. all elements of the scan are non-zero, then a11Non-singular, the scan result can be represented by the following matrix:
and thirdly, if the negative solution exists, determining the serial number of the main diagonal element corresponding to the negative solution.
By adopting a forward scanning operator, carrying out forward scanning on diagonal elements in the expanded inversion coefficient matrix to obtain all solutions of a matrix equation, including a positive solution, a negative solution and a zero solution, wherein in an actual problem, the negative solution has no significance, and if the negative solution exists, the serial number of a main diagonal element corresponding to the negative solution is determined; and carrying out negative scanning according to the serial numbers of the main diagonal elements corresponding to the negative solutions to obtain negative scanning results, and updating the positive scanning results until all the negative solutions are removed.
And finally, determining the initial amplitude P of the transverse relaxation component according to the serial number of the main diagonal element corresponding to the negative solution.
And according to the sequence number of the main diagonal element corresponding to the determined negative solution, removing the solution obtained by scanning the diagonal element of the corresponding sequence number by the positive scanning operator, eliminating the negative solution, ensuring the non-negativity of the P component, and finally determining the initial amplitude P of the transverse relaxation component.
Optionally, determining an initial amplitude P of the transverse relaxation component according to the sequence number of the main diagonal element corresponding to the negative solution, includes:
step A: and according to the sequence number of the main diagonal element corresponding to the first largest negative solution in the negative solutions, performing negative scanning on the element corresponding to the sequence number by using a negative scanning operator to obtain a negative scanning result.
And scanning the elements corresponding to the sequence numbers by adopting a negative scanning operator according to the sequence numbers of the main diagonal elements corresponding to the first maximum negative solution in the negative solutions, wherein the scanning formula is as follows:
where i ≠ k, j ≠ k. And the negative scanning result of the main diagonal element which is subjected to negative scanning is that the solution of the corresponding sequence number of the main diagonal element is zero.
The main diagonal element corresponding to the negative solution is firstly solved by positive scanning through a positive scanning operator, and then is restored by negative scanning through a negative scanning operator, which is equivalent to that the main diagonal element corresponding to the negative solution is not scanned, and the element (variable) is excluded from participating in matrix equation solving, namely equivalent to that the element is 0 solution.
And B: and B, judging whether negative solutions exist in the negative scanning results, if so, determining a second maximum negative solution in the negative scanning results as a new first maximum negative solution, and repeatedly executing the steps A-B until no negative solution exists in the negative scanning results.
And B, negatively scanning the main diagonal element corresponding to the first maximum negative solution through the step A, updating the solution of P, determining the second maximum negative solution as the first maximum negative solution from the updated scanning result, and repeatedly executing the step A-the step B until no negative value exists in the solution of P, namely no negative solution exists in the negative scanning result. After scanning, a matrix is obtained:
and finally, determining the initial amplitude P of the transverse relaxation component according to the negative scanning result.
Obtaining the matrix according to the result after scanning
I.e., the least squares solution to the equation XP — Y, the initial amplitude P of the transverse relaxation component is determined.
According to the T2 spectrum inversion method provided by the embodiment of the invention, the inversion coefficient matrix is determined according to the point distribution data input by a user, so that the inversion matrix is prevented from being established back and forth according to each processing point in echo parameters, then, multiple groups of echo parameters are collected, the inversion coefficient matrix is expanded according to the multiple groups of echo parameters, the expanded inversion coefficient matrix is obtained, finally, the initial amplitude P of the transverse relaxation component is determined according to the expanded inversion coefficient matrix, and the inversion of the T2 spectrum is realized. Because the inversion coefficient matrix is established, the efficiency of T2 spectrum inversion is improved, and in the solving process, all measured data are added to expand the inversion coefficient matrix, so that the accuracy of T2 spectrum inversion is improved.
Fig. 2 is a schematic structural diagram of a T2 spectrum inversion algorithm device according to an embodiment of the present invention, where the T2 spectrum inversion algorithm device may be an independent server or a device integrated in a server, and the device may be implemented by software, hardware, or a combination of software and hardware. As shown in fig. 2, the apparatus includes:
a receiving module 21, configured to receive point distribution data input by a user;
a determining module 22, configured to determine an inversion coefficient matrix according to the stationing data;
the processing module 23 is configured to acquire multiple sets of echo data, and respectively perform expansion processing on the inversion coefficient matrix according to the multiple sets of echo data to obtain an expanded inversion coefficient matrix;
the determining module 22 is further configured to determine an initial amplitude P of the transverse relaxation component according to the extended inversion coefficient matrix.
According to the T2 spectrum inversion algorithm device provided by the embodiment of the invention, point distribution data input by a user are received through a receiving module, an inversion coefficient matrix is determined through a determining module according to the point distribution data, an inversion matrix is prevented from being established back and forth in echo parameters according to each processing point, then a plurality of groups of echo parameters are acquired by an acquisition and expansion module, the inversion coefficient matrix is expanded according to the echo parameters to obtain an expanded inversion coefficient matrix, and finally the initial amplitude P of a transverse relaxation component is determined according to the expanded inversion coefficient matrix according to a calculating module. Because the inversion coefficient matrix is established, the efficiency of T2 spectrum inversion is improved, and in the solving process, all measured data are added to expand the inversion coefficient matrix, so that the accuracy of T2 spectrum inversion is improved.
Fig. 3 is a schematic structural diagram of a second embodiment of a T2 spectrum inversion algorithm apparatus according to an embodiment of the present invention, and based on the embodiment of fig. 2, as shown in fig. 3, in a possible implementation manner, the determining module 32 includes:
a receiving submodule 321 for receiving the logarithmic minimum T input by the user2minSum logarithmic maximum T2max；
A determination submodule 322 for determining the logarithmic minimum T from the stationing data2minSum logarithmic maximum T2maxDetermining the transverse relaxation time T of the ith relaxation component2i；
A determination submodule 322 for determining2iAnd determining an inversion coefficient matrix.
In another possible implementation, as also shown in fig. 3, the determining module includes:
a receiving submodule for receiving the index minimum value T input by the user2eminAnd exponential step increment Δ T2e；
A determining submodule for determining the minimum value T of the index according to the stationing data2eminAnd exponential step increment Δ T2eDetermining the transverse relaxation time T of the ith relaxation component2i；
A determination submodule for determining the value of T2iAnd determining an inversion coefficient matrix.
Optionally, the determining submodule is specifically configured to:
receiving an echo interval value Te, an echo start sequence number Is and an echo end sequence number Ie, an echo polarization time Tw and a ratio T of longitudinal relaxation time to transverse relaxation time input by a user12R；
Calculating each time point t of the echo according to the echo interval value Te, the echo start sequence number Is and the end sequence number Isk；
According to the echo polarization time Tw and the ratio T of longitudinal relaxation time to transverse relaxation time12RCalculating the polarization correction Pck,i；
From the echo at the respective time tkAnd polarization correction amount Pck,iAnd determining an inversion coefficient matrix.
Optionally, the processing module is specifically configured to:
performing matrix transformation on the inversion coefficient matrix to obtain a transformed inversion coefficient matrix;
and according to the multiple groups of echo data, performing expansion processing on the transformed inversion coefficient matrix to obtain an expanded inversion coefficient matrix.
Fig. 4 is a schematic structural diagram of a third embodiment of a T2 spectrum inversion algorithm apparatus according to the present invention, and based on fig. 2 or fig. 3, optionally, the determining module 42 includes:
the scanning submodule 421 is configured to perform forward scanning on all elements of a diagonal line in the expanded inversion coefficient matrix by using a forward scanning operator to obtain a forward scanning result;
a judging submodule 422, configured to judge whether a negative solution exists in the forward scanning result;
the determining submodule 423 is configured to determine, when the determining submodule determines that a negative solution exists, a sequence number of a main diagonal element corresponding to the negative solution;
the determining sub-module 423 is further configured to determine an initial amplitude P of the transverse relaxation component according to the sequence number of the main diagonal element corresponding to the negative solution.
Optionally, the determining submodule is specifically configured to:
step A: according to the sequence number of the main diagonal element corresponding to the first largest negative solution in the negative solutions, performing negative scanning on the element corresponding to the sequence number by using a negative scanning operator to obtain a negative scanning result;
and B: judging whether negative solutions exist in the negative scanning results, if so, determining a second maximum negative solution in the negative scanning results as a new first maximum negative solution, and repeatedly executing the steps A-B until no negative solution exists in the negative scanning results;
and C: from the negative scan results, the initial amplitude P of the transverse relaxation component is determined.
Fig. 5 is a schematic structural diagram of a server according to an embodiment of the present invention. The server includes: a processor; a memory and a computer program, wherein the computer program is stored in the memory and configured to be executed by the processor, the computer program comprising instructions for performing the method of any of the embodiments above.
An embodiment of the present invention further provides a computer-readable storage medium, where the computer-readable storage medium stores a computer program, and the computer program enables a server to execute the data query method provided in any of the foregoing embodiments. The readable storage medium may be implemented by any type of volatile or non-volatile memory device or combination thereof, such as Static Random Access Memory (SRAM), electrically erasable programmable read-only memory (EEPROM), erasable programmable read-only memory (EPROM), programmable read-only memory (PROM), read-only memory (ROM), magnetic memory, flash memory, magnetic or optical disk.
Those of ordinary skill in the art will understand that: all or a portion of the steps of implementing the above-described method embodiments may be performed by hardware associated with program instructions. The program may be stored in a computer-readable storage medium. When executed, the program performs steps comprising the method embodiments described above; and the aforementioned storage medium includes: various media that can store program codes, such as ROM, RAM, magnetic or optical disks.
Finally, it should be noted that: the above embodiments are only used to illustrate the technical solution of the present invention, and not to limit the same; while the invention has been described in detail and with reference to the foregoing embodiments, it will be understood by those skilled in the art that: the technical solutions described in the foregoing embodiments may still be modified, or some or all of the technical features may be equivalently replaced; and the modifications or the substitutions do not make the essence of the corresponding technical solutions depart from the scope of the technical solutions of the embodiments of the present invention.
Claims (10)
1. A method of T2 spectral inversion, comprising:
receiving stationing data input by a user;
determining an inversion coefficient matrix according to the point distribution data;
collecting a plurality of groups of echo data, and respectively performing expansion processing on the inversion coefficient matrix according to the plurality of groups of echo data to obtain an expanded inversion coefficient matrix;
and determining the initial amplitude P of the transverse relaxation component according to the expanded inversion coefficient matrix.
2. The method of claim 1, wherein determining an inversion coefficient matrix from the stationing data comprises:
receiving a user-entered logarithmic minimum T2minSum logarithmic maximum T2max；
According to the point distribution data and the logarithm minimum value T2minAnd said logarithmic maximum T2maxDetermining the transverse relaxation time T of the ith relaxation component2i；
According to the T2iAnd determining the inversion coefficient matrix.
3. The method of claim 1, wherein determining an inversion coefficient matrix from the stationing data comprises:
receiving a user-entered exponential minimum value T2eminAnd exponential step increment Δ T2e；
According to the distribution data and the index minimum value T2eminAnd the exponential step increment Δ T2eDetermining the transverse relaxation time T of the ith relaxation component2i；
According to the T2iAnd determining the inversion coefficient matrix.
4. Method according to claim 2 or 3, characterized in that said method is based on said T2iDetermining the matrix of inversion coefficients, comprising:
receivingEcho interval value Te, echo starting sequence number Is and ending sequence number Ie, echo polarization time Tw and ratio T of longitudinal relaxation time to transverse relaxation time input by user12R；
Calculating each time point t of the echo according to the echo interval value Te, the echo starting sequence number Is and the end sequence number Isk；
According to the echo polarization time Tw and the ratio T of the longitudinal relaxation time to the transverse relaxation time12RCalculating the polarization correction Pck,i；
According to each time point t of the echokAnd said polarization correction amount Pck,iAnd determining the inversion coefficient matrix.
5. The method according to any one of claims 1 to 3, wherein the respectively performing expansion processing on the inversion coefficient matrix according to the multiple sets of echo data to obtain an expanded inversion coefficient matrix comprises:
performing matrix transformation on the inversion coefficient matrix to obtain a transformed inversion coefficient matrix;
and according to the multiple groups of echo parameters, performing expansion processing on the transformed inversion coefficient matrix to obtain the expanded inversion coefficient matrix.
6. The method according to any of claims 1-3, wherein said determining an initial amplitude P of a transverse relaxation component from said augmented matrix of inversion coefficients comprises:
adopting a forward scanning operator to perform forward scanning on all diagonal elements in the expanded inversion coefficient matrix to obtain a forward scanning result;
judging whether a negative solution exists in the positive scanning result;
if the negative solution exists, determining the sequence number of the main diagonal element corresponding to the negative solution;
and determining the initial amplitude P of the transverse relaxation component according to the sequence number of the main diagonal element corresponding to the negative solution.
7. The method according to claim 6, wherein said determining an initial amplitude P of a transverse relaxation component from the sequence number of the main diagonal element corresponding to said negative solution comprises:
step A: according to the sequence number of the main diagonal element corresponding to the first largest negative solution in the negative solutions, performing negative scanning on the element corresponding to the sequence number by using a negative scanning operator to obtain a negative scanning result;
and B: judging whether negative solutions exist in the negative scanning result, if so, determining a second maximum negative solution in the negative scanning result as a new first maximum negative solution, and repeatedly executing the steps A-B until no negative solution exists in the negative scanning result;
and C: and determining the initial amplitude P of the transverse relaxation component according to the negative direction scanning result.
8. A T2 spectral inversion apparatus, comprising:
the receiving module is used for receiving the point distribution data input by the user;
the determining module is used for determining an inversion coefficient matrix according to the stationing data;
the processing module is used for acquiring a plurality of groups of echo data and respectively expanding the inversion coefficient matrix according to the plurality of groups of echo data to obtain an expanded inversion coefficient matrix;
the determining module is further configured to determine an initial amplitude P of the transverse relaxation component according to the extended inversion coefficient matrix.
9. A server, comprising:
a processor;
a memory; and
a computer program;
wherein the computer program is stored in the memory and configured to be executed by the processor, the computer program comprising instructions for performing the method of any of claims 1-7.
10. A computer-readable storage medium, characterized in that it stores a computer program that causes a server to execute the method of any one of claims 1-7.
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