Nuclear magnetic resonance relaxation spectrum resolving method and device, computer device and storage medium

Abstract

The embodiment of the application provides a nuclear magnetic resonance relaxation spectrum deconvolution method and device, computer equipment and a storage medium, and particularly relates to the technical field of nuclear magnetic resonance. The nuclear magnetic resonance relaxation spectrum deconvolution method comprises the following steps: obtaining nuclear magnetic resonance data, and constructing a non-negative constraint target function model based on the low rank and sparsity of the nuclear magnetic resonance relaxation spectrum; decomposing the non-negative constraint target function model; obtaining a relaxation spectrum nuclear norm solution, a relaxation spectrum sparse solution and a relaxation spectrum residual error solution; iteratively updating the non-negative constraint target function model, determining a final solution and a final relaxation spectrum corresponding to the final solution, and outputting the final relaxation spectrum. The nuclear magnetic resonance relaxation spectrum deconvolution method controls the resolution of the relaxation spectrum by using the sparsity of the relaxation spectrum when solving the spectrum sparse function model, and controls the accuracy of the graph spectrum by using the residual term when solving the residual norm function model, thereby improving the resolution of the obtained final relaxation spectrum, and solving the problem of low resolution of the relaxation spectrum obtained by the existing inversion method.

Description

Technical Field

[0001] This application relates to the field of oilfield development technology, and more particularly to the field of nuclear magnetic resonance technology. This application provides a nuclear magnetic resonance relaxation spectrum interpretation method, apparatus, computer equipment, and storage medium. Background Technology

[0002] Nuclear magnetic resonance (NMR) can directly detect and accurately acquire important reservoir parameters such as fluid molecules, pore structure, reservoir permeability, fluid mobility, fluid properties, and wettability. However, NMR detection methods require NMR inversion of the acquired NMR data. The inversion spectral solution process involves solving an objective function through NMR inversion to obtain the NMR relaxation spectrum.

[0003] Currently, among existing technologies, the most widely used method is the objective function optimization inversion spectrum solution based on regularization.

[0004] However, the inventors have found that the existing technology has at least the following technical problems: When processing nuclear magnetic resonance data with complex fluid composition information, the redundancy of the relaxation spectrum due to the complexity of the fluid composition indicates the spurious peak characteristics caused by the uncertainty of inversion. The relaxation spectrum obtained from the feature acquisition is prone to being too sparse or too smooth, resulting in the problem of low resolution of the relaxation spectrum obtained by inversion. Summary of the Invention

[0005] This application provides a method, apparatus, computer equipment, and storage medium for interpreting nuclear magnetic resonance relaxation spectra, in order to improve the resolution of the obtained relaxation spectra.

[0006] Firstly, this application provides a method for interpreting nuclear magnetic resonance relaxation spectra, including:

[0007] Acquire nuclear magnetic resonance (NMR) data and construct a non-negative constrained objective function model based on the low-rank and sparsity of NMR relaxation spectra;

[0008] The nonnegativity constraint objective function model is decomposed into a matrix low-rank function model, a spectral sparse function model, and a residual norm function model;

[0009] The nuclear magnetic resonance data are substituted into the matrix low-rank function model, the spectral sparse function model and the residual norm function model according to the preset calculation method for iterative updates, to obtain the relaxation spectrum nuclear norm solution, the relaxation spectrum sparse solution and the relaxation spectrum residual solution respectively;

[0010] The non-negative constraint objective function model is iteratively updated based on the relaxation spectrum nuclear norm solution, the relaxation spectrum sparse solution, and the relaxation spectrum residual solution to determine the final solution and the final relaxation spectrum corresponding to the final solution, and then output them.

[0011] In one possible implementation, the construction of the nonnegativity-constrained objective function model based on the low-rank and sparsity of the nuclear magnetic resonance relaxation spectrum includes:

[0012] Acquire transverse relaxation time measurement data and construct the first signal response equation for one-dimensional transverse relaxation time measurement; acquire two-dimensional longitudinal-transverse relaxation time measurement data and construct the second signal response equation for two-dimensional longitudinal-transverse relaxation time measurement.

[0013] The transverse relaxation time measurement data is discretized into vector data to obtain the first discretized equation of the first signal response equation. The two-dimensional longitudinal-transverse relaxation time measurement data is discretized into vector data to obtain the second discretized equation of the second signal response equation. Based on the first and second discretized equations, the matrix model to be solved is determined.

[0014] The matrix model to be solved is transformed into a first non-negative model to be solved, and an application is made to the solution of the first non-negative model to be solved. Regularization constraints yield the second non-negative model to be solved.

[0015] The second nonnegative model to be solved is subjected to nonnegative low-rank and sparsity constraints to obtain the third nonnegative model to be solved.

[0016] Obtain the nuclear norm number variable, Normative variables and The residual variable, and based on the nuclear norm variable, Normative variables and The residual variable transforms the third non-negative unsolved model into a constrained unsolved model.

[0017] Based on the augmented Lagrangian function, the constrained model to be solved is transformed into a non-negative constrained objective function model.

[0018] In one possible implementation, the first signal response equation is:

[0019]

[0020] In the formula, To obtain the time point for the lateral relaxation time data, For measurement Signal strength at time , For the lateral relaxation time, for The result obtained by the inverse Laplace transform Measurement noise is used to obtain the transverse relaxation time measurement data;

[0021] The second signal response equation is:

[0022]

[0023] In the formula, The longitudinal relaxation time is the time specified in the longitudinal-lateral relaxation measurement time data. The lateral relaxation time is the value in the longitudinal-lateral relaxation time measurement data. To obtain the time points for the longitudinal-lateral relaxation measurement time data, The first preset waiting time, The measured waiting time Interval Signal strength at time , for The result obtained by inverse Placian transform Measurement noise during the acquisition of the longitudinal-lateral relaxation measurement time data;

[0024] The first discretization equation is:

[0025]

[0026] In the formula, The amplitude of the echo signal of the transverse relaxation time measurement data. ,in The number of discrete relaxation times. , Number of echoes The time for collecting the lateral relaxation time data. The first of the upper and lower boundaries of the constraint A horizontal relaxation time component The maximum lateral relaxation time. This is the minimum lateral relaxation time. Measurement noise during the acquisition of the transverse relaxation time data For the first The amplitude of each horizontal relaxation time component;

[0027] The second discretization equation is:

[0028]

[0029] In the formula, Discrete longitudinal relaxation time The number of components, ,in, A natural number greater than or equal to 1. Discrete transverse relaxation time The number of components, The amplitude of the echo signal of the longitudinal-lateral relaxation time measurement data. This is the second preset waiting time. Two-dimensional The amplitude of the relaxation spectrum Measurement noise during the acquisition of the longitudinal-lateral relaxation time measurement data, The first of the upper and lower boundaries of the constraint A longitudinal relaxation time component The first of the upper and lower boundaries of the constraint One horizontal relaxation time component;

[0030] The model of the matrix to be solved is:

[0031]

[0032] In the formula, The amplitude vector of the echo. Given the kernel matrix, This represents the noise amplitude during echo acquisition. The solution is non-negative.

[0033] The first non-negative model to be solved is:

[0034]

[0035] In the formula, For matrix nuclear norm number, This indicates that the constraints are satisfied. ;

[0036] The second nonnegative model to be solved is:

[0037]

[0038] In the formula, To make the matrix The variable at which the nuclear norm reaches its minimum value. To be solved nuclear norm number, For adjustment Preset parameters for regularization weights;

[0039] The third non-negative model to be solved is:

[0040]

[0041] In the formula, For preset Regularization parameters, For preset Regularization parameters, Transformation operators for converting vectors to matrices;

[0042] The constrained model to be solved is:

[0043]

[0044]

[0045] In the formula, The constraints are as follows: ,in, for residual variable, For nuclear norm variables, for Normative variable;

[0046] The non-negativity constraint objective function model is as follows:

[0047]

[0048]

[0049]

[0050] In the formula, All are Lagrange multipliers. for The inner product, for and The inner product, for The inner product, The step size for iterative updates, To and corresponding Norm operator, To and The square of the corresponding norm operator, To and corresponding The square of the norm operator.

[0051] In one possible implementation, the step of substituting the nuclear magnetic resonance data into the matrix low-rank function model, the spectral sparse function model, and the residual norm function model according to a preset calculation method for iterative updates, to obtain the relaxation spectrum nuclear norm solution, the relaxation spectrum sparse solution, and the relaxation spectrum residual solution, respectively, includes:

[0052] By fixing the other variables in the non-negativity constraint objective function model, the nuclear norm number variables are iteratively updated based on the nuclear magnetic resonance data to obtain the relaxation spectrum nuclear norm number solution.

[0053] By fixing the other variables in the non-negativity constraint objective function model, the norm term variable is iteratively updated based on the nuclear magnetic resonance data to obtain the relaxation spectrum sparse solution.

[0054] With other variables fixed in the nonnegativity constraint objective function model, the nuclear magnetic resonance data is used to analyze the... The residual variable is iteratively updated to obtain the relaxation spectrum residual solution;

[0055] If the difference between the maximum value of the relaxation spectrum nuclear norm solution, relaxation spectrum sparse solution, and relaxation spectrum residual solution obtained in the previous update and the maximum value of the relaxation spectrum nuclear norm solution, relaxation spectrum sparse solution, and relaxation spectrum residual solution obtained in the next update is less than a preset threshold, then the iterative update stops.

[0056] In one possible implementation, the step of iteratively updating the non-negative constraint objective function model based on the relaxation spectrum kernel norm solution, the relaxation spectrum sparse solution, and the relaxation spectrum residual solution, determining the final solution and the final relaxation spectrum corresponding to the final solution, and outputting them includes:

[0057] Each time, the nuclear magnetic resonance data is substituted into the matrix low-rank function model, the spectral sparse function model, and the residual norm function model according to a preset calculation method for iterative updating, resulting in the relaxation spectrum nuclear norm solution, the relaxation spectrum sparse solution, and the relaxation spectrum residual solution.

[0058] Fixing the other variables in the non-negative constraint objective function model, the relaxation spectrum nuclear norm solution, the relaxation spectrum sparse solution and the relaxation spectrum residual solution are substituted into the non-negative constraint objective function model for iterative updating to obtain the solution to be solved, and the solution to be solved is converted into the form of matrix-vector multiplication and summation;

[0059] The nuclear magnetic resonance relaxation spectrum is determined based on the solution in the form of matrix-vector product and summation.

[0060] Based on the confidence interval of the area integral value of the nuclear magnetic resonance relaxation spectrum, update the learning rate, iteration step size and iteration number for each iteration;

[0061] If the area integral value of the relaxation spectrum is determined to meet the preset confidence threshold, then the solution to be solved is taken as the final solution, and the nuclear magnetic resonance relaxation spectrum is taken as the final relaxation spectrum and output.

[0062] In one possible implementation, the formula for determining whether the relaxation spectrum area integral value satisfies a preset confidence threshold is:

[0063]

[0064] In the formula, The area integral value of the nuclear magnetic resonance relaxation spectrum is given. This represents the maximum amplitude of the echo signal in the nuclear magnetic resonance data.

[0065] In one possible implementation, acquiring nuclear magnetic resonance data includes:

[0066] Acquire raw nuclear magnetic resonance echo train data;

[0067] If the original nuclear magnetic resonance echo train data is determined to be two-dimensional or multi-dimensional data, then the original nuclear magnetic resonance echo train data is converted into a one-dimensional numerical vector.

[0068] Secondly, this application provides a nuclear magnetic resonance relaxation spectrum interpretation device, comprising:

[0069] The acquisition module is used to acquire nuclear magnetic resonance data;

[0070] The model building module is used to construct a non-negative constraint objective function model based on the low rank and sparsity of nuclear magnetic resonance relaxation spectra.

[0071] The computation and solution module is used to decompose the non-negativity constraint objective function model into a matrix low-rank function model, a spectral sparse function model, and a residual norm function model.

[0072] The computation and solution module is also used to substitute the nuclear magnetic resonance data into the matrix low-rank function model, the spectral sparse function model and the residual norm function model according to the preset calculation method for iterative updates, so as to obtain the relaxation spectrum nuclear norm solution, the relaxation spectrum sparse solution and the relaxation spectrum residual solution respectively.

[0073] The computation and solution module is further used to iteratively update the non-negative constraint objective function model based on the relaxation spectrum nuclear norm solution, the relaxation spectrum sparse solution, and the relaxation spectrum residual solution, to determine the final solution and the final relaxation spectrum corresponding to the final solution and output them.

[0074] Thirdly, this application provides a computer device, including: at least one processor and a memory;

[0075] The memory stores computer-executed instructions;

[0076] The at least one processor executes computer execution instructions stored in the memory, causing the at least one processor to perform the method as described in the first aspect above.

[0077] Fourthly, this application provides a computer-readable storage medium storing an instruction to be executed by a computer, which, when executed by a processor, implements the method described in the first aspect above.

[0078] This application provides a method, apparatus, computer equipment, and storage medium for interpreting nuclear magnetic resonance (NMR) relaxation spectra. After acquiring NMR data, a non-negative constraint objective function model is constructed based on the low-rank and sparsity properties of the NMR relaxation spectrum. This model is then decomposed into three sub-problems: a matrix low-rank function model, a spectral sparse function model, and a residual norm function model. The solutions to these three sub-problems are used to update the non-negative constraint objective function model, yielding the final solution and the corresponding final relaxation spectrum output. Throughout the interpretation process, features of the relaxation spectrum are extracted and redundant interference is removed during the solution of the matrix low-rank function model. The sparsity of the relaxation spectrum is used to control the resolution of the relaxation spectrum during the solution of the spectral sparse function model. The residual term is used to control the accuracy of the spectrum during the solution of the residual norm function model, thereby improving the resolution of the final relaxation spectrum. Attached Figure Description

[0079] To more clearly illustrate the technical solutions in the embodiments of this application or the prior art, the drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are some embodiments of this application. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0080] Figure 1 A schematic diagram illustrating the application scenario of the nuclear magnetic resonance relaxation spectrum interpretation method provided in the embodiments of this application;

[0081] Figure 2 A schematic flowchart illustrating the nuclear magnetic resonance relaxation spectrum interpretation method provided in this application embodiment;

[0082] Figure 3 This is a diagram of a transverse relaxation time spectrum model with bimodal characteristics.

[0083] Figure 4(a) shows the residual norm distribution under the condition of signal-to-noise ratio = 100;

[0084] Figure 4(b) shows the residual norm distribution under the condition of signal-to-noise ratio = 50;

[0085] Figure 4(c) shows the residual norm distribution under the condition of signal-to-noise ratio = 20;

[0086] Figure 4(d) shows the residual norm distribution under the condition of signal-to-noise ratio = 10;

[0087] Figure 5(a) is a schematic diagram of the inversion results under the condition of signal-to-noise ratio = 100;

[0088] Figure 5(b) is a schematic diagram of the inversion results under the condition of signal-to-noise ratio = 50;

[0089] Figure 5(c) is a schematic diagram of the inversion results under the condition of signal-to-noise ratio = 20;

[0090] Figure 5(d) is a schematic diagram of the inversion results under the condition of signal-to-noise ratio = 10;

[0091] Figure 6(a) is a schematic diagram of the forward model obtained based on the fluid relaxation parameters and pulse sequence acquisition parameters;

[0092] Figure 6(b) is a schematic diagram of the longitudinal-lateral relaxation time correlation spectrum obtained by the spectral decomposition method in the prior art;

[0093] Figure 6(c) is a schematic diagram of the longitudinal-lateral relaxation time correlation spectrum obtained by the nuclear magnetic resonance relaxation spectrum despectroscopy method provided in the embodiment of this application;

[0094] Figure 7 A schematic diagram of a nuclear magnetic resonance relaxation spectrum interpretation device provided in this application embodiment;

[0095] Figure 8 A schematic diagram of the hardware structure of a computer device is provided for the embodiments of this application. Detailed Implementation

[0096] To make the objectives, technical solutions, and advantages of the embodiments of this application clearer, the technical solutions of the embodiments of this application will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of this application, not all embodiments. Based on the embodiments of this application, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of this application.

[0097] Currently, nuclear magnetic resonance (NMR) can directly detect and accurately acquire important reservoir parameters such as fluid molecules, pore structure, reservoir permeability, fluid mobility, fluid properties, and wettability. NMR detection methods require NMR inversion of the acquired NMR data. The process of obtaining the NMR relaxation spectrum by solving the objective function after NMR inversion is called NMR relaxation spectrum interpretation. The inventors discovered that in existing technologies, the peak values ​​of the relaxation spectrum need to maintain a certain sparsity, and the shape of the relaxation spectrum needs to maintain a certain smoothness. However, existing inversion methods do not effectively balance these two aspects. Therefore, when using existing NMR relaxation spectrum inversion methods to process NMR signals with complex fluid composition information, excessive sparsity or excessive smoothness can occur, resulting in low resolution of the NMR relaxation spectrum obtained through interpretation.

[0098] To address the aforementioned technical problems, this application provides the following technical concept: First, based on the low rank and sparsity of the relaxation spectrum, a non-negative constraint objective function model is constructed. Then, the objective function model is decomposed into three sub-problems: the relaxation spectrum nuclear norm, the relaxation spectrum sparse norm, and the relaxation spectrum residual norm. The collected nuclear magnetic resonance data is then used to solve each of the three sub-problems simultaneously. During the solution process, the sparsity of the relaxation spectrum is used to control the spectrum resolution, and the residual term is used to control the spectrum accuracy. Finally, the solutions to the three sub-problems are used to update the objective function model, yielding the final solution for the spectrum, thereby improving the resolution of the obtained relaxation spectrum.

[0099] Figure 1 This is a schematic diagram illustrating an application scenario of the nuclear magnetic resonance relaxation spectrum interpretation method provided in the embodiments of this application, such as... Figure 1 As shown, it includes: terminal 101 and server 102.

[0100] The terminal 101 is used for users to input and view dialogue information. The server 102 is used to receive dialogue information transmitted from the cloud, other servers, or mobile devices, and to perform dialogue interactions.

[0101] Figure 2 This is a flowchart illustrating the nuclear magnetic resonance relaxation spectrum interpretation method. The execution entity in this embodiment can be... Figure 1 The server 102 in the illustrated embodiment can also be other computer devices, and no particular limitation is made to this embodiment.

[0102] like Figure 2 As shown, the nuclear magnetic resonance relaxation spectrum interpretation method includes the following steps:

[0103] S201: Acquire nuclear magnetic resonance data and construct a non-negative constraint objective function model based on the low rank and sparsity of the nuclear magnetic resonance relaxation spectrum.

[0104] In this embodiment, the nuclear magnetic resonance data can be echo train data, and the signal characteristics of the echo train data can be related to the number of echoes in the pulse sequence, the echo interval, and the physical and chemical properties of the fluid in the measurement environment.

[0105] In this embodiment, the low-rank property of the NMR relaxation spectrum is that the rank of the coefficient matrix of the image data of the NMR relaxation spectrum image in a transform domain is less than a fixed value. The sparsity property of the NMR relaxation spectrum is that most elements of the coefficient matrix of the image data of the NMR relaxation spectrum image in a certain transform domain are zero.

[0106] Specifically, in an optional embodiment of this application, a non-negativity-constrained objective function model is constructed based on the low-rank and sparsity of the nuclear magnetic resonance relaxation spectrum, including:

[0107] Step a: Obtain transverse relaxation time measurement data and construct the first signal response equation for one-dimensional transverse relaxation time measurement; obtain two-dimensional longitudinal-transverse relaxation time measurement data and construct the second signal response equation for two-dimensional longitudinal-transverse relaxation time measurement.

[0108] In this embodiment, the transverse relaxation time can be measured using a CPMG (Carr-Purcell-Meiboom-Gill) pulse sequence. Obtain transverse relaxation time measurement data, one-dimensional The signal attenuation in nuclear magnetic resonance (NMR) measurements conforms to a multi-exponential mathematical model, and the first signal response equation is an integral equation. Similarly, two-dimensional longitudinal-transverse relaxation time measurement data can be acquired using the CPMG pulse-charge sequence method, and the second response equation is an integral equation obtained using the CPMG pulse sequence method.

[0109] Step b: Discretize the transverse relaxation time measurement data into vector data to obtain the first discretized equation of the first signal response equation. Discretize the two-dimensional longitudinal-transverse relaxation time measurement data into vector data to obtain the second discretized equation of the second signal response equation. Based on the first and second discretized equations, determine the matrix model to be solved.

[0110] In this embodiment, data discretization divides the continuous attribute space into several regions by using a set of breakpoints, and ensures that instances in the same region have the same attributes. The first discretization equation is the discretized form of the first signal response equation, and the second discretization equation is the discretized form of the second signal response equation. The matrix model to be solved is a shared matrix model of the first and second discretization equations, and the conversion to a matrix model is based on the common contribution of each echo amplitude from different relaxation time components.

[0111] Step c: Transform the matrix model to be solved into a first non-negative model to be solved, and apply regularization constraints to the first non-negative model to be solved to obtain a second non-negative model to be solved.

[0112] In this embodiment, the first nonnegative model to be solved is the square root of the sum of squares of all vector elements in the matrix model to be solved. Therefore, the solution to the first nonnegative model is nonnegative. The regularization constraint is the square root of the sum of squares of all parameters in the model.

[0113] Step d: Apply non-negative low-rank and sparsity constraints to the solution of the second non-negative model to obtain the third non-negative model to be solved.

[0114] In this embodiment, the non-negative low-rank and sparsity constraints assume that the graph is sparse and low-rank and is transformed by a preset vector transformation matrix transformation operator.

[0115] Step e: Obtain the nuclear norm variable, norm variable, and residual variable, and based on the nuclear norm variable, norm variable, and residual variable, transform the third non-negative model to be solved into a constrained model to be solved.

[0116] Step f: Based on the augmented Lagrangian function, the constrained model to be solved is transformed into a non-negative constrained objective function model.

[0117] In this embodiment, the nuclear norm is the sum of the singular values ​​of the matrix, used to constrain the low rank of the matrix. Specifically, the norm term can be... The number of terms, among which, The norm is the sum of the absolute values ​​of the elements in a matrix or vector. The residual term represents the noise disturbance term, which can be specifically used... The sum of squared residuals calculated using the norm.

[0118] Furthermore, in an optional example of this application, the equations and function models used in steps a to f are described in more detail with reference to the embodiments.

[0119] In this embodiment, the first signal response equation is:

[0120]

[0121] In the formula, To obtain the time points for lateral relaxation time data, For measurement Signal strength at time , For the lateral relaxation time, for The result obtained by the inverse Laplace transform Measurement noise for obtaining transverse relaxation time measurement data.

[0122] The second signal response equation is:

[0123]

[0124] In the formula, The longitudinal relaxation time is the value in the longitudinal-lateral relaxation time measurement data. The lateral relaxation time is the value in the longitudinal-lateral relaxation time measurement data. To obtain the time points for the longitudinal-lateral relaxation time measurement data, The first preset waiting time, The measured waiting time Interval Signal strength at time , for The result obtained by inverse Placian transform Measurement noise when acquiring the longitudinal-lateral relaxation time measurement data.

[0125] The first discretization equation is:

[0126]

[0127] In the formula, The amplitude of the echo signal of the transverse relaxation time measurement data. ,in The number of discrete relaxation times. , Number of echoes The time of data acquisition for the transverse relaxation time measurement is denoted as tv. The first of the upper and lower boundaries of the constraint A horizontal relaxation time component The maximum lateral relaxation time. This is the minimum lateral relaxation time. Measurement noise during the acquisition of the transverse relaxation time measurement data. For the first The amplitude of each horizontal relaxation time component.

[0128] In this embodiment, the acquisition time of the lateral relaxation time data is... The echo interval is defined as follows, and the relaxation time of the sample under test is less than... At that time, this part of the signal will not be detected.

[0129] The second discretization equation is:

[0130]

[0131] In the formula, Discrete longitudinal relaxation time The number of components, ,in, A natural number greater than or equal to 1. Discrete transverse relaxation time The number of components, The amplitude of the echo signal of the longitudinal-lateral relaxation time measurement data. This is the second preset waiting time. Two-dimensional The amplitude of the relaxation spectrum Measurement noise during the acquisition of the longitudinal-lateral relaxation time measurement data, The first of the upper and lower boundaries of the constraint A longitudinal relaxation time component The first of the upper and lower boundaries of the constraint One horizontal relaxation time component.

[0132] The matrix model to be solved is:

[0133]

[0134] In the formula, The amplitude vector of the echo. Given the kernel matrix, This represents the noise amplitude during echo acquisition. The non-negative ones are to be solved.

[0135] In this embodiment, when measuring transverse relaxation time data, the known kernel matrix equation in the matrix model to be solved is: When performing longitudinal-lateral relaxation time data measurements, the known kernel matrix equation in the matrix model to be solved is: , where the symbol Represents the tensor product.

[0136] The first nonnegative model to be solved is:

[0137]

[0138] In the formula, For matrix nuclear norm number, This indicates that the constraints are satisfied. .

[0139] The second nonnegative model to be solved is:

[0140]

[0141] In the formula, To make the matrix The variable at which the nuclear norm reaches its minimum value. To be solved nuclear norm number, For adjustment Preset parameters for regularization weights.

[0142] The third nonnegative model to be solved is:

[0143]

[0144] In the formula, For preset Regularization parameters, For preset Regularization parameters, This is a transformation operator for converting vectors to matrices.

[0145] In this embodiment, the first term of the third non-negative model constrains the low-rank property of the relaxation spectrum. The second term of the third non-negative model constrains the sparsity of the relaxation spectrum. The third term of the third non-negative model constrains the accuracy of the relaxation spectrum and reflects the perturbation to be solved in the third non-negative model. Under the condition of low signal-to-noise ratio, the accuracy of some low-sacrifice solutions can be considered to ensure the sparsity of the spectral peaks, thereby improving the fluid identification capability.

[0146] In this embodiment, the problem is addressed as a one-dimensional problem. For a one-dimensional relaxation spectrum, This can be a Hankel matrix transformation operator, used to convert the solution of a one-dimensional problem into a two-dimensional matrix. For two-dimensional problems, It is a two-dimensional relaxation spectrum. This is a two-dimensional matrix transformation operator. For example, If the vector is 2500, then It is a two-dimensional relaxation spectrum of 50×50.

[0147] The constrained model to be solved is:

[0148]

[0149]

[0150] In the formula, The constraints are as follows: ,in, for residual variable, For nuclear norm variables, for Normative variable.

[0151] The non-negativity constraint objective function model is:

[0152]

[0153]

[0154]

[0155] In the formula, All are Lagrange multipliers. for The inner product, for and The inner product, for The inner product, The step size for iterative updates, To and corresponding Norm operator, To and The square of the corresponding norm operator, To and corresponding The square of the norm operator.

[0156] The above provides a detailed explanation of how to construct a non-negativity-constrained objective function model. The following section provides a detailed explanation of how to solve the non-negativity-constrained objective function model, combined with specific examples.

[0157] S202: Decompose the nonnegative constraint objective function model into a matrix low-rank function model, a spectral sparse function model, and a residual norm function model.

[0158] In this embodiment, the non-negativity constraint objective function model is:

[0159]

[0160]

[0161]

[0162] The formula contains three subproblems that need to be decomposed. The decomposition method can be the cross-directional multiplier method, specifically obtained from the decomposition. The low-rank matrix function model is a combination of the first and seventh terms of the non-negative constraint objective function model, as shown in the following equation:

[0163]

[0164] In this embodiment, the spectral sparse function model is a combination of the second and eighth terms of the non-negativity constrained objective function model, as shown in the following equation:

[0165]

[0166] In this embodiment, the residual norm model is a combination of the third and ninth terms of the non-negative constraint objective function model, as shown in the following equation:

[0167]

[0168] S203: Substitute the nuclear magnetic resonance data into the matrix low-rank function model, the spectral sparse function model, and the residual norm function model according to the preset calculation method, and iteratively update them to obtain the relaxation spectrum nuclear norm solution, the relaxation spectrum sparse solution, and the relaxation spectrum residual solution, respectively.

[0169] In this embodiment, the preset calculation method is to fix other variables and update only one variable, thereby updating and solving the subproblem. The preset calculation method can be a singular value thresholding algorithm or a shrinking soft thresholding algorithm used to obtain the relaxation kernel norm solution.

[0170] Specifically, in an optional embodiment of this application, S203 includes the following steps:

[0171] S203a: Fix other variables in the non-negative constraint objective function model, and iteratively update the nuclear norm number variable based on nuclear magnetic resonance data to obtain the relaxation spectrum nuclear norm number solution.

[0172] In this embodiment, when iteratively updating the nuclear norm variables, the variables need to be fixed. The relaxation spectrum nuclear norm solution is ,in, To minimize the nuclear norm operator, In the low-rank function model of a matrix The threshold of the norm operator It is one of several Lagrange multipliers.

[0173] S203b: Fix other variables in the non-negative constraint objective function model, and iteratively update the norm term variables based on nuclear magnetic resonance data to obtain the relaxation spectrum sparse solution.

[0174] In this embodiment, the norm term variable can be Normative variable, for When iterating over and updating the norm variable, the variable needs to be fixed. The relaxed spectrum sparse solution obtained by iterative update is , To minimize Operator, In the spectral sparse function model The threshold of the norm operator It is one of several Lagrange multipliers.

[0175] S203c: Other variables in the non-negativity constraint objective function model are fixed, and the model is based on NMR data. The residual variable is iteratively updated to obtain the relaxation spectrum residual solution.

[0176] In this embodiment, for When iteratively updating the residual variable, the variable needs to be fixed. The relaxation spectrum residual solution obtained by iterative update is , To minimize Operator, In the residual norm model Threshold of norm operator.

[0177] S203d: If the difference between the maximum value of the relaxation spectrum nuclear norm solution, relaxation spectrum sparse solution and relaxation spectrum residual solution obtained in the previous iteration update and the maximum value of the relaxation spectrum nuclear norm solution, relaxation spectrum sparse solution and relaxation spectrum residual solution obtained in the next update is less than a preset threshold, then stop the iteration update.

[0178] In this embodiment, the preset threshold is a value defined by the user. For example, the preset threshold could be... When the iterative update stops, it indicates that the optimal solution criterion has been reached.

[0179] S204: Iteratively update the non-negative constraint objective function model based on the relaxation spectrum nuclear norm solution, the relaxation spectrum sparse solution, and the relaxation spectrum residual solution, determine the final solution and the final relaxation spectrum corresponding to the final solution, and output them.

[0180] In this embodiment, the final solution is the solution obtained when performing the final iterative update on the non-negative constraint objective function model, and the final relaxation spectrum can be a one-dimensional relaxation spectrum and / or a multi-dimensional relaxation spectrum.

[0181] Specifically, in an optional embodiment of this application, S204 includes the following steps:

[0182] S204a: Obtain the relaxation spectrum nuclear norm solution, relaxation spectrum sparse solution, and relaxation spectrum residual solution by substituting the nuclear magnetic resonance data into the matrix low-rank function model, spectral sparse function model, and residual norm function model according to the preset calculation method for each iteration.

[0183] S204b: Fix other variables in the non-negative constraint objective function model, substitute the relaxation spectrum kernel norm solution, relaxation spectrum sparse solution and relaxation spectrum residual solution into the non-negative constraint objective function model for iterative update, obtain the solution to be solved, and transform the solution to be solved into the form of matrix-vector multiplication and summation.

[0184] In this embodiment, each iteration update yields a set of relaxation spectrum kernel norm solutions, relaxation spectrum sparse solutions, and relaxation spectrum residual solutions. The form of the matrix-vector product and summation to be solved is:

[0185]

[0186] In the formula, A matrix operator for converting a two-dimensional matrix to a one-dimensional matrix. This is the matrix transpose symbol. It is an identity matrix.

[0187] S204c: Determine the nuclear magnetic resonance relaxation spectrum based on the form of matrix-vector product and summation.

[0188] S204d: Based on the confidence interval of the area integral value of the nuclear magnetic resonance relaxation spectrum, update the learning rate, iteration step size and iteration number for each iteration.

[0189] In this embodiment, the learning rate controls the model's learning progress during iterative updates. The iteration step size can be the dual variable in the method embodiment provided in S201. The iteration count is the current iteration count.

[0190] Specifically, the iteration step size is the step size of the alternating iteration update. This iteration step size can be adaptively transformed according to the solution accuracy, and the transformation equation of the step size is:

[0191]

[0192] In the formula, For learning rate, A smaller value indicates higher iteration convergence accuracy. The maximum iteration step size is the maximum value in the range. This represents the iteration step size from the previous iteration.

[0193] S204c: If the area integral value of the relaxation spectrum meets the preset confidence threshold, then the solution to be solved is taken as the final solution, and the nuclear magnetic resonance relaxation spectrum is taken as the final relaxation spectrum and output.

[0194] In this embodiment, the preset threshold can be a number less than 1, used to determine whether the obtained solution is the optimal solution.

[0195] Furthermore, in an optional embodiment of this application, the formula for determining whether the area integral value of the relaxation spectrum meets a preset confidence threshold is as follows:

[0196]

[0197] In the formula, This represents the area integral value of the nuclear magnetic resonance relaxation spectrum. This represents the maximum amplitude of the echo signal in the nuclear magnetic resonance (NMR) data. If the determination result meets the confidence threshold, the solution obtained in this iteration is determined to be the optimal solution and can be output as the final solution. If the determination result does not meet the threshold, the iteration step size is adjusted and the process returns to S204a, while the iteration count is incremented by 1.

[0198] In summary, the NMR relaxation spectrum interpretation method provided in this application, after acquiring NMR data, constructs a non-negative constraint objective function model based on the low-rank and sparsity properties of the NMR relaxation spectrum. This non-negative constraint objective function model is then decomposed into three sub-problems: a matrix low-rank function model, a spectral sparse function model, and a residual norm function model. The solutions to these three sub-problems are used to update the non-negative constraint objective function model, yielding the final solution and the corresponding final relaxation spectrum output. Throughout the interpretation process, features of the relaxation spectrum are extracted and redundant interference is removed during the solution of the matrix low-rank function model. The sparsity of the relaxation spectrum is used to control the resolution of the relaxation spectrum during the solution of the spectral sparse function model. Finally, residual terms are used to control the accuracy of the spectrum during the solution of the residual norm function model, thereby improving the resolution of the final relaxation spectrum.

[0199] Meanwhile, by setting a preset threshold, it is determined whether the solutions of the matrix low-rank function model, the spectral sparse function model, and the residual norm function model can be used as the optimal solution, thereby obtaining the final relaxation spectrum with high spectral accuracy, few redundant interference parts, and high resolution.

[0200] Meanwhile, by setting a pre-set confidence threshold, it is determined whether the final solution is the global optimal solution, thereby obtaining the relaxation spectrum with the highest resolution.

[0201] In an optional embodiment of this application, obtaining nuclear magnetic resonance data in step S201 includes the following steps:

[0202] Step A: Obtain raw NMR echo train data.

[0203] Step B: If the original NMR echo train data is determined to be two-dimensional or multi-dimensional, then the original NMR echo train data is converted into a one-dimensional numerical vector.

[0204] In this embodiment, the original NMR echo train data can be the echo train signal acquired by the NMR spectrometer. This echo train signal can be a one-dimensional, two-dimensional, or multi-dimensional echo train signal. When a one-dimensional echo train signal is acquired, it can be upgraded in dimensionality using a matrix transformation operator. If it is determined to be a two-dimensional echo train signal, the solution of the relaxation spectrum is a two-dimensional matrix. When solving the spectral sparse function model and the residual norm function model, the two-dimensional or multi-dimensional original NMR echo train data is converted into a one-dimensional numerical vector for calculation.

[0205] In summary, by converting two-dimensional or multi-dimensional raw NMR echo train data into one-dimensional numerical vectors for computation, the dimensionality of the vectors is reduced, thereby improving computational performance.

[0206] The above describes the specific process of a nuclear magnetic resonance relaxation spectrum interpretation method provided in the embodiments of this application. Below, the implementation principle of the nuclear magnetic resonance relaxation spectrum interpretation method is introduced using Example 1 (one-dimensional transverse relaxation time spectrum interpretation) and Example 2 (two-dimensional longitudinal-transverse relaxation time spectrum interpretation).

[0207] Example 1:

[0208] Figure 3 This is a diagram of a transverse relaxation time spectrum model with bimodal characteristics.

[0209] Figure 4(a) shows the residual norm distribution under the condition of noise ratio = 100.

[0210] Figure 4(b) shows the residual norm distribution under the condition of noise ratio = 50.

[0211] Figure 4(c) shows the residual norm distribution under the condition of noise ratio = 20.

[0212] Figure 4(d) shows the residual norm distribution under the condition of noise ratio = 10.

[0213] Figure 5(a) is a schematic diagram of the inversion results under the condition of signal-to-noise ratio = 100.

[0214] Figure 5(b) is a schematic diagram of the inversion results under the condition of signal-to-noise ratio = 50.

[0215] Figure 5(c) is a schematic diagram of the inversion results under the condition of signal-to-noise ratio = 20.

[0216] Figure 5(d) is a schematic diagram of the inversion results under the condition of signal-to-noise ratio = 10.

[0217] To simplify the model, in this embodiment, a one-dimensional transverse relaxation time relaxation spectrum bimodal model with two components of the same composition but different relative contents was first established to simulate the case where the pores contain bound water (CBW) and movable oil (MO), with CBW being dominant as an example.

[0218] like Figure 3 As shown, when CBW is dominant, the component ratio of bound water to movable oil is 3:2. At this point, the relaxation time of bound water is set to 8 ms, the relaxation time of movable oil is set to 150 ms, and the total porosity is 10 p.u. The echo interval TE is set to 0.2 ms, and the number of echoes is set to 2500. Regularization parameters are then set separately. The range is [0.01 100], with 50 logarithmic points taken at equal intervals. The nuclear magnetic resonance spectral analysis method provided in this embodiment is used to invert echo train data with different signal-to-noise ratios in forward modeling, exploring the selection range of the regularization parameter. In this case, the signal-to-noise ratio (SNR) of the echo train data is set to 100, 50, 20, and 10, respectively.

[0219] Then, by calculating the RMSE (Root-Mean-Square Error) of the inversion spectrum and the model spectrum, the optimal regularization parameter is obtained, as shown in Figures 4(a) to 4(d), where the bright spots represent the optimal value of the regularization parameter. The expression for RMSE is:

[0220]

[0221] In the formula, For the inversion spectrum, For the model spectrum, It is a natural number greater than 0.

[0222] As shown in Figures 5(a) to 5(d), the solid line represents the actual one-dimensional relaxation spectrum, and the dashed line represents the one-dimensional relaxation spectrum obtained by prior art processing. The dotted line represents the one-dimensional relaxation spectrum obtained by the NMR relaxation spectrum interpretation method provided in the embodiments of this application. Obviously, the fluid saturation ratio obtained by the NMR relaxation spectrum interpretation method provided in the embodiments of this application is closer to the actual component ratio of bound water and mobile oil of 3:2, and the obtained one-dimensional relaxation spectrum has a higher spectral resolution.

[0223] Example 2:

[0224] Figure 6(a) is a schematic diagram of the forward model obtained based on the fluid relaxation parameters and pulse sequence acquisition parameters.

[0225] Figure 6(b) is a schematic diagram of the longitudinal-lateral relaxation time correlation spectrum obtained by the spectral decomposition method in the prior art.

[0226] Figure 6(c) is a schematic diagram of the longitudinal-transverse relaxation time correlation spectrum obtained by the nuclear magnetic resonance relaxation spectrum despectroscopy method provided in the embodiment of this application.

[0227] To simplify the model, this embodiment first introduces three fluid components: bound water, movable oil, and movable water. The longitudinal relaxation times of the three fluids are 5 ms for bound water, 30 ms for movable oil, and 200 ms for movable water. The transverse relaxation times of the three fluids are 4 ms for bound water, 25 ms for movable oil, and 150 ms for movable water. The ratio between the longitudinal and transverse relaxation times can then be calculated to be between 1 and 2. The porosity is set to 12 p.u., and the component ratio of bound water, movable oil, and movable water is 4:4:4. Based on this fluid model, the selected pulse sequence acquisition parameters are as follows: waiting time TW = [5000, 4000, 2000, 1000, 800, 500, 250, 125, 100, 50, 25, 15, 10, 8, 6, 5, 4, 2, 1, 0.1] milliseconds, echo interval TE = 0.2 milliseconds, and the number of echoes is 2500.

[0228] Please refer to Figures 6(a) and 6(b). At this point, the signal-to-noise ratio (SNR) is 10. Compared to Figure 6(a), Figure 6(b) shows a lower SNR. Under this SNR condition, in the longitudinal-lateral relaxation time correlation spectrum obtained by the NMR relaxation spectroscopy method provided in this application embodiment, the peaks of different components are relatively symmetrical, and the peak separation is high. As shown in Figure 6(b), in the longitudinal-lateral relaxation time correlation spectrum obtained by the prior art, the morphology of different fluid components is more irregular, and the separation of each peak gradually merges, making separation difficult. As shown in Figure 6(c), it is clear that under low SNR conditions, the NMR spectroscopy method provided in this application embodiment can fully divide the regions of different fluid components, thereby enabling quantitative calculation of the content of different fluid components. Furthermore, the improved spectral resolution and the final fluid saturation ratio closer to 4:4:4 improve fluid identification accuracy.

[0229] Furthermore, the nuclear magnetic resonance relaxation spectrum interpretation method provided in this application embodiment can also be applied to the interpretation of other two-dimensional or three-dimensional nuclear magnetic resonance relaxation spectra, such as D-T2, T1-D-T2, T1-DG-T2, etc., which will not be described in detail in this embodiment.

[0230] The above describes the specific implementation process and application examples of the nuclear magnetic resonance relaxation spectrum interpretation method provided in the embodiments of this application. The following is an embodiment of a nuclear magnetic resonance relaxation spectrum interpretation device provided in the embodiments of this application.

[0231] Figure 7 This is a schematic diagram of a nuclear magnetic resonance relaxation spectrum interpretation device provided in an embodiment of this application. The device includes: an acquisition module 71, a model building module 72, and a calculation and solution module 73.

[0232] Among them, the acquisition module 71 is used to acquire nuclear magnetic resonance data.

[0233] Model building module 72 is used to construct a non-negative constraint objective function model based on the low rank and sparsity of nuclear magnetic resonance relaxation spectrum.

[0234] The computation and solution module 73 is used to decompose the non-negative constraint objective function model into a matrix low-rank function model, a spectral sparse function model, and a residual norm function model.

[0235] The computation and solution module 73 is also used to substitute the nuclear magnetic resonance data into the matrix low-rank function model, the spectral sparse function model and the residual norm function model according to the preset calculation method, and to iteratively update them to obtain the relaxation spectrum nuclear norm solution, the relaxation spectrum sparse solution and the relaxation spectrum residual solution, respectively.

[0236] The computation and solution module 73 is also used to iteratively update the non-negative constraint objective function model based on the relaxation spectrum nuclear norm solution, the relaxation spectrum sparse solution, and the relaxation spectrum residual solution, to determine the final solution and the final relaxation spectrum corresponding to the final solution and output them.

[0237] The nuclear magnetic resonance relaxation spectrum interpretation device provided in this embodiment can be used to execute the technical solution of the above method embodiment. Its implementation principle and technical effect are similar, and will not be described again here.

[0238] In an optional embodiment of this application, the acquisition module 71 is specifically used to acquire transverse relaxation time measurement data.

[0239] The model building module 72 is specifically used to construct the first signal response equation for one-dimensional transverse relaxation time measurement, obtain two-dimensional longitudinal-transverse relaxation time measurement data, and construct the second signal response equation for two-dimensional longitudinal-transverse relaxation time measurement.

[0240] The model building module 72 is further configured to discretize the transverse relaxation time measurement data into vector data to obtain the first discretized equation of the first signal response equation, and to discretize the two-dimensional longitudinal-transverse relaxation time measurement data into vector data to obtain the second discretized equation of the second signal response equation. Based on the first and second discretized equations, the matrix model to be solved is determined. It is also configured to transform the matrix model to be solved into a first non-negative model to be solved, and to apply a solution to the first non-negative model to be solved. Regularization constraints are applied to obtain the second nonnegative model to be solved. These constraints are then used to apply nonnegative low-rank and sparsity constraints to the second nonnegative model to obtain the third nonnegative model to be solved.

[0241] Module 71 is also specifically used to obtain nuclear norm variables. Normative variables and Residual term variables. Model building module 72 is also specifically used to determine the residual term variables based on the nuclear norm variable. Normative variables and The residual variable transforms the third non-negative model into a constrained model. Model building module 72 is also specifically used to transform the constrained model into a non-negative constrained objective function model based on the augmented Lagrangian function.

[0242] In an optional embodiment of this application, when the model building module 72 constructs the non-negative constraint objective function model, the first signal response equation generated by the model building module 72 in this embodiment is:

[0243]

[0244] In the formula, The time point for obtaining the transverse relaxation time measurement data. For measurement Signal strength at time , For the lateral relaxation time, for The result obtained by the inverse Laplace transform Measurement noise is used to obtain the transverse relaxation time measurement data.

[0245] In this embodiment, the second signal response equation generated by the model building module 72 is:

[0246]

[0247] In the formula, The longitudinal relaxation time is the value in the longitudinal-lateral relaxation time measurement data. The lateral relaxation time is the value in the longitudinal-lateral relaxation time measurement data. To obtain the time points for the longitudinal-lateral relaxation time measurement data, The first preset waiting time, The measured waiting time Interval Signal strength at time , for The result obtained by inverse Placian transform Measurement noise when acquiring the longitudinal-lateral relaxation time measurement data.

[0248] In this embodiment, the first discretization equation generated by the model building module 72 is:

[0249]

[0250] In the formula, The amplitude of the echo signal of the transverse relaxation time measurement data. ,in The number of discrete relaxation times. , Number of echoes The time of data acquisition for the transverse relaxation time measurement is denoted as tv. The first of the upper and lower boundaries of the constraint A horizontal relaxation time component The maximum lateral relaxation time. This is the minimum lateral relaxation time. Measurement noise during the acquisition of the transverse relaxation time measurement data. For the first The amplitude of each horizontal relaxation time component.

[0251] In this embodiment, the second discretized equation generated by the model building module 72 is:

[0252]

[0253] In the formula, Discrete longitudinal relaxation time The number of components, ,in, A natural number greater than or equal to 1. Discrete transverse relaxation time The number of components, The amplitude of the echo signal of the longitudinal-lateral relaxation time measurement data. This is the second preset waiting time. Two-dimensional The amplitude of the relaxation spectrum Measurement noise during the acquisition of the longitudinal-lateral relaxation time measurement data, The first of the upper and lower boundaries of the constraint A longitudinal relaxation time component The first of the upper and lower boundaries of the constraint One horizontal relaxation time component.

[0254] In this embodiment, the matrix model to be solved generated by the model building module 72 is as follows:

[0255]

[0256] In the formula, The amplitude vector of the echo. Given the kernel matrix, This represents the noise amplitude during echo acquisition. The non-negative ones are to be solved.

[0257] In this embodiment, the first non-negative model to be solved generated by the model building module 72 is:

[0258]

[0259] In the formula, For matrix nuclear norm number, This indicates that the constraints are satisfied. .

[0260] In this embodiment, the second nonnegative model to be solved generated by the model building module 72 is:

[0261]

[0262] In the formula, To make the matrix The variable at which the nuclear norm reaches its minimum value. To be solved nuclear norm number, For adjustment Preset parameters for regularization weights.

[0263] In this embodiment, the third nonnegative model to be solved generated by the model building module 72 is:

[0264]

[0265] In the formula, For preset Regularization parameters, For preset Regularization parameters, This is a transformation operator for converting vectors to matrices.

[0266] In this embodiment, the constrained model to be solved generated by the model building module 72 is as follows:

[0267]

[0268]

[0269] In the formula, The constraints are as follows: ,in, for residual variable, For nuclear norm variables, for Normative variable.

[0270] In this embodiment, the non-negative constraint objective function model generated by the model building module 72 is as follows:

[0271]

[0272]

[0273]

[0274] In the formula, All are Lagrange multipliers. for The inner product, for and The inner product, for The inner product, The step size for iterative updates, To and corresponding Norm operator, To and The square of the corresponding norm operator, To and corresponding The square of the norm operator.

[0275] In an optional embodiment of this application, the computation and solution module 73 is further specifically used to fix other variables in the non-negativity constraint objective function model, and iteratively update the nuclear norm term variable based on nuclear magnetic resonance data to obtain a relaxation spectrum nuclear norm solution. Fixing other variables in the non-negativity constraint objective function model, iteratively updating the norm term variable based on nuclear magnetic resonance data to obtain a relaxation spectrum sparse solution. The residual variable is iteratively updated to obtain the relaxation spectrum residual solution. If the difference between the maximum value of the relaxation spectrum nuclear norm solution, relaxation spectrum sparse solution, and relaxation spectrum residual solution obtained in the previous update and the maximum value of the relaxation spectrum nuclear norm solution, relaxation spectrum sparse solution, and relaxation spectrum residual solution obtained in the next update is less than a preset threshold, the iterative update is stopped.

[0276] In an optional embodiment of this application, the acquisition module 71 is further specifically used to acquire the relaxation spectrum nuclear norm solution, relaxation spectrum sparse solution and relaxation spectrum residual solution obtained by iteratively updating the nuclear magnetic resonance data by substituting it into the matrix low-rank function model, the spectral sparse function model and the residual norm function model according to the preset calculation method.

[0277] The computational solution module 73 is also specifically used to fix other variables in the non-negative constraint objective function model, substitute the relaxation spectrum kernel norm solution, relaxation spectrum sparse solution, and relaxation spectrum residual solution into the non-negative constraint objective function model for iterative updates, obtain the solution to be solved, and transform the solution to be solved into the form of matrix-vector product and summation. Based on the solution to be solved in the form of matrix-vector product and summation, the nuclear magnetic resonance relaxation spectrum is determined. Based on the confidence interval of the area integral value of the nuclear magnetic resonance relaxation spectrum, the learning rate, iteration step size, and iteration number of each iteration are updated. If the area integral value of the relaxation spectrum is determined to meet the preset confidence threshold, the solution to be solved is taken as the final solution, and the nuclear magnetic resonance relaxation spectrum is taken as the final relaxation spectrum and output.

[0278] In an optional embodiment of this application, the calculation and solving module 73 determines whether the area integral value of the relaxation spectrum meets a preset confidence threshold using the following formula:

[0279]

[0280] In the formula, The area integral value of the nuclear magnetic resonance relaxation spectrum is given. This represents the maximum amplitude of the echo signal in the nuclear magnetic resonance data.

[0281] In an optional embodiment of this application, the acquisition module 71 is further specifically used to acquire the original nuclear magnetic resonance echo string data. If it is determined that the original nuclear magnetic resonance echo string data is two-dimensional or multi-dimensional data, the original nuclear magnetic resonance echo string data is converted into a one-dimensional numerical vector.

[0282] Figure 8 A schematic diagram of the hardware structure of a computer device is provided for the embodiments of this application, such as... Figure 8 As shown, the computer device includes at least one processor 801 and a memory 802.

[0283] The processor 801 is used to store computer execution instructions.

[0284] The memory 802 is used to execute computer execution instructions stored in the memory to implement the various steps involved in the above method embodiments. For details, please refer to the relevant descriptions in the foregoing method embodiments.

[0285] Alternatively, the memory 802 can be either standalone or integrated with the processor 801.

[0286] When the memory 802 is set up independently, the computer device also includes a bus 803 for connecting the memory 802 and the processor 801.

[0287] This invention also provides a computer-readable storage medium storing computer-executable instructions, which, when executed by a processor, implement the method described above.

[0288] This application also provides a computer program product, including a computer program that, when executed by a processor, implements the above-described method.

[0289] In the several embodiments provided by this invention, it should be understood that the disclosed apparatus and methods can be implemented in other ways. For example, the apparatus embodiments described above are merely illustrative; for instance, the division of modules described above is only a logical functional division, and in actual implementation, there may be other division methods. For example, multiple modules may be combined or integrated into another system, or some features may be ignored or not executed. Furthermore, the coupling or direct coupling or communication connection shown or discussed may be through some interfaces, indirect coupling or communication connection between devices or modules, and may be electrical, mechanical, or other forms.

[0290] The modules described above as separate components may or may not be physically separate. The components shown as modules may or may not be physical units; that is, they may be located in one place or distributed across multiple network units. Some or all of the modules can be selected to implement the solution of this embodiment according to actual needs.

[0291] Furthermore, the functional modules in the various embodiments of the present invention can be integrated into one processing unit, or each module can exist physically separately, or two or more modules can be integrated into one unit. The unit composed of the above modules can be implemented in hardware or in the form of hardware plus software functional units.

[0292] The integrated modules implemented as software functional modules described above can be stored in a computer-readable storage medium. These software functional modules, stored in a storage medium, include several instructions to cause a computer device (which may be a personal computer, server, or network device, etc.) or processor to execute partial steps of the methods of the various embodiments of this application.

[0293] It should be understood that the aforementioned processor can be a Central Processing Unit (CPU), or other general-purpose processors, digital signal processors (DSPs), application-specific integrated circuits (ASICs), etc. A general-purpose processor can be a microprocessor or any conventional processor. The steps of the method disclosed in this invention can be directly manifested as execution by a hardware processor, or execution by a combination of hardware and software modules within the processor.

[0294] The memory may include high-speed RAM, and may also include non-volatile storage (NVM), such as at least one disk storage device, and may also be a USB flash drive, external hard drive, read-only memory, disk or optical disc, etc.

[0295] The bus can be an Industry Standard Architecture (ISA) bus, a Peripheral Component Interconnect (PCI) bus, or an Extended Industry Standard Architecture (EISA) bus, etc. Buses can be categorized as address buses, data buses, control buses, etc. For ease of illustration, the buses shown in the accompanying drawings are not limited to a single bus or a single type of bus.

[0296] The aforementioned storage medium can be implemented by any type of volatile or non-volatile storage device or a 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 storage, flash memory, magnetic disk, or optical disk. The storage medium can be any available medium that can be accessed by a general-purpose or special-purpose computer.

[0297] An exemplary storage medium is coupled to a processor, enabling the processor to read information from and write information to the storage medium. Alternatively, the storage medium can be an integral part of the processor. Both the processor and the storage medium can reside in an Application Specific Integrated Circuit (ASIC). Alternatively, the processor and storage medium can exist as discrete components in an electronic device or host device.

[0298] Those skilled in the art will understand that all or part of the steps of the above-described method embodiments can be implemented by hardware related to program instructions. The aforementioned program can be stored in a computer-readable storage medium. When executed, the program performs the steps of the above-described method embodiments; and the aforementioned storage medium includes various media capable of storing program code, such as ROM, RAM, magnetic disks, or optical disks.

[0299] This description is intended to illustrate the technical solutions of this application, and not to limit them. Although this application has been described in detail with reference to the foregoing embodiments, those skilled in the art should understand that modifications can still be made to the technical solutions described in the foregoing embodiments, or equivalent substitutions can be made to some or all of the technical features therein. Such modifications or substitutions do not cause the essence of the corresponding technical solutions to deviate from the scope of the technical solutions of the embodiments of this application.

Claims

1. A method for interpreting nuclear magnetic resonance relaxation spectra, characterized in that, include: Acquire nuclear magnetic resonance (NMR) data and construct a non-negative constrained objective function model based on the low-rank and sparsity of NMR relaxation spectra; The nonnegativity constraint objective function model is decomposed into a matrix low-rank function model, a spectral sparse function model, and a residual norm function model; The nuclear magnetic resonance data are substituted into the matrix low-rank function model, the spectral sparse function model and the residual norm function model according to the preset calculation method for iterative updates, to obtain the relaxation spectrum nuclear norm solution, the relaxation spectrum sparse solution and the relaxation spectrum residual solution respectively; The non-negative constraint objective function model is iteratively updated based on the relaxation spectrum nuclear norm solution, the relaxation spectrum sparse solution, and the relaxation spectrum residual solution to determine the final solution and the final relaxation spectrum corresponding to the final solution, and then output them.

2. The method according to claim 1, characterized in that, The non-negativity-constrained objective function model constructed based on the low-rank and sparsity of nuclear magnetic resonance relaxation spectra includes: Acquire transverse relaxation time measurement data and construct the first signal response equation for one-dimensional transverse relaxation time measurement; acquire two-dimensional longitudinal-transverse relaxation time measurement data and construct the second signal response equation for two-dimensional longitudinal-transverse relaxation time measurement. The transverse relaxation time measurement data is discretized into vector data to obtain the first discretized equation of the first signal response equation. The two-dimensional longitudinal-transverse relaxation time measurement data is discretized into vector data to obtain the second discretized equation of the second signal response equation. Based on the first and second discretized equations, the matrix model to be solved is determined. The matrix model to be solved is transformed into a first non-negative model to be solved, and an application is made to the solution of the first non-negative model to be solved. Regularization constraints yield the second non-negative model to be solved. The second nonnegative model to be solved is subjected to nonnegative low-rank and sparsity constraints to obtain the third nonnegative model to be solved. Obtain the nuclear norm number variable, Normative variables and The residual variable, and based on the nuclear norm variable, Normative variables and The residual variable transforms the third non-negative unsolved model into a constrained unsolved model. Based on the augmented Lagrangian function, the constrained model to be solved is transformed into a non-negative constrained objective function model.

3. The method according to claim 2, characterized in that, The first signal response equation is: In the formula, The time point for obtaining the transverse relaxation time measurement data. For measurement Signal strength at any given time For the lateral relaxation time, for The result obtained by the inverse Laplace transform Measurement noise is used to obtain the transverse relaxation time measurement data; The second signal response equation is: In the formula, The longitudinal relaxation time is the value in the longitudinal-lateral relaxation time measurement data. The lateral relaxation time is the value in the longitudinal-lateral relaxation time measurement data. To obtain the time points for the longitudinal-lateral relaxation time measurement data, The first preset waiting time, The measured waiting time Interval Signal strength at any given time for The result obtained by inverse Placian transform Measurement noise during the acquisition of the longitudinal-lateral relaxation time measurement data; The first discretization equation is: In the formula, The amplitude of the echo signal of the transverse relaxation time measurement data. ,in The number of discrete relaxation times. , The number of echoes The time of data acquisition for the transverse relaxation time measurement is denoted as tv. The first of the upper and lower boundaries of the constraint A horizontal relaxation time component The maximum lateral relaxation time. This is the minimum lateral relaxation time. Measurement noise during the acquisition of the transverse relaxation time measurement data. For the first The amplitude of each horizontal relaxation time component; The second discretization equation is: In the formula, Discrete longitudinal relaxation time The number of components, ,in, A natural number greater than or equal to 1. Discrete transverse relaxation time The number of components, The amplitude of the echo signal of the longitudinal-lateral relaxation time measurement data. This is the second preset waiting time. Two-dimensional The amplitude of the relaxation spectrum Measurement noise during the acquisition of the longitudinal-lateral relaxation time measurement data, The first of the upper and lower boundaries of the constraint A longitudinal relaxation time component The first of the upper and lower boundaries of the constraint One horizontal relaxation time component; The model of the matrix to be solved is: In the formula, The amplitude vector of the echo. Given the kernel matrix, This represents the noise amplitude during echo acquisition. The solution is non-negative. The first non-negative model to be solved is: In the formula, For matrix nuclear norm number, This indicates that the constraints are satisfied. ; The second nonnegative model to be solved is: In the formula, To make the matrix The variable at which the nuclear norm reaches its minimum value. To be solved nuclear norm number, For adjustment Preset parameters for regularization weights; The third non-negative model to be solved is: In the formula, For preset Regularization parameters, For preset Regularization parameters, Transformation operators for converting vectors to matrices; The constrained model to be solved is: In the formula, The constraints are as follows: ,in, for residual variable, For nuclear norm variables, for Normative variable; The non-negativity constraint objective function model is as follows: In the formula, All are Lagrange multipliers. for The inner product, for and The inner product, for The inner product, The step size for iterative updates, To and corresponding Norm operator, To and The square of the corresponding norm operator, To and corresponding The square of the norm operator.

4. The method according to claim 2, characterized in that, The step involves iteratively updating the nuclear magnetic resonance data by substituting it into the matrix low-rank function model, the spectral sparse function model, and the residual norm function model according to a preset calculation method, respectively, to obtain the relaxation spectrum nuclear norm solution, the relaxation spectrum sparse solution, and the relaxation spectrum residual solution, including: By fixing the other variables in the non-negativity constraint objective function model, the nuclear norm number variables are iteratively updated based on the nuclear magnetic resonance data to obtain the relaxation spectrum nuclear norm number solution. By fixing the other variables in the non-negativity constraint objective function model, the norm term variable is iteratively updated based on the nuclear magnetic resonance data to obtain the relaxation spectrum sparse solution. With other variables fixed in the nonnegativity constraint objective function model, the nuclear magnetic resonance data is used to analyze the... The residual variable is iteratively updated to obtain the relaxation spectrum residual solution; If the difference between the maximum value of the relaxation spectrum nuclear norm solution, relaxation spectrum sparse solution, and relaxation spectrum residual solution obtained in the previous update and the maximum value of the relaxation spectrum nuclear norm solution, relaxation spectrum sparse solution, and relaxation spectrum residual solution obtained in the next update is less than a preset threshold, then the iterative update stops.

5. The method according to claim 1, characterized in that, The step of iteratively updating the non-negative constraint objective function model based on the relaxation spectrum nuclear norm solution, the relaxation spectrum sparse solution, and the relaxation spectrum residual solution, determining the final solution and the final relaxation spectrum corresponding to the final solution, and outputting them includes: Each time, the nuclear magnetic resonance data is substituted into the matrix low-rank function model, the spectral sparse function model, and the residual norm function model according to a preset calculation method for iterative updating, resulting in the relaxation spectrum nuclear norm solution, the relaxation spectrum sparse solution, and the relaxation spectrum residual solution. Fixing the other variables in the non-negative constraint objective function model, the relaxation spectrum nuclear norm solution, the relaxation spectrum sparse solution and the relaxation spectrum residual solution are substituted into the non-negative constraint objective function model for iterative updating to obtain the solution to be solved, and the solution to be solved is converted into the form of matrix-vector multiplication and summation; The nuclear magnetic resonance relaxation spectrum is determined based on the solution in the form of matrix-vector product and summation. Based on the confidence interval of the area integral value of the nuclear magnetic resonance relaxation spectrum, update the learning rate, iteration step size and iteration number for each iteration; If the area integral value of the relaxation spectrum is determined to meet the preset confidence threshold, then the solution to be solved is taken as the final solution, and the nuclear magnetic resonance relaxation spectrum is taken as the final relaxation spectrum and output.

6. The method according to claim 5, characterized in that, The formula for determining whether the area integral value of the relaxation spectrum meets the preset confidence threshold is as follows: In the formula, The area integral value of the nuclear magnetic resonance relaxation spectrum is given. This represents the maximum amplitude of the echo signal in the nuclear magnetic resonance data.

7. The method according to any one of claims 1 to 6, characterized in that, The acquisition of nuclear magnetic resonance data includes: Acquire raw nuclear magnetic resonance echo train data; If the original nuclear magnetic resonance echo train data is determined to be two-dimensional or multi-dimensional data, then the original nuclear magnetic resonance echo train data is converted into a one-dimensional numerical vector.

8. A nuclear magnetic resonance relaxation spectrum interpretation device, characterized in that, include: The acquisition module is used to acquire nuclear magnetic resonance data; The model building module is used to construct a non-negative constraint objective function model based on the low rank and sparsity of nuclear magnetic resonance relaxation spectra. The computation and solution module is used to decompose the non-negativity constraint objective function model into a matrix low-rank function model, a spectral sparse function model, and a residual norm function model. The computation and solution module is also used to substitute the nuclear magnetic resonance data into the matrix low-rank function model, the spectral sparse function model and the residual norm function model according to the preset calculation method for iterative updates, so as to obtain the relaxation spectrum nuclear norm solution, the relaxation spectrum sparse solution and the relaxation spectrum residual solution respectively. The computation and solution module is further used to iteratively update the non-negative constraint objective function model based on the relaxation spectrum nuclear norm solution, the relaxation spectrum sparse solution, and the relaxation spectrum residual solution, to determine the final solution and the final relaxation spectrum corresponding to the final solution and output them.

9. A computer device, characterized in that, include: At least one processor and memory; The memory stores computer-executed instructions; The at least one processor executes computer execution instructions stored in the memory, causing the at least one processor to perform the nuclear magnetic resonance relaxation spectrum interpretation method as described in any one of claims 1 to 7.

10. A computer-readable storage medium, characterized in that, The computer-readable storage medium stores computer-executable instructions, which, when executed by the processor, implement the nuclear magnetic resonance relaxation spectrum interpretation method as described in any one of claims 1 to 7.

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