Electrical impedance tomography data processing method and device based on low-rank matrix recovery
The low-rank matrix recovery method is used to process electrical impedance tomography data, which solves the problem of signal instability caused by user movement and achieves stable and accurate imaging.
Patent Information
- Application Number
- CN202410800537.X
- Authority / Receiving Office
- CN · China
- Patent Type
- Patents(China)
- Current Assignee / Owner
- Filing Date
- 2024-06-20
- Publication Date
- 2024-12-13
- Estimated Expiration
- 2044-06-20
AI Technical Summary
The user's movement during electrical impedance tomography leads to measurement interference, resulting in signal instability and affecting imaging performance.
Using a data processing method based on low-rank matrix recovery, the residual vectors in the target matrix are obtained, the confidence interval is calculated using robust statistical theory, the observation matrix is generated, and the low-rank matrix recovery problem model is constructed using gradient projection algorithm, and the iterative processing is performed to recover. Target impedance imaging data.
Effectively remove interference caused by body movement, obtain stable and continuous data, and improve the accuracy and comprehensiveness of imaging results.
Smart Images
Figure CN118365741B_ABST
Abstract
Description
Technical Field
[0001] The present invention relates to the technical field of electrical impedance imaging data processing, and in particular to an electrical impedance tomography data processing method and device based on low-rank matrix recovery. Background Art
[0002] Electrical Impedance Tomography (EIT) is a real-time non-invasive imaging technology widely used in thoracic medicine. It can perform imaging based on the obtained electrical impedance imaging data.
[0003] However, in the current electrical impedance tomography process, measurement interference is generated due to the movement of the user, making the obtained signal unstable. The unstable data will lead to poor imaging performance and affect the imaging results.
[0004] Therefore, the prior art still needs to be improved and developed. Summary of the invention
[0005] The main purpose of the present invention is to provide an electrical impedance tomography data processing method, device, terminal and computer-readable storage medium based on low-rank matrix recovery, aiming to solve the problem in the prior art that in the process of electrical impedance tomography scanning, measurement interference will be generated due to the movement of the user, thereby making the obtained signal unstable, and unstable data will lead to poor imaging performance and affect the imaging results.
[0006] To achieve the above object, the present invention provides an electrical impedance tomography data processing method based on low-rank matrix recovery, the electrical impedance tomography data processing method based on low-rank matrix recovery comprising the following steps:
[0007] Acquire target electrical impedance imaging data, and construct a target matrix according to the target electrical impedance imaging data;
[0008] Obtaining the residual vector of each row in the target matrix according to the target matrix, obtaining the confidence interval corresponding to the residual vector of each row according to the robust statistical theory, performing indicator function processing on the corresponding residual vector according to the confidence interval of each row, and generating an observation matrix;
[0009] A low-rank matrix recovery problem model is constructed according to the target matrix and the observation matrix, the low-rank matrix recovery problem model is iteratively processed based on the gradient projection algorithm to obtain a restored target electrical impedance imaging data matrix, and a target electrical impedance image is constructed according to the restored target electrical impedance imaging data matrix.
[0010] Optionally, obtaining the residual vector of each row in the target matrix according to the target matrix specifically includes:
[0011] Preprocessing the data of each row in the target matrix based on a median filter to obtain a plurality of filter vectors;
[0012] According to the data of each row in the target matrix and the corresponding filter vector, a residual vector of each row in the target matrix is calculated.
[0013] Optionally, obtaining the confidence interval corresponding to each row of the residual vector according to robust statistical theory specifically includes:
[0014] Processing each of the residual vectors according to the truncated mean to obtain an average value corresponding to each of the residual vectors;
[0015] Processing each of the residual vectors according to a median operation to obtain a standard deviation corresponding to each of the residual vectors;
[0016] A preset control parameter is obtained, and a confidence interval corresponding to each row of the residual vector is generated according to the control parameter and the mean value and standard deviation corresponding to each residual vector.
[0017] Optionally, performing indicator function processing on the corresponding residual vector according to the confidence interval of each row to generate an observation matrix specifically includes:
[0018] According to the confidence interval of each row, determine whether the corresponding element in the residual vector is contaminated by outlier points, and obtain the contamination state of each element in the residual vector;
[0019] According to the contamination state of each element in the residual vector, an indicator function is used to process each element in the residual vector, and an observation matrix is generated.
[0020] Optionally, constructing a low-rank matrix recovery problem model according to the target matrix and the observation matrix specifically includes:
[0021] Obtaining missing value elements in the observation matrix;
[0022] According to the observation matrix and the missing value elements, the target electrical impedance imaging data imaging denoising problem is modeled as the low-rank matrix recovery problem model.
[0023] Optionally, the iterative processing of the low-rank matrix restoration problem model based on the gradient projection algorithm to obtain the restored target electrical impedance imaging data matrix specifically includes:
[0024] Initializing a solution matrix to be solved in the low-rank matrix recovery problem model to obtain an initial solution matrix;
[0025] The initial solution matrix is iterated based on the gradient projection algorithm, and after each iteration update, it is determined whether an iteration condition is met. When the iteration condition is met, the iteration is terminated, and the solution matrix obtained in the iteration is used as the restored target electrical impedance imaging data matrix.
[0026] Optionally, each iteration process of iterating the initial solution matrix based on the gradient projection algorithm specifically includes:
[0027] The solution matrix obtained in the previous iteration is updated along the current gradient direction to obtain the update matrix of this iteration, wherein in the first iteration, the initial solution matrix is updated along the initial gradient direction;
[0028] Projecting the updated matrix of this iteration onto the first constraint region in the low-rank matrix recovery problem model to obtain the intermediate matrix of this iteration;
[0029] The intermediate matrix of this iteration is projected onto the second constraint region in the low-rank matrix recovery problem model to obtain the solution matrix of this iteration.
[0030] In addition, to achieve the above-mentioned purpose, the present invention also provides an electrical impedance tomography data processing device based on low-rank matrix recovery, wherein the electrical impedance tomography data processing device based on low-rank matrix recovery includes:
[0031] A target matrix building module is used to obtain target electrical impedance imaging data and build a target matrix according to the target electrical impedance imaging data;
[0032] An observation matrix generation module is used to obtain the residual vector of each row in the target matrix according to the target matrix, obtain the confidence interval corresponding to the residual vector of each row according to the robust statistical theory, perform indicator function processing on the corresponding residual vector according to the confidence interval of each row, and generate an observation matrix;
[0033] A solution module is used to construct a low-rank matrix recovery problem model based on the target matrix and the observation matrix, iteratively process the low-rank matrix recovery problem model based on the gradient projection algorithm to obtain a restored target electrical impedance imaging data matrix, and construct a target electrical impedance image based on the restored target electrical impedance imaging data matrix.
[0034] In addition, to achieve the above-mentioned purpose, the present invention also provides a terminal, wherein the terminal includes: a memory, a processor, and an electrical impedance tomography data processing program based on low-rank matrix recovery stored in the memory and run on the processor, and when the electrical impedance tomography data processing program based on low-rank matrix recovery is executed by the processor, the steps of the electrical impedance tomography data processing method based on low-rank matrix recovery as described above are implemented.
[0035] In addition, to achieve the above-mentioned purpose, the present invention also provides a computer-readable storage medium, wherein the computer-readable storage medium stores an electrical impedance tomography data processing program based on low-rank matrix recovery, and when the electrical impedance tomography data processing program based on low-rank matrix recovery is executed by a processor, the steps of the electrical impedance tomography data processing method based on low-rank matrix recovery as described above are implemented.
[0036] In the present invention, target electrical impedance imaging data is obtained, and a target matrix is constructed according to the target electrical impedance imaging data; the residual vector of each row in the target matrix is obtained according to the target matrix, the confidence interval corresponding to the residual vector of each row is obtained according to the robust statistical theory, and the corresponding residual vector is processed by the indicator function according to the confidence interval of each row to generate an observation matrix; a low-rank matrix recovery problem model is constructed according to the target matrix and the observation matrix, the low-rank matrix recovery problem model is iteratively processed based on the gradient projection algorithm to obtain the restored target electrical impedance imaging data matrix, and a target electrical impedance image is constructed according to the restored target electrical impedance imaging data matrix. The present invention models the electrical impedance imaging data into a matrix and reveals its approximate low-order properties. In order to resist the interference caused by body movement in the process of acquiring electrical impedance imaging data, the present invention establishes a customized denoising scheme, that is, modeling a low-rank matrix recovery problem model, wherein the application first performs outlier detection, that is, constructs an observation matrix. Through outlier detection, abnormal data points contaminated by outliers can be well detected, and then they are regarded as missing elements, thereby modeling a low-rank matrix recovery problem model. The low-rank property of the EIT data matrix is utilized, and a gradient projection algorithm is used to restore the missing elements. While eliminating the interference caused by body movement from the EIT data, stable and continuous data are obtained, thereby generating accurate and comprehensive imaging results. BRIEF DESCRIPTION OF THE DRAWINGS
[0037] Figure 1 It is a flow chart of a preferred embodiment of the electrical impedance tomography data processing method based on low-rank matrix recovery of the present invention;
[0038] Figure 2 It is a flow chart of an embodiment of an electrical impedance tomography data processing method based on low-rank matrix recovery of the present invention;
[0039] Figure 3 It is a schematic diagram of impedance comparison of different methods in the electrical impedance tomography data processing method based on low-rank matrix recovery of the present invention;
[0040] Figure 4 It is an impedance linear comparison diagram of different methods in the electrical impedance tomography data processing method based on low-rank matrix recovery of the present invention;
[0041] Figure 5It is a schematic diagram of image error comparison after being processed by different methods in the electrical impedance tomography data processing method based on low-rank matrix recovery of the present invention;
[0042] Figure 6 It is a schematic diagram of image phase relationship comparison after being processed by different methods in the electrical impedance tomography data processing method based on low-rank matrix recovery of the present invention;
[0043] Figure 7 It is a structural diagram of a preferred embodiment of an electrical impedance tomography data processing device based on low-rank matrix recovery of the present invention;
[0044] Figure 8 It is a structural diagram of a preferred embodiment of the terminal of the present invention. DETAILED DESCRIPTION
[0045] In order to make the purpose, technical solution and advantages of the present invention clearer and more specific, the present invention is further described in detail below with reference to the accompanying drawings and examples. It should be understood that the specific embodiments described herein are only used to explain the present invention and are not used to limit the present invention.
[0046] Electrical impedance tomography is a real-time non-invasive imaging technology widely used in thoracic medicine. Currently, EIT is a versatile and safe imaging examination method. However, the movement of the user will cause measurement interference, making the obtained signal unstable.
[0047] At present, the methods for removing body motion interference from biological signals can be divided into three categories: the first category is to design adaptive filters, but they require additional input signals through additional measurement channels in the hardware; the second category also requires the design of filters but does not require additional input, such as Wiener filters and Kalman filters, where Wiener filters rely on pre-acquired knowledge of expected signal characteristics, such as power spectra, while Kalman filters require a predefined model to determine the noise distribution; the last type includes subspace projection, independent component analysis, and spline interpolation. However, the underlying mathematical models of these methods are not well suited to the characteristics of EIT signals.
[0048] The current methods can obtain high-quality EIT images in the absence of interference such as impulse noise, but if there is interference such as impulse noise, the imaging performance of the current algorithm will be greatly reduced if the current algorithm is used to obtain EIT images without processing the corresponding interference. Some methods will change the EIT data when processing impulse noise, or fail to suppress the impulse interference caused by body movement interference, resulting in unstable recovered EIT data, which in turn makes the imaging performance poor and affects the imaging results.
[0049] In response to one or more of the above problems, the present application obtains target electrical impedance imaging data and constructs a target matrix based on the target electrical impedance imaging data; obtains the residual vector of each row in the target matrix based on the target matrix, obtains the confidence interval corresponding to the residual vector of each row based on robust statistical theory, performs indicator function processing on the corresponding residual vector according to the confidence interval of each row to generate an observation matrix; constructs a low-rank matrix recovery problem model based on the target matrix and the observation matrix, iteratively processes the low-rank matrix recovery problem model based on the gradient projection algorithm to obtain the restored target electrical impedance imaging data matrix, and constructs a target electrical impedance image based on the restored target electrical impedance imaging data matrix.
[0050] The electrical impedance tomography data processing method based on low-rank matrix recovery described in the preferred embodiment of the present invention is as follows: Figure 1 As shown, the electrical impedance tomography data processing method based on low-rank matrix recovery includes the following steps:
[0051] Step S10: Acquire target electrical impedance imaging data, and construct a target matrix according to the target electrical impedance imaging data.
[0052] It should be noted that, in the present application, the acquired target electrical impedance imaging data is acquired by the EIT system. At the same time, one pair of opposing electrodes generates excitation, and the remaining adjacent electrodes measure the resulting surface voltage. The excitation pairs are then turned on until all opposing electrode pairs are used for excitation; thus, the surface voltage can be measured from The EIT measurement value, i.e., the target electrical impedance imaging data, is obtained from each channel and the The target electrical impedance imaging data acquired in the channels is composed of The real matrix of , which is the target matrix.
[0053] Specific, built The target matrix , each column is represented by a corresponding vector, which can be expressed as the following formula (1):
[0054] ; (1)
[0055] Among them, Indicates the frame number. is the real matrix in (1) No. The vector corresponding to the row, , and Respectively The first and second rows of The vector corresponding to the rows.
[0056] In one embodiment of the present application, an EIT system with 16 electrodes is considered. At the moment, one pair of opposing electrodes generates excitation, and the remaining 12 pairs of adjacent electrodes measure the resulting surface voltage; then the excitation pairs are turned on until all opposing electrode pairs are used as excitations; therefore, EIT measurement values can be obtained from 16×12=192 channels, and the corresponding EIT measurement value composition dimensions are The target matrix , among which middle, = 192. Further, when each snapshot of the EIT system lasts for 50 milliseconds, 1200 frames are generated in one minute.
[0057] Step S20: obtaining the residual vector of each row in the target matrix according to the target matrix, obtaining the confidence interval corresponding to the residual vector of each row according to the robust statistical theory, performing indicator function processing on the corresponding residual vector according to the confidence interval of each row, and generating an observation matrix.
[0058] It should be noted that in this application, the corresponding Residual vectors are obtained according to the corresponding residual vectors and the preset control parameters. The confidence interval of the residual vector corresponding to each row in . By processing each residual vector through the confidence interval, the corresponding observation matrix can be obtained.
[0059] Further, the obtaining the residual vector of each row in the target matrix according to the target matrix specifically includes:
[0060] Preprocessing the data of each row in the target matrix based on a median filter to obtain a plurality of filter vectors;
[0061] According to the data of each row in the target matrix and the corresponding filter vector, a residual vector of each row in the target matrix is calculated.
[0062] Specifically, in this application, a median filter is used to preprocess the data of each row in the target matrix to obtain multiple filter vectors. The specific processing formula is shown in the following formula:
[0063] ; (2)
[0064] in represents the median filter, , The median filter is used to The filtered filter vector. In the process of preprocessing the data of each row in the target matrix using the median filter, in order to ensure performance, the window size used has a minimum value and is set ,in is the window size.
[0065] After obtaining the filter vector corresponding to each row of the target matrix, calculate and The residual vector between , the specific calculation process of the residual vector is shown as follows:
[0066] ; (3)
[0067] Corresponding can be obtained residual vector, where express One of the residual vectors.
[0068] Furthermore, obtaining the confidence interval corresponding to each row of the residual vector according to the robust statistical theory specifically includes:
[0069] Processing each of the residual vectors according to the truncated mean to obtain an average value corresponding to each of the residual vectors;
[0070] Processing each of the residual vectors according to a median operation to obtain a standard deviation corresponding to each of the residual vectors;
[0071] A preset control parameter is obtained, and a confidence interval corresponding to each row of the residual vector is generated according to the control parameter and the mean value and standard deviation corresponding to each residual vector.
[0072] Specifically, for each residual vector , robust statistical methods are needed to distinguish Therefore, we need to set a confidence interval first. ,in and Represent the mean and standard deviation respectively, and the preset control parameters , which is used to control the size of the confidence interval. If the corresponding residual vectors fall within this interval, they are considered to be normal elements that are not damaged by outliers, otherwise they are considered to be contaminated by outliers.
[0073] In this application, the confidence interval is set using the following formula:
[0074] ; (4)
[0075] ; (5)
[0076] ; (6)
[0077] in and denote the trimmed mean and median operators respectively; the mean and standard deviation corresponding to each residual vector can be obtained accordingly; and the trimmed mean is a simple arithmetic mean calculated from the 90% of elements with the smallest absolute values; and in this application, set is the optimal value chosen empirically.
[0078] Furthermore, performing indicator function processing on the corresponding residual vector according to the confidence interval of each row to generate an observation matrix specifically includes:
[0079] According to the confidence interval of each row, determine whether the corresponding element in the residual vector is contaminated by outlier points, and obtain the contamination state of each element in the residual vector;
[0080] According to the contamination state of each element in the residual vector, an indicator function is used to process each element in the residual vector, and an observation matrix is generated.
[0081] Specifically, after obtaining a suitable confidence interval, according to the confidence interval of each row, it is determined whether the corresponding element in the residual vector is contaminated by outliers, that is, when the element in the residual vector falls within the confidence interval, the element is a normal element that is not damaged by outliers, and its contamination state is a normal state. When the element does not fall within the confidence interval, it is considered that the residual vector is contaminated by outliers, and its contamination state is a contaminated state. Through the contamination state of the elements in each corresponding residual vector, through the indicator function, the elements with a normal contamination state are set to 1, and the elements with a contaminated contamination state are set to 0, and the elements in the corresponding observation matrix are generated, and the observation matrix is generated through the elements in the observation matrix.
[0082] Among them, the process of judging whether the elements in the corresponding residual vector are contaminated by outliers and generating the elements in the observation matrix is expressed by the following formula:
[0083] ; (7)
[0084] in , Residual vector No. elements, is a binary element, which represents the corresponding The pollution state of is the element in the corresponding observation matrix; 1 means is a normal value, and a value of 0 indicates is contaminated by outliers. According to its subscript Arranged in order to form a matrix observation matrix .
[0085] Step S30, constructing a low-rank matrix recovery problem model based on the target matrix and the observation matrix, iteratively processing the low-rank matrix recovery problem model based on the gradient projection algorithm to obtain a restored target electrical impedance imaging data matrix, and constructing a target electrical impedance image based on the restored target electrical impedance imaging data matrix.
[0086] It should be noted that the projected gradient algorithm is an iterative algorithm for solving constrained optimization problems. The basic idea is that in each iteration, the current iteration point is first updated along the gradient direction, and then projected onto the constraint area defined by the constraint condition. When the iteration reaches the requirement, it stops falling and obtains the corresponding result. In this application, after constructing a low-rank matrix recovery problem model, the corresponding model can be processed by the gradient projection algorithm to obtain the restored target impedance imaging data matrix.
[0087] After obtaining the restored target electrical impedance imaging data matrix, the EIT imaging algorithm is used to construct the target electrical impedance image; in the present application, the EIT imaging algorithm can adopt a variety of algorithms without limitation, for example, the Graz consensus reconstruction algorithm for lung EIT imaging (GREIT) is used to construct the target electrical impedance image.
[0088] Furthermore, constructing a low-rank matrix recovery problem model according to the target matrix and the observation matrix specifically includes:
[0089] Obtaining missing value elements in the observation matrix;
[0090] According to the observation matrix and the missing value elements, the target electrical impedance imaging data imaging denoising problem is modeled as the low-rank matrix recovery problem model.
[0091] Specifically, after obtaining the observation matrix After that, the elements corresponding to the positions of all 0 elements are regarded as missing value elements, and the target electrical impedance imaging data denoising model is modeled as a low-rank matrix recovery problem model, where the low-rank matrix recovery problem model is specifically expressed as the following formula:
[0092] ; (8)
[0093] in, represents the constraint area, , X represents the solution matrix to be solved, for X Middle Line The elements of the column, represents the point-wise product, represents the constraints, That is, subject to, which means constraint. express F The square of the norm; rank() represents the rank of the matrix; R is a pre-set integer, where R is much smaller than and ; and They represent the maximum and minimum values of the signal in the normal segment respectively.
[0094] Among them, Each row in is represented by a vector, where the i-th row is represented as ,pass The i-th row in and The i-th row in Perform point-by-point multiplication and convert each and The calculated results are arranged according to the number of rows, and the matrix can be obtained. ,in and The calculation process can be expressed as the following formula:
[0095] ; (9)
[0096] Will Arrange in the order of i, and you can get the matrix .
[0097] Furthermore, the low-rank matrix restoration problem model is iteratively processed based on the gradient projection algorithm to obtain the restored target electrical impedance imaging data matrix, specifically including:
[0098] Initializing a solution matrix to be solved in the low-rank matrix recovery problem model to obtain an initial solution matrix;
[0099] The initial solution matrix is iterated based on the gradient projection algorithm, and after each iteration update, it is determined whether an iteration condition is met. When the iteration condition is met, the iteration is terminated, and the solution matrix obtained in the iteration is used as the restored target electrical impedance imaging data matrix.
[0100] In order to process the low-rank matrix recovery problem model in formula (8), this application uses the gradient projection method to process it. In the process, X Initialize to get the initial solution matrix, where the initialization adopts a random method, that is, first X Initialize randomly and then project the variable into the constraint region.
[0101] After obtaining the initial solution matrix, the initial solution matrix is iterated for multiple times, and whether the iteration condition is met is determined after each iteration update. When the relative error of the solution matrices corresponding to two adjacent iterations reaches a predetermined limit, the iteration condition is considered to be met; when the iteration condition is met, the iteration is terminated, and the solution matrix obtained in the iteration is used as the restored target electrical impedance imaging data matrix; and when the current iteration does not meet the iteration condition, the iteration continues.
[0102] Furthermore, each iteration process of iterating the initial solution matrix based on the gradient projection algorithm specifically includes:
[0103] The solution matrix obtained in the previous iteration is updated along the current gradient direction to obtain the update matrix of this iteration, wherein in the first iteration, the initial solution matrix is updated along the initial gradient direction;
[0104] Projecting the updated matrix of this iteration onto the first constraint region in the low-rank matrix recovery problem model to obtain the intermediate matrix of this iteration;
[0105] The intermediate matrix of this iteration is projected onto the second constraint region in the low-rank matrix recovery problem model to obtain the solution matrix of this iteration.
[0106] In each iteration, the solution matrix obtained in the previous iteration is first Along the current gradient direction , update and obtain the update matrix of this iteration . In the first iteration, is 0, and the corresponding update is performed along the initial gradient direction. Then the update matrix of this iteration is projected to the constraint area On, directly Projection into the constraint region The difficulty is relatively large, so the restriction area of this application is divided into two parts, namely the first restriction area and the second constraint region , and projected twice; first Project to The intermediate matrix of this iteration is obtained , and then Continue projecting to The solution matrix of this iteration is obtained ,in Indicates the number of iterations.
[0107] Furthermore, the process of generating the update matrix of the current iteration in the present application is specifically shown in the following formula:
[0108] ; (10)
[0109] Correspondingly, the specific process of projecting the updated matrix of this iteration to the first constraint region in the low-rank matrix recovery problem model to obtain the intermediate matrix of this iteration can be expressed as the following formula:
[0110] ; (11)
[0111] The process of projecting the intermediate matrix of this iteration to the second constraint region in the low-rank matrix recovery problem model to obtain the solution matrix of this iteration can be expressed as the following formula:
[0112] ; (12)
[0113] in, is the step length, , ,and It is a projection operator that can project variables into the feasible domain , where the corresponding and are the projection operators of the first constraint area and the second constraint area respectively. Specifically, the projection operator of the first constraint area can be expressed as the following formula:
[0114] ; (13)
[0115] in, Representation Matrix The left singular matrix of Representation Matrix Right singular matrix, Represented by the matrix The non-negative diagonal matrix composed of all singular values of is the truncation operator, which preserves the matrix The largest The singular values make Satisfying the low-rank constraint, Indicates transpose.
[0116] The projection operator for the second constraint region , which can be expressed as:
[0117] ; (14)
[0118] in, express Middle Line The elements corresponding to the columns; after two projections, the solution matrix for this iteration can be obtained.
[0119] Furthermore, in this application, by Figure 2 Further describing the electrical impedance tomography data processing method based on low-rank matrix recovery of the present application, Figure 2 This is a flow chart of an embodiment of an electrical impedance tomography data processing method based on low-rank matrix recovery of the present invention. Consider an EIT system with 16 electrodes and the corresponding mobile phone EIT signal data, i.e., target electrical impedance imaging data, so as to construct a corresponding target matrix, and perform outlier detection on the corresponding residual vectors in the 192 columns of the target matrix, i.e., determine whether the elements in the corresponding residual vectors are contaminated by outlier points, and fuse the results accordingly to obtain an observation matrix, and use a low-rank recovery algorithm to obtain the recovered target electrical impedance imaging data matrix, wherein the low-rank recovery algorithm is the process of constructing a low-rank matrix recovery problem model and solving it accordingly.
[0120] Furthermore, this application is Figure 3 , showing the EIT images, i.e. target electrical impedance images, restored by different algorithms. Figure 3 It was observed in the time series EIT images that each algorithm showed serious artifacts caused by body motion interference, which completely distorted the respiratory waveform and regional ventilation distribution. After correspondingly processing the boundary voltage with impulse noise, only the new algorithm could obtain EIT images showing the local ventilation distribution of both lungs, while other algorithms could not recover it. The new algorithm is the electrical impedance tomography data processing method based on low-rank matrix recovery in the present invention, and other algorithms for comparison include Butterworth filtering algorithm, FIR (Finite Impulse Response, FIR) filtering algorithm, mean filtering algorithm, and median filtering algorithm.
[0121] Figure 4 This is a linear comparison diagram of impedances of different methods shown in this application, which shows the original global chest impedance and the chest impedance estimated by different methods. Figure 4 It can be seen that the electrical impedance tomography data processing method based on low-rank matrix recovery proposed in this application can remove pulse noise and restore a continuous and stable EIT signal. The new algorithm is the electrical impedance tomography data processing method based on low-rank matrix recovery in this application.
[0122] Figure 5 and Figure 6 The image errors and image correlations between the original time series EIT images and the estimated time series EIT images using various processing methods are shown respectively. Figure 5 It can be seen that compared with several other algorithms, the image error obtained by the proposed new algorithm is greatly reduced, from about 19 to below 1, specifically 0.389, where the image error is a ratio operation. The new algorithm is the electrical impedance tomography data processing method based on low-rank matrix recovery in this application. Figure 6 It can be seen that compared with other algorithms, the image correlation of the image restored by the proposed new algorithm is greatly improved from about 0.2 to 0.94. The new algorithm is the electrical impedance tomography data processing method based on low-rank matrix recovery in this application.
[0123] The present invention obtains target electrical impedance imaging data, and constructs a target matrix according to the target electrical impedance imaging data; obtains the residual vector of each row in the target matrix according to the target matrix, obtains the confidence interval corresponding to the residual vector of each row according to the robust statistical theory, performs indicator function processing on the corresponding residual vector according to the confidence interval of each row, and generates an observation matrix; constructs a low-rank matrix recovery problem model according to the target matrix and the observation matrix, iterates the low-rank matrix recovery problem model based on the gradient projection algorithm to obtain a restored target electrical impedance imaging data matrix, and constructs a target electrical impedance image according to the restored target electrical impedance imaging data matrix. The present invention models the electrical impedance imaging data into a matrix and reveals its approximate low-order properties. In order to resist the interference caused by body movement in the process of acquiring electrical impedance imaging data, the present invention establishes a customized denoising scheme, that is, modeling a low-rank matrix recovery problem model, wherein the application first performs outlier detection, that is, constructs an observation matrix. Through outlier detection, abnormal data points contaminated by outliers can be well detected, and then they are regarded as missing elements, thereby modeling a low-rank matrix recovery problem model. The low-rank property of the EIT data matrix is utilized, and a gradient projection algorithm is used to restore the missing elements. While eliminating the interference caused by body movement from the EIT data, stable and continuous data are obtained, thereby generating accurate and comprehensive imaging results.
[0124] Furthermore, if Figure 7 As shown, based on the above-mentioned electrical impedance tomography data processing method based on low-rank matrix recovery, the present invention also provides an electrical impedance tomography data processing device based on low-rank matrix recovery, wherein the electrical impedance tomography data processing device based on low-rank matrix recovery includes:
[0125] A target matrix building module 71 is used to obtain target electrical impedance imaging data and build a target matrix according to the target electrical impedance imaging data;
[0126] An observation matrix generation module 72 is used to obtain the residual vector of each row in the target matrix according to the target matrix, obtain the confidence interval corresponding to the residual vector of each row according to the robust statistical theory, perform indicator function processing on the corresponding residual vector according to the confidence interval of each row, and generate an observation matrix;
[0127] The solution module 73 is used to construct a low-rank matrix recovery problem model based on the target matrix and the observation matrix, iteratively process the low-rank matrix recovery problem model based on the gradient projection algorithm to obtain a restored target impedance imaging data matrix, and construct a target impedance image based on the restored target impedance imaging data matrix.
[0128] Furthermore, if Figure 8 As shown, based on the above-mentioned electrical impedance tomography data processing method and device based on low-rank matrix recovery, the present invention also provides a terminal accordingly, and the terminal includes a processor 10, a memory 20 and a display 30. Figure 8 Only some components of the terminal are shown, but it should be understood that it is not required to implement all of the components shown, and more or fewer components may be implemented instead.
[0129] In some embodiments, the memory 20 may be an internal storage unit of the terminal, such as a hard disk or memory of the terminal. In other embodiments, the memory 20 may also be an external storage device of the terminal, such as a plug-in hard disk, a smart memory card (Smart Media Card, SMC), a secure digital (SecureDigital, SD) card, a flash card (Flash Card), etc. equipped on the terminal. Further, the memory 20 may also include both an internal storage unit of the terminal and an external storage device. The memory 20 is used to store application software and various types of data installed on the terminal, such as the program code of the installation terminal. The memory 20 may also be used to temporarily store data that has been output or is to be output. In one embodiment, the memory 20 stores an electrical impedance tomography data processing program 40 based on low-rank matrix recovery, and the electrical impedance tomography data processing program 40 based on low-rank matrix recovery can be executed by the processor 10, thereby realizing the electrical impedance tomography data processing method based on low-rank matrix recovery in the present application.
[0130] In some embodiments, the processor 10 may be a central processing unit (CPU), a microprocessor or other data processing chip, used to run the program code or process data stored in the memory 20, such as executing the electrical impedance tomography data processing method based on low-rank matrix recovery.
[0131] In some embodiments, the display 30 may be an LED display, a liquid crystal display, a touch-sensitive liquid crystal display, an OLED (Organic Light-Emitting Diode) touch device, etc. The display 30 is used to display information on the terminal and to display a visual user interface. The components 10-30 of the terminal communicate with each other via a device bus.
[0132] In one embodiment, when the processor 10 executes the electrical impedance tomography data processing program 40 based on low-rank matrix recovery in the memory 20, the following steps are implemented:
[0133] Acquire target electrical impedance imaging data, and construct a target matrix according to the target electrical impedance imaging data;
[0134] Obtaining the residual vector of each row in the target matrix according to the target matrix, obtaining the confidence interval corresponding to the residual vector of each row according to the robust statistical theory, performing indicator function processing on the corresponding residual vector according to the confidence interval of each row, and generating an observation matrix;
[0135] A low-rank matrix recovery problem model is constructed according to the target matrix and the observation matrix, the low-rank matrix recovery problem model is iteratively processed based on the gradient projection algorithm to obtain a restored target electrical impedance imaging data matrix, and a target electrical impedance image is constructed according to the restored target electrical impedance imaging data matrix.
[0136] The step of obtaining the residual vector of each row in the target matrix according to the target matrix specifically includes:
[0137] Preprocessing the data of each row in the target matrix based on a median filter to obtain a plurality of filter vectors;
[0138] According to the data of each row in the target matrix and the corresponding filter vector, a residual vector of each row in the target matrix is calculated.
[0139] The step of obtaining the confidence interval corresponding to each row of the residual vector according to the robust statistical theory specifically includes:
[0140] Processing each of the residual vectors according to the truncated mean to obtain an average value corresponding to each of the residual vectors;
[0141] Processing each of the residual vectors according to a median operation to obtain a standard deviation corresponding to each of the residual vectors;
[0142] A preset control parameter is obtained, and a confidence interval corresponding to each row of the residual vector is generated according to the control parameter and the mean value and standard deviation corresponding to each residual vector.
[0143] Among them, performing indicator function processing on the corresponding residual vector according to the confidence interval of each row to generate an observation matrix specifically includes:
[0144] According to the confidence interval of each row, determine whether the corresponding element in the residual vector is contaminated by outlier points, and obtain the contamination state of each element in the residual vector;
[0145] According to the contamination state of each element in the residual vector, an indicator function is used to process each element in the residual vector, and an observation matrix is generated.
[0146] The step of constructing a low-rank matrix recovery problem model according to the target matrix and the observation matrix specifically includes:
[0147] Obtaining missing value elements in the observation matrix;
[0148] According to the observation matrix and the missing value elements, the target electrical impedance imaging data imaging denoising problem is modeled as the low-rank matrix recovery problem model.
[0149] The iterative processing of the low-rank matrix recovery problem model based on the gradient projection algorithm to obtain the restored target electrical impedance imaging data matrix specifically includes:
[0150] Initializing a solution matrix to be solved in the low-rank matrix recovery problem model to obtain an initial solution matrix;
[0151] The initial solution matrix is iterated based on the gradient projection algorithm, and after each iteration update, it is determined whether an iteration condition is met. When the iteration condition is met, the iteration is terminated, and the solution matrix obtained in the iteration is used as the restored target electrical impedance imaging data matrix.
[0152] Wherein, each iteration process of iterating the initial solution matrix based on the gradient projection algorithm specifically includes:
[0153] The solution matrix obtained in the previous iteration is updated along the current gradient direction to obtain the update matrix of this iteration, wherein in the first iteration, the initial solution matrix is updated along the initial gradient direction;
[0154] Projecting the updated matrix of this iteration onto the first constraint region in the low-rank matrix recovery problem model to obtain the intermediate matrix of this iteration;
[0155] The intermediate matrix of this iteration is projected onto the second constraint region in the low-rank matrix recovery problem model to obtain the solution matrix of this iteration.
[0156] The present invention also provides a computer-readable storage medium, wherein the computer-readable storage medium stores an electrical impedance tomography data processing program based on low-rank matrix recovery, and when the electrical impedance tomography data processing program based on low-rank matrix recovery is executed by a processor, the steps of the electrical impedance tomography data processing method based on low-rank matrix recovery as described above are implemented.
[0157] It should be noted that, in this article, the terms "include", "comprises" or any other variations thereof are intended to cover non-exclusive inclusion, so that a process, method, article or terminal including a series of elements includes not only those elements, but also other elements not explicitly listed, or also includes elements inherent to such process, method, article or terminal. In the absence of further restrictions, an element defined by the sentence "includes a ..." does not exclude the existence of other identical elements in the process, method, article or terminal including the element.
[0158] Of course, those skilled in the art can understand that all or part of the processes in the above-mentioned embodiments can be implemented by instructing related hardware (such as a processor, a controller, etc.) through a computer program, and the program can be stored in a computer-readable storage medium that can be read by a computer, and the program can include the processes of the above-mentioned method embodiments when executed. The computer-readable storage medium can be a memory, a disk, an optical disk, etc.
[0159] It should be understood that the application of the present invention is not limited to the above examples. For ordinary technicians in this field, improvements or changes can be made based on the above description. All these improvements and changes should fall within the scope of protection of the claims attached to the present invention.
Claims
1. A method for processing electrical impedance tomography data based on low-rank matrix recovery, characterized in that: The electrical impedance tomography data processing method based on low-rank matrix recovery includes: Acquire target electrical impedance imaging data, and construct a target matrix according to the target electrical impedance imaging data; Obtaining the residual vector of each row in the target matrix according to the target matrix, obtaining the confidence interval corresponding to the residual vector of each row according to the robust statistical theory, performing indicator function processing on the corresponding residual vector according to the confidence interval of each row, and generating an observation matrix; The step of performing indicator function processing on the corresponding residual vector according to the confidence interval of each row to generate an observation matrix specifically includes: According to the confidence interval of each row, determine whether the corresponding element in the residual vector is contaminated by outlier points, and obtain the contamination state of each element in the residual vector; According to the pollution state of each element in the residual vector, an indicator function is used to process each element in the residual vector, and an observation matrix is generated; The indicator function is expressed as: ； in, , Indicates the frame number. Residual vector No. elements, Is a binary element, indicating the corresponding The pollution status, and Represent the mean and standard deviation of each residual vector, , are pre-set control parameters; Will According to the subscript Arrange in order to form an observation matrix; A low-rank matrix recovery problem model is constructed according to the target matrix and the observation matrix, the low-rank matrix recovery problem model is iteratively processed based on a gradient projection algorithm to obtain a restored target electrical impedance imaging data matrix, and a target electrical impedance image is constructed according to the restored target electrical impedance imaging data matrix; The constructing of a low-rank matrix recovery problem model according to the target matrix and the observation matrix specifically includes: Obtaining missing value elements in the observation matrix; According to the observation matrix and the missing value elements, the target electrical impedance imaging data imaging denoising problem is modeled as the low-rank matrix recovery problem model; The low-rank matrix restoration problem model is iteratively processed based on the gradient projection algorithm to obtain a restored target electrical impedance imaging data matrix, specifically comprising: Initializing a solution matrix to be solved in the low-rank matrix recovery problem model to obtain an initial solution matrix; The initial solution matrix is iterated based on the gradient projection algorithm, and after each iteration update, it is determined whether an iteration condition is met. When the iteration condition is met, the iteration is terminated, and the solution matrix obtained in the iteration is used as the restored target electrical impedance imaging data matrix.
2. The electrical impedance tomography data processing method based on low-rank matrix recovery according to claim 1, characterized in that: The step of obtaining the residual vector of each row in the target matrix according to the target matrix specifically includes: Preprocessing the data of each row in the target matrix based on a median filter to obtain a plurality of filter vectors; According to the data of each row in the target matrix and the corresponding filter vector, a residual vector of each row in the target matrix is calculated.
3. The electrical impedance tomography data processing method based on low-rank matrix recovery according to claim 1, characterized in that: The step of obtaining the confidence interval corresponding to each row of the residual vector according to the robust statistical theory specifically includes: Processing each of the residual vectors according to the truncated mean to obtain an average value corresponding to each of the residual vectors; Processing each of the residual vectors according to a median operation to obtain a standard deviation corresponding to each of the residual vectors; A preset control parameter is obtained, and a confidence interval corresponding to each row of the residual vector is generated according to the control parameter and the mean value and standard deviation corresponding to each residual vector.
4. The electrical impedance tomography data processing method based on low-rank matrix recovery according to claim 1, characterized in that: Each iteration process of iterating the initial solution matrix based on the gradient projection algorithm specifically includes: The solution matrix obtained in the previous iteration is updated along the current gradient direction to obtain the update matrix of this iteration, wherein in the first iteration, the initial solution matrix is updated along the initial gradient direction; Projecting the updated matrix of this iteration onto the first constraint region in the low-rank matrix recovery problem model to obtain the intermediate matrix of this iteration; The intermediate matrix of this iteration is projected onto the second constraint region in the low-rank matrix recovery problem model to obtain the solution matrix of this iteration.
5. An electrical impedance tomography data processing device based on low-rank matrix recovery, characterized in that: The electrical impedance tomography data processing device based on low-rank matrix recovery includes: A target matrix building module is used to obtain target electrical impedance imaging data and build a target matrix according to the target electrical impedance imaging data; An observation matrix generation module is used to obtain the residual vector of each row in the target matrix according to the target matrix, obtain the confidence interval corresponding to the residual vector of each row according to the robust statistical theory, perform indicator function processing on the corresponding residual vector according to the confidence interval of each row, and generate an observation matrix; The step of performing indicator function processing on the corresponding residual vector according to the confidence interval of each row to generate an observation matrix specifically includes: According to the confidence interval of each row, determine whether the corresponding element in the residual vector is contaminated by outlier points, and obtain the contamination state of each element in the residual vector; According to the pollution state of each element in the residual vector, an indicator function is used to process each element in the residual vector, and an observation matrix is generated; The indicator function is expressed as: ； in, , Indicates the frame number. Residual vector No. elements, Is a binary element, indicating the corresponding The pollution status, and Represent the mean and standard deviation of each residual vector, , are pre-set control parameters; Will According to the subscript Arrange in order to form an observation matrix; A solution module is used to construct a low-rank matrix recovery problem model according to the target matrix and the observation matrix, iteratively process the low-rank matrix recovery problem model based on a gradient projection algorithm to obtain a restored target electrical impedance imaging data matrix, and construct a target electrical impedance image according to the restored target electrical impedance imaging data matrix; The constructing of a low-rank matrix recovery problem model according to the target matrix and the observation matrix specifically includes: Obtaining missing value elements in the observation matrix; According to the observation matrix and the missing value elements, the target electrical impedance imaging data imaging denoising problem is modeled as the low-rank matrix recovery problem model; The low-rank matrix restoration problem model is iteratively processed based on the gradient projection algorithm to obtain a restored target electrical impedance imaging data matrix, specifically comprising: Initializing a solution matrix to be solved in the low-rank matrix recovery problem model to obtain an initial solution matrix; The initial solution matrix is iterated based on the gradient projection algorithm, and after each iteration update, it is determined whether an iteration condition is met. When the iteration condition is met, the iteration is terminated, and the solution matrix obtained in the iteration is used as the restored target electrical impedance imaging data matrix.
6. A terminal, characterized in that: The terminal includes: a memory, a processor, and an electrical impedance tomography data processing program based on low-rank matrix recovery stored in the memory and executable on the processor. When the electrical impedance tomography data processing program based on low-rank matrix recovery is executed by the processor, the steps of the electrical impedance tomography data processing method based on low-rank matrix recovery as described in any one of claims 1 to 4 are implemented.
7. A computer-readable storage medium, characterized in that: The computer-readable storage medium stores an electrical impedance tomography data processing program based on low-rank matrix recovery, and when the electrical impedance tomography data processing program based on low-rank matrix recovery is executed by a processor, the steps of the electrical impedance tomography data processing method based on low-rank matrix recovery as described in any one of claims 1-4 are implemented.