Multicolor magnetic nanoparticle aliasing signal separation method based on adaptive signal processing

Abstract

The present application belongs to the field of magnetic particle imaging, and particularly relates to a multi-color magnetic nanoparticle aliasing signal separation method based on adaptive signal processing, aiming at solving the problem that the prior art cannot accurately distinguish various SPIONs signals. The method of the present application comprises: obtaining an initial signal to be separated for preprocessing to obtain a target signal; using an improved FastICA algorithm to perform blind source separation on the target signal to obtain various independent signals; analyzing the various independent signals to obtain an analysis result, and iteratively adjusting the learning rate and the target function of the algorithm according to the analysis result until the analysis result meets a preset threshold. Based on the method, the separation accuracy of different signals is effectively improved by adaptively adjusting the related parameters of the blind source separation process.

Description

Technical Field

[0001] This invention belongs to the field of magnetic particle imaging, and specifically relates to a method for separating multicolor magnetic nanoparticle aliasing signals based on adaptive signal processing. Background Technology

[0002] Magnetic Particle Imaging (MPI) is a radiation-free, highly sensitive medical imaging technique that generates images by detecting the nonlinear response of superparamagnetic iron oxide nanoparticles (SPIONs) in an applied magnetic field. MPI technology constructs a magnetic field gradient to create a field-free point (FFP) or field-free line (FFL) in space, and then uses an external coil to detect the SPION signals at the FFP or FFL to reconstruct the image distribution of the SPIONs. However, existing MPI techniques typically target only a single type of SPION, limiting their application in multifunctional labeling and complex tissue environments.

[0003] To address this limitation, multi-color magnetic particle imaging (MPI) aims to simultaneously detect multiple targets or markers using various types or different physical properties of SPIONs. This technology holds great potential in tumor labeling, drug delivery, and the research of multifunctional molecular probes. However, in actual signal measurement, the spectral responses of different SPIONs can cause signal aliasing and separation difficulties. Existing separation methods based on spectrum or relaxation effects struggle to accurately distinguish between different SPION signals, thus affecting the accuracy of quantitative analysis in imaging. Summary of the Invention

[0004] To address the aforementioned problems in existing technologies, namely the difficulty of accurately distinguishing various SPION signals by current signal separation schemes based on spectrum or relaxation effects, thus affecting the accuracy of quantitative imaging analysis, this invention proposes a method for separating multicolor magnetic nanoparticle aliased signals based on adaptive signal processing, comprising:

[0005] Obtain the initial signal to be separated, which is composed of the aliasing of independent signals from multiple SPIONs;

[0006] The initial signal is preprocessed to obtain the target signal; the preprocessing is as follows: the initial signal is denoised using a preset adaptive filter, and the denoised initial signal is normalized to obtain the target signal. The filter coefficients of the adaptive filter are adaptively adjusted during the denoising process to reduce the filter residual.

[0007] An improved FastICA algorithm is used to perform blind source separation on the target signal to obtain independent signals of various SPIONs; the learning rate and separation matrix of the improved FastICA algorithm are adaptively adjusted during the blind source separation process to correspond to the feature changes of the target signal.

[0008] The independent signals of various SPIONs are analyzed to obtain analysis results. Based on the analysis results, the learning rate and objective function of the improved FastICA algorithm are iteratively adjusted until the analysis results meet the preset threshold.

[0009] In some preferred embodiments, the initial signal is:

[0010] ;

[0011] In the formula, For time, As the initial signal, The mixture matrix is ​​unknown. It is the source signal for various SPIONs.

[0012] In some preferred embodiments, the preprocessing of the initial signal includes:

[0013] ;

[0014] ;

[0015] ;

[0016] In the formula, For time, As the initial signal, The noise of the initial signal, The initial signal for noise reduction processing. To The result of normalization This is the preprocessed target signal.

[0017] In some preferred embodiments, the filter coefficients of the adaptive filter satisfy the following when adaptively adjusted:

[0018] ;

[0019] ;

[0020] In the formula, These are the adjusted filter coefficients. These are the filter coefficients before adjustment. The learning rate of the adaptive filter. For time, For residuals, The initial signal after denoising. This is the initial signal before noise reduction.

[0021] In some preferred embodiments, the improved FastICA algorithm is used to perform blind source separation on the target signal to obtain independent signals of various SPIONs, including:

[0022] The separation matrix, learning rate, and objective function of the improved FastICA algorithm are initialized, and the learning rate and objective function are adaptively adjusted in response to the feature changes of the target signal after initialization.

[0023] The target signal is separated using an initialized separation matrix to obtain a first signal, and the Gaussian form of the first signal is calculated.

[0024] Based on the Gaussian form of the first signal, the objective function is updated, and the current separation matrix is ​​iteratively updated according to the current learning rate and the objective function until the updated separation matrix converges, thus obtaining a converged separation matrix.

[0025] Using the convergent separation matrix, the independent signals of various SPIONs are calculated.

[0026] In some preferred embodiments, the learning rate of the improved FastICA algorithm, when adaptively adjusted, satisfies the following:

[0027] ;

[0028] In the formula, For the updated learning rate, The learning rate before the update. As an adaptive adjustment factor, The objective function is...

[0029] The objective function of the improved FastICA algorithm, when the non-Gaussianity of the target signal is greater than a first threshold, is:

[0030] ;

[0031] The objective function of the improved FastICA algorithm, when the non-Gaussianity of the target signal is greater than the second threshold, is:

[0032] ;

[0033] In the formula, y is the target signal.

[0034] In some preferred embodiments, the iterative update of the separation matrix satisfies:

[0035] ;

[0036] In the formula, This is the correction vector used to maintain the orthogonality constraint. The objective function is...

[0037] The separation matrix satisfies the following upon convergence:

[0038] ;

[0039] In the formula, The updated separation matrix, The separation matrix before the update. This is the preset convergence threshold.

[0040] In some preferred embodiments, the analysis results include the mutual information between the individual signals. and Pearson correlation coefficient ;

[0041] The mutual information The calculation formula is:

[0042] ;

[0043] In the formula, For the preset entropy function, These are the separated, independent signals;

[0044] The Pearson correlation coefficient The calculation formula is:

[0045] ;

[0046] In the formula, For covariance, Standard deviation, These are the independent signals after separation.

[0047] In some preferred embodiments, the step of iteratively adjusting the learning rate and objective function of the improved FastICA algorithm based on the analysis results until the analysis results meet a preset threshold includes:

[0048] Determine whether the mutual information and Pearson correlation coefficient in the analysis results both meet the preset thresholds;

[0049] If the mutual information and Pearson correlation coefficient do not meet the threshold, then it is determined that the individual signals have not been completely separated.

[0050] If it is determined that the individual signals cannot be completely separated, the learning rate and objective function of the improved FastICA algorithm are iteratively adjusted, and the improved FastICA algorithm is repeatedly executed until the mutual information and Pearson correlation coefficient both meet the threshold.

[0051] In some preferred embodiments, the method further includes:

[0052] Calculate the energy of the independent signals of various SPIONs. :

[0053] ;

[0054] In the formula, For the i-th SPIONs, For time, , The sampling time of the signal for the i-th SPION;

[0055] Fourier transforms are performed on the independent signals of various SPIONs to extract frequency features. The formula for the Fourier transform is as follows:

[0056] ;

[0057] In the formula, Let i be the frequency domain signal of the i-th SPION. Let be the time-domain signal of the i-th SPION. For time, This is the kernel function for the Fourier transform;

[0058] Based on the energy of each independent signal Based on the frequency characteristics, determine whether to re-separate the target signal.

[0059] The beneficial effects of this invention are:

[0060] (1) The improved FastICA algorithm in this invention (hereinafter referred to as AF-ICA algorithm, i.e. Adaptive Fast Independent Component Analysis Signal Separation, AF-ICA) combines the fast convergence characteristics of the classic FastICA with the dynamic adjustment capability of adaptive signal processing, thereby enabling dynamic adjustment of the relevant parameters of the blind source separation process, significantly improving the separation accuracy of different SPION signals, ensuring the accuracy of each separated signal, and enhancing the robustness and flexibility of the overall system.

[0061] (2) This invention combines adaptive signal processing technology and dynamically adjusts the filtering bandwidth and the learning rate and objective function in the AF-ICA algorithm to ensure that the algorithm can run efficiently under different experimental conditions, which greatly enhances the adaptability of the system and enables it to maintain good separation effect in complex signal aliasing scenarios.

[0062] (3) Through improved signal separation methods and efficient adaptive optimization techniques, this invention can effectively address the signal aliasing problem in multicolor MPI, significantly improving the real-time performance and accuracy of multicolor imaging. As a result, this invention shows broad application prospects in fields such as multifunctional molecular markers, drug delivery monitoring, and complex biological tissue imaging. Attached Figure Description

[0063] Other features, objects, and advantages of this application will become more apparent from the following detailed description of non-limiting embodiments with reference to the accompanying drawings:

[0064] Figure 1 This is a schematic flowchart of a method for separating multicolor magnetic nanoparticle aliasing signals based on adaptive signal processing, as proposed in an embodiment of the present invention.

[0065] Figure 2 This is a detailed flowchart illustrating a method for separating multicolor magnetic nanoparticle aliased signals based on adaptive signal processing, as proposed in an embodiment of the present invention.

[0066] Figure 3 This is a schematic diagram illustrating the separation of aliased signals of SPIONs with similar frequencies, as proposed in an embodiment of the present invention.

[0067] Figure 4 This is a schematic diagram illustrating the separation of SPION particle aliasing signals at different frequencies as proposed in an embodiment of the present invention;

[0068] Figure 5 This is a schematic diagram of the structure of a computer system proposed in an embodiment of the present invention. Detailed Implementation

[0069] The present application will now be described in further detail with reference to the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are for illustrative purposes only and are not intended to limit the invention. Furthermore, it should be noted that, for ease of description, only the parts relevant to the invention are shown in the accompanying drawings.

[0070] It should be noted that, unless otherwise specified, the embodiments and features described in this application can be combined with each other. This application will now be described in detail with reference to the accompanying drawings and embodiments.

[0071] Reference Figures 1-2 ,like Figure 1 As shown, this invention provides a method for separating aliased signals of multicolor magnetic nanoparticles based on adaptive signal processing, comprising:

[0072] Step S10: Obtain the initial signal to be separated, wherein the initial signal is composed of the aliasing of independent signals of multiple SPIONs;

[0073] It is easy to understand that SPIONs exhibit nonlinear magnetization response in alternating magnetic fields, and their signal characteristics depend on physicochemical properties such as particle size, relaxation time, and surface modification. Therefore, different types of SPIONs (such as nanoprobes targeting different biomarkers) will generate unique harmonic signals under the same excitation. These signals can be further captured by magnetic particle imaging devices through receiving coils.

[0074] This embodiment can acquire mixed signals from multiple superparamagnetic iron oxide nanoparticles (SPIONs) using a magnetic particle imaging (MPI) device. Specifically, an external magnetic field is generated by the MPI device, and a known gradient field is used to scan a sample containing n types of SPIONs. Thus, under the influence of the external magnetic field, the magnetization response of the n types of SPIONs can be acquired via an induction coil. The SPIONs generate magnetization intensity under the influence of the external magnetic field, and the change of their signal over time can be described by the following formula:

[0075] ;

[0076] in, The particle magnetization intensity Let be the magnetic susceptibility of each particle. An external magnetic field is applied.

[0077] When a point or line without a magnetic field passes through a magnetic particle, the magnetization response changes, causing the signal to change as a time-domain voltage. The form is preserved, and it is easy to understand that the mixed signal contains the responses of n different SPIONs at the same time, so the signals may overlap in terms of spectrum and time.

[0078] Ultimately, the initial signal formed It should be a mixed signal vector that satisfies:

[0079] ;

[0080] In the formula, For time, As the initial signal, The mixture matrix is ​​unknown. It is the source signal for various SPIONs.

[0081] Step S20: Preprocess the initial signal to obtain the target signal; the preprocessing is: using a preset adaptive filter to denoise the initial signal and normalize the denoised initial signal to obtain the target signal; the filter coefficients of the adaptive filter are dynamically adjusted during the denoising process to reduce the filtering residual.

[0082] In this embodiment, the purpose of preprocessing the initial signal is to improve the signal-to-noise ratio (SNR) and unify the signal scale, thereby providing a standardized input for the blind source separation algorithm in the subsequent steps of this embodiment.

[0083] It is easy to understand that the acquired mixed signal x(t) is usually accompanied by system noise and environmental noise, requiring denoising processing to eliminate interference signals. To this end, this embodiment pre-constructs an adaptive filter processor, combining adaptive signal processing techniques during the filtering process to dynamically adjust the filtering parameters, minimizing noise while preserving the key features of the signal as much as possible.

[0084] Specifically, the basic form of the filter selected in this embodiment can be an LMS (Least Mean Square) filter, which has the characteristics of low computational complexity and is suitable for real-time processing, but is sensitive to non-stationary noise; it can also be an RLS (Recursive Least Squares) filter, which has the characteristics of fast convergence speed, but large computational load, and is suitable for offline analysis; it can also be a frequency domain adaptive filter, etc., which accelerates frequency domain filtering through FFT and is more suitable for broadband noise suppression.

[0085] Based on this, adaptive signal processing technology is combined to dynamically filter the signal in response to real-time changes, thereby achieving the desired filtering effect.

[0086] Step S30: The improved FastICA algorithm is used to perform blind source separation on the target signal to obtain independent signals of various SPIONs; the learning rate and separation matrix of the improved FastICA algorithm are dynamically adjusted during the blind source separation process to respond to the feature changes of the target signal.

[0087] To facilitate understanding of the improved FastICA algorithm of this application, a brief introduction to the classic FastICA algorithm in this field will be given first.

[0088] Those skilled in the art will understand that the classic FastICA algorithm, as a fast independent component analysis algorithm, generally separates source signals by maximizing non-Gaussianity, and can efficiently process mixed signals. However, the FastICA algorithm may not be able to cope with dynamic changes in signals under complex environments. Therefore, this embodiment introduces adaptive signal processing technology to improve the classic FastICA algorithm. The purpose is to dynamically adjust the algorithm parameters according to the characteristics of the real-time signal processed by the algorithm to adapt to the dynamic changes of the signal, thereby improving the accuracy and convergence speed of signal separation.

[0089] For ease of distinction, this application names the optimized algorithm the Adaptive Fast Independent Component Analysis Signal Separation Algorithm (AF-ICA). Please refer to... Figure 3-4 ,like Figure 3 The diagram shows the separation of aliased signals of SPIONs with similar frequencies when using the AF-ICA algorithm for blind source separation. Figure 4 The diagram shows the separation of SPION particle aliasing signals at different frequencies when using the AF-ICA algorithm for blind source separation.

[0090] In this embodiment, a pre-built adaptive signal processing module is used to dynamically adjust the learning rate and non-Gaussian objective function in AF-ICA. This allows for optimized separation performance under different signal conditions.

[0091] On the one hand, based on the introduced adaptive signal processing module, the learning rate is adjusted in a timely manner by detecting the changing characteristics of the current signal. When the signal changes drastically, the learning rate is increased to accelerate convergence; when the signal changes slowly, the learning rate is decreased to avoid overfitting.

[0092] On the other hand, based on the introduced adaptive signal processing module, the non-Gaussianity of the source signal is detected, and the objective function is dynamically selected or adjusted. When the signal strength is large, the objective function is chosen as follows:

[0093] ;

[0094] When the signal strength is weak, the objective function is selected as follows:

[0095] ;

[0096] In the formula, y is the target signal.

[0097] Based on this, this embodiment combines an adaptive signal processing module to continuously iterate the learning rate and objective function of the algorithm, thereby enabling the separation matrix of the AF-ICA algorithm to dynamically adapt to the characteristics of the target signal, until the final separation matrix converges.

[0098] After the separation matrix converges, the estimated source signal value of each independent SPION can be obtained by calculating the product of the separation matrix and the mixed signal, which includes the independent response signals of various SPIONs.

[0099] Step S40: Analyze the independent signals of various SPIONs to obtain analysis results, and iteratively adjust the learning rate and objective function of the improved FastICA algorithm based on the analysis results until the analysis results meet the preset threshold.

[0100] It is easy to understand that the purpose of signal analysis is to quantify the results of this signal separation, so as to adjust the signal separation process in accordance with preset thresholds, so that the final independent signal meets the preset thresholds. The preset thresholds can be set based on statistical data of historical signal separation processes, or according to performance analysis indicators or industry standards and specifications, etc. This embodiment does not impose too many limitations on this.

[0101] Specifically, the analysis results of this embodiment include, but are not limited to, the detection results of the energy and power of each independent signal, the detection results of the independence and consistency between each independent signal, the detection results of the signal quality of each independent signal, and the analysis generated based on the results of detection from multiple dimensions.

[0102] More specifically, in this embodiment, the above-mentioned preprocessing of the initial signal includes:

[0103] ;

[0104] ;

[0105] ;

[0106] In the formula, For time, As the initial signal, The noise of the initial signal, The initial signal for noise reduction processing. To The result of normalization This is the preprocessed target signal.

[0107] More specifically, in this embodiment, the adaptive adjustment of the filter coefficients of the above-mentioned adaptive filter during the denoising process satisfies:

[0108] ;

[0109] ;

[0110] In the formula, These are the adjusted filter coefficients. These are the filter coefficients before adjustment. The learning rate of the adaptive filter. For time, For residuals, The initial signal after denoising. This is the initial signal before noise reduction.

[0111] More specifically, in this embodiment, the improved FastICA algorithm is used to perform blind source separation on the target signal to obtain independent signals of various SPIONs, including:

[0112] The separation matrix, learning rate, and objective function of the improved FastICA algorithm are initialized, and the learning rate and objective function are adaptively adjusted in response to the feature changes of the target signal after initialization.

[0113] The target signal is separated using an initialized separation matrix to obtain a first signal, and the Gaussian form of the first signal is calculated.

[0114] Based on the Gaussian form of the first signal, the objective function is updated, and the current separation matrix is ​​iteratively updated according to the current learning rate and the objective function until the updated separation matrix converges, thus obtaining a converged separation matrix.

[0115] Using the convergent separation matrix, the independent signals of various SPIONs are calculated.

[0116] More specifically, in this embodiment, the learning rate of the improved FastICA algorithm described above satisfies the following when adaptively adjusted:

[0117] ;

[0118] In the formula, For the updated learning rate, The learning rate before the update. As an adaptive adjustment factor, The objective function is...

[0119] The objective function of the improved FastICA algorithm, when the non-Gaussianity of the target signal is greater than a first threshold, is:

[0120] ;

[0121] The objective function of the improved FastICA algorithm, when the non-Gaussianity of the target signal is greater than a first threshold, is:

[0122]

[0123] In the formula, y is the target signal.

[0124] More specifically, in this embodiment, updating the separation matrix through the objective function as described above specifically involves:

[0125] ;

[0126] In the formula, This is the correction vector used to maintain the orthogonality constraint. The objective function is...

[0127] The separation matrix satisfies the following upon convergence:

[0128] ;

[0129] In the formula, The updated separation matrix, The separation matrix before the update. This is the preset convergence threshold.

[0130] More specifically, in this embodiment, the above analysis results include the mutual information between each independent signal. and Pearson correlation coefficient ;

[0131] Wherein, the mutual information The calculation formula is:

[0132] ;

[0133] In the formula, For the preset entropy function, These are the separated, independent signals;

[0134] The Pearson correlation coefficient The calculation formula is:

[0135] ;

[0136] In the formula, For covariance, Standard deviation, These are the independent signals after separation.

[0137] More specifically, in this embodiment, the iterative adjustment of the learning rate and objective function of the improved FastICA algorithm based on the analysis results until the analysis results meet a preset threshold includes:

[0138] Determine whether the mutual information and Pearson correlation coefficient in the analysis results both meet the preset thresholds;

[0139] If the mutual information and Pearson correlation coefficient do not meet the threshold, then it is determined that the individual signals have not been completely separated.

[0140] If it is determined that the individual signals cannot be completely separated, the learning rate and objective function of the improved FastICA algorithm are iteratively adjusted, and the improved FastICA algorithm is repeatedly executed until the mutual information and Pearson correlation coefficient both meet the threshold.

[0141] Furthermore, it also includes:

[0142] Calculate the energy of the independent signals of various SPIONs. :

[0143] ;

[0144] In the formula, For the i-th SPIONs, For time, , The sampling time of the signal for the i-th SPION;

[0145] Fourier transforms are performed on the independent signals of various SPIONs, and frequency features are extracted. The formula for the Fourier transform is as follows:

[0146] ;

[0147] In the formula, Let i be the frequency domain signal of the i-th SPION. Let be the time-domain signal of the i-th SPION. For time, This is the kernel function for the Fourier transform;

[0148] Based on the energy of each independent signal Based on the frequency characteristics, determine whether to re-separate the target signal.

[0149] In this embodiment, the validity of each independent signal is initially determined by statistically analyzing its energy and frequency characteristics. Specifically, the frequency characteristics of each independent signal include, but are not limited to, mean, variance, and peak value. At the same time, multiple thresholds can be set to independently compare the above indicators, and a preliminary judgment is made based on the overall comparison results, that is, to determine whether the current signal is initially valid and whether the target signal needs to be separated again.

[0150] Furthermore, embodiments of this application also propose a multicolor magnetic nanoparticle aliasing signal separation system based on adaptive signal processing, comprising:

[0151] The data acquisition module is used to acquire the initial signal to be separated, which is composed of the superposition of independent signals of multiple SPIONs;

[0152] A preprocessing module is used to preprocess the initial signal to obtain a target signal. The preprocessing is as follows: the initial signal is denoised using a preset adaptive filter, and the denoised initial signal is normalized to obtain the target signal. The filter coefficients of the adaptive filter are adaptively adjusted during the denoising process to reduce the filter residual.

[0153] The signal separation module is used to perform blind source separation on the target signal using an improved FastICA algorithm to obtain independent signals of various SPIONs; the learning rate and separation matrix of the improved FastICA algorithm are adaptively adjusted during the blind source separation process to correspond to the feature changes of the target signal;

[0154] The signal analysis module is used to analyze the independent signals of various SPIONs, obtain analysis results, and iteratively adjust the learning rate and objective function of the improved FastICA algorithm based on the analysis results until the analysis results meet the preset threshold.

[0155] The following is for reference. Figure 5 It shows a schematic diagram of the structure of a computer system suitable for implementing the methods, systems, and apparatus embodiments of this application. Figure 5 The server shown is merely an example and should not impose any limitations on the functionality and scope of use of the embodiments of this application.

[0156] like Figure 5As shown, the computer system includes a Central Processing Unit (CPU) 301, which can perform various appropriate actions and processes based on programs stored in Read Only Memory (ROM) 302 or programs loaded from storage section 308 into Random Access Memory (RAM) 303. The RAM 303 also stores various programs and data required for system operation. The CPU 301, ROM 302, and RAM 303 are interconnected via a bus 304. An Input / Output (I / O) interface 305 is also connected to the bus 304.

[0157] The following components are connected to I / O interface 305: an input section 306 including a keyboard, mouse, etc.; an output section 307 including a cathode ray tube (CRT), liquid crystal display (LCD), etc., and speakers, etc.; a storage section 303 including a hard disk, etc.; and a communication section 309 including a network interface card such as a LAN (Local Area Network) card, modem, etc. The communication section 309 performs communication processing via a network such as the Internet. A drive 310 is also connected to I / O interface 305 as needed. Removable media 311, such as a disk, optical disk, magneto-optical disk, semiconductor memory, etc., are installed on drive 310 as needed so that computer programs read from them can be installed into storage section 308 as needed.

[0158] In particular, according to embodiments of the present invention, the processes described above with reference to the flowcharts can be implemented as computer software programs. For example, embodiments of the present invention include a computer program product comprising a computer program carried on a computer-readable medium, the computer program containing program code for performing the methods shown in the flowcharts. In such embodiments, the computer program can be downloaded and installed from a network via communication section 309, and / or installed from removable medium 311. When the computer program is executed by central processing unit (CPU) 301, it performs the functions defined in the methods of this application. It should be noted that the computer-readable medium described above in this application can be a computer-readable signal medium or a computer-readable storage medium or any combination thereof. The computer-readable storage medium can be, for example,—but not limited to—an electrical, magnetic, optical, electromagnetic, infrared, or semiconductor system, apparatus, or device, or any combination thereof.

[0159] More specific examples of computer-readable storage media may include, but are not limited to: electrical connections having one or more wires, portable computer disks, hard disks, random access memory (RAM), read-only memory (ROM), erasable programmable read-only memory (EPROM or flash memory), optical fiber, portable compact disk read-only memory (CD-ROM), optical storage devices, magnetic storage devices, or any suitable combination thereof. In this application, a computer-readable storage medium can be any tangible medium containing or storing a program that can be used by or in connection with an instruction execution system, apparatus, or device. In this application, a computer-readable signal medium may include a data signal propagated in baseband or as part of a carrier wave, carrying computer-readable program code. Such propagated data signals can take various forms, including but not limited to electromagnetic signals, optical signals, or any suitable combination thereof. A computer-readable signal medium can also be any computer-readable medium other than a computer-readable storage medium, which can send, propagate, or transmit a program for use by or in connection with an instruction execution system, apparatus, or device. The program code contained on a computer-readable medium can be transmitted using any suitable medium, including but not limited to: wireless, wire, optical fiber, RF, etc., or any suitable combination thereof.

[0160] Computer program code for performing the operations of this application can be written in one or more programming languages ​​or a combination thereof, including object-oriented programming languages ​​such as Java, Smalltalk, and C++, and conventional procedural programming languages ​​such as the "C" language or similar programming languages. The program code can be executed entirely on the user's computer, partially on the user's computer, as a standalone software package, partially on the user's computer and partially on a remote computer, or entirely on a remote computer or server. In cases involving remote computers, the remote computer can be connected to the user's computer via any type of network—including a local area network (LAN) or a wide area network (WAN)—or can be connected to an external computer (e.g., via the Internet using an Internet service provider).

[0161] The flowcharts and block diagrams in the accompanying drawings illustrate the architecture, functionality, and operation of possible implementations of systems, methods, and computer program products according to various embodiments of this application. In this regard, each block in a flowchart or block diagram may represent a module, segment, or portion of code containing one or more executable instructions for implementing a specified logical function. It should also be noted that in some alternative implementations, the functions indicated in the blocks may occur in a different order than those indicated in the drawings. For example, two consecutively indicated blocks may actually be executed substantially in parallel, and they may sometimes be executed in reverse order, depending on the functions involved. It should also be noted that each block in the block diagrams and / or flowcharts, and combinations of blocks in the block diagrams and / or flowcharts, can be implemented using a dedicated hardware-based system that performs the specified function or operation, or using a combination of dedicated hardware and computer instructions.

[0162] The terms “first”, “second”, etc., are used to distinguish similar objects, not to describe or indicate a specific order or sequence.

[0163] The term "comprising" or any other similar term is intended to cover non-exclusive inclusion, such that a process, method, article, or apparatus / device that comprises a list of elements includes not only those elements but also other elements not expressly listed, or elements inherent in such process, method, article, or apparatus / device.

[0164] The technical solution of the present invention has now been described in conjunction with the preferred embodiments shown in the accompanying drawings.

[0165] The above description is merely an embodiment of this application and is not intended to limit this application. Various modifications and variations can be made to this application by those skilled in the art. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principle of this application should be included within the scope of the claims of this application.

Claims

1. A method for separating aliased signals from multicolor magnetic nanoparticles based on adaptive signal processing, characterized in that, The method includes: Obtain the initial signal to be separated, which is composed of the aliasing of independent signals from multiple SPIONs; The initial signal is preprocessed to obtain the target signal; the preprocessing is as follows: the initial signal is denoised using a preset adaptive filter, and the denoised initial signal is normalized to obtain the target signal. The filter coefficients of the adaptive filter are adaptively adjusted during the denoising process to reduce the filter residual. An improved FastICA algorithm is used to perform blind source separation on the target signal to obtain independent signals of various SPIONs. The learning rate and separation matrix of the improved FastICA algorithm are adaptively adjusted during the blind source separation process to correspond to the feature changes of the target signal. When the signal changes drastically, the learning rate is increased to accelerate convergence; when the signal changes slowly, the learning rate is decreased to avoid overfitting. The independent signals of various SPIONs are analyzed to obtain analysis results. Based on the analysis results, the learning rate and objective function of the improved FastICA algorithm are iteratively adjusted, and the signal separation is performed again until the analysis results meet the preset threshold. The learning rate of the improved FastICA algorithm, when adaptively adjusted, satisfies the following: ； In the formula, For the updated learning rate, The learning rate before the update. As an adaptive adjustment factor, The objective function is... The objective function of the improved FastICA algorithm, when the non-Gaussianity of the target signal is greater than a first threshold, is: ； The objective function of the improved FastICA algorithm, when the non-Gaussianity of the target signal is greater than the second threshold, is: ； In the formula, y is the target signal.

2. The method for separating multicolor magnetic nanoparticle aliased signals based on adaptive signal processing according to claim 1, characterized in that, The initial signal is: ； In the formula, For time, As the initial signal, The mixture matrix is ​​unknown. It is the source signal for various SPIONs.

3. The method according to claim 1, characterized in that, The preprocessing of the initial signal includes: ； ； ； In the formula, For time, As the initial signal, The noise of the initial signal, The initial signal for noise reduction processing. To The result of normalization This is the preprocessed target signal.

4. The method according to claim 1, characterized in that, The filter coefficients of the adaptive filter satisfy the following when adaptively adjusted: ； ； In the formula, These are the adjusted filter coefficients. These are the filter coefficients before adjustment. The learning rate of the adaptive filter. For time, For residuals, The initial signal after denoising. This is the initial signal before noise reduction.

5. The method according to claim 1, characterized in that, The improved FastICA algorithm is used to perform blind source separation on the target signal to obtain independent signals of various SPIONs, including: The separation matrix, learning rate, and objective function of the improved FastICA algorithm are initialized, and the learning rate and objective function are adaptively adjusted in response to the feature changes of the target signal after initialization. The target signal is separated using an initialized separation matrix to obtain a first signal, and the Gaussian form of the first signal is calculated. Based on the Gaussian form of the first signal, the objective function is updated, and the current separation matrix is ​​iteratively updated according to the current learning rate and the objective function until the updated separation matrix converges, thus obtaining a converged separation matrix. Using the convergent separation matrix, the independent signals of various SPIONs are calculated.

6. The method according to claim 5, characterized in that, The iterative update of the separation matrix satisfies: ； In the formula, This is the correction vector used to maintain the orthogonality constraint. Let be the objective function. This is the first signal; The separation matrix satisfies the following upon convergence: ； In the formula, The updated separation matrix, The separation matrix before the update. This is the preset convergence threshold.

7. The method according to claim 1, characterized in that, The analysis results include the mutual information between individual signals. and Pearson correlation coefficient ; The mutual information The calculation formula is: ； In the formula, For the preset entropy function, These are the separated, independent signals; The Pearson correlation coefficient The calculation formula is: ； In the formula, For covariance, Standard deviation, These are the independent signals after separation.

8. The method according to claim 1, characterized in that, The step of iteratively adjusting the learning rate and objective function of the improved FastICA algorithm based on the analysis results until the analysis results meet a preset threshold includes: Determine whether the mutual information and Pearson correlation coefficient in the analysis results both meet the preset thresholds; If the mutual information and Pearson correlation coefficient do not meet the threshold, then it is determined that the individual signals have not been completely separated. If it is determined that the individual signals cannot be completely separated, the learning rate and objective function of the improved FastICA algorithm are iteratively adjusted, and the improved FastICA algorithm is repeatedly executed until the mutual information and Pearson correlation coefficient both meet the threshold.

9. The method according to claim 1, characterized in that, The method further includes: Calculate the energy of the independent signals of various SPIONs. : ； In the formula, For the i-th SPIONs, For time, , The sampling time of the signal for the i-th SPION; Fourier transforms are performed on the independent signals of various SPIONs to extract frequency features. The formula for the Fourier transform is as follows: ； In the formula, Let i be the frequency domain signal of the i-th SPION. Let be the time-domain signal of the i-th SPION. For time, This is the kernel function for the Fourier transform; Based on the energy of each independent signal Based on the frequency characteristics, determine whether to re-separate the target signal.

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