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

Abstract

The invention belongs to the field of magnetic particle imaging, particularly relates to a multicolor magnetic nanoparticle aliasing signal separation method based on adaptive signal processing, and aims to solve the problem that various SPIONs signals are difficult to accurately distinguish in the prior art. The method comprises the following steps: acquiring a to-be-separated initial signal, and preprocessing the initial signal to obtain a target signal; carrying out blind source separation on the target signal by adopting an improved FastICA algorithm to obtain various independent signals; and analyzing the various independent signals to obtain an analysis result, and iteratively adjusting the learning rate and the objective function of the algorithm according to the analysis result until the analysis result meets a preset threshold value. Based on the method, the separation precision of different signals is effectively improved by adaptively adjusting related parameters in the blind source separation process.

Description

TECHNICAL FIELD

[0001] The 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. BACKGROUND

[0002] Magnetic particle imaging (MPI) is a non-radiation, high-sensitivity medical imaging technology that generates images by detecting the nonlinear response of superparamagnetic iron oxide nanoparticles (SPIONs) in an applied magnetic field. MPI technology forms a field-free point (FFP) or field-free line (FFL) in space by constructing a magnetic field gradient field, and detects the SPIONs signal at the FFP (field-free point) or FFL (field-free line) through an external coil to realize image reconstruction of the SPIONs distribution. However, the existing MPI technology is usually only for a single type of SPIO, which limits its application in multifunctional labeling and complex tissue environments.

[0003] To address this limitation, multi-color MPI technology aims to detect multiple targets or markers simultaneously through multiple types or different physical properties of SPIONs. This technology has great potential in tumor labeling, drug delivery, and multifunctional molecular probe research. However, in actual signal measurement processes, the spectral response of different SPIONs will cause signal aliasing and separation difficulties, and existing separation methods based on spectrum or relaxation effect cannot accurately distinguish the signals of various SPIONs, thereby affecting the quantitative analysis accuracy of imaging. SUMMARY

[0004] To solve the above problems in the prior art, i.e., the existing signal separation scheme based on spectrum or relaxation effect cannot accurately distinguish the signals of various SPIONs, thereby affecting the quantitative analysis accuracy of imaging, the application proposes a multi-color magnetic nanoparticle aliasing signal separation method based on adaptive signal processing, comprising: acquiring an initial signal to be separated, the initial signal being composed of aliasing of independent signals of multiple SPIONs; preprocessing the initial signal to obtain a target signal; the preprocessing is: using a preset adaptive filter to perform denoising processing on the initial signal, and performing normalization processing on the denoised initial signal to obtain the target signal, the filter coefficient of the adaptive filter being adaptively adjusted in the process of denoising processing to reduce filter residual error; The improved FastICA algorithm is used to perform blind source separation on the target signal to obtain independent signals of various SPIONs; and the learning rate and separation matrix of the improved FastICA algorithm are self-adaptively adjusted in the process of blind source separation to correspond to the characteristic changes of the target signal. The independent signals of various SPIONs are analyzed to obtain an analysis result, and the learning rate and objective function of the improved FastICA algorithm are iteratively adjusted according to the analysis result until the analysis result meets a preset threshold.

[0005] In some preferred embodiments, the initial signal is: ; In the formula, is time, is the initial signal, is an unknown mixing matrix, is a source signal of various SPIONs.

[0006] In some preferred embodiments, the pre-processing of the initial signal comprises: ; ; ; In the formula, is time, is the initial signal, is noise of the initial signal, is the initial signal after denoising processing, is the result of normalizing the , and is the target signal after pre-processing.

[0007] In some preferred embodiments, when the filter coefficient of the adaptive filter is self-adaptively adjusted, the following condition is met: ; ; In the formula, is the adjusted filter coefficient, is the filter coefficient before adjustment, is the learning rate of the adaptive filter, is time, is a residual error, is the initial signal after denoising, is the initial signal before denoising.

[0008] 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: The separation matrix, learning rate and objective function of the improved FastICA algorithm are initialized, and the learning rate and objective function are adapted in response to changes in characteristics of the target signal after being initialized; The target signal is separated using the initialized separation matrix to obtain a first signal, and a Gaussian form of the first signal is calculated; The target function is updated according to the Gaussian form of the first signal, and the current separation matrix is iteratively updated according to the current learning rate and target function until the updated separation matrix converges, obtaining a converged separation matrix; The independent signals of various SPIONs are calculated using the converged separation matrix.

[0009] In some preferred embodiments, the learning rate of the improved FastICA algorithm satisfies the following condition when it is adaptively adjusted: ; In the formula, is the updated learning rate, is the previous learning rate, is an adaptive adjustment factor, is the target function; The target function of the improved FastICA algorithm is: when the non-Gaussianity of the target signal is greater than a first threshold value; The target function of the improved FastICA algorithm is: when the non-Gaussianity of the target signal is greater than a second threshold value; In the formula, y is the target signal.

[0010] In some preferred embodiments, the iterative update of the separation matrix satisfies the following condition: ; In the formula, is a correction vector for maintaining orthogonality constraints, is the target function; The separation matrix satisfies the following condition when it converges: ; In the formula, is the updated separation matrix, is the previous separation matrix, is a preset convergence threshold.

[0011] In some preferred embodiments, the analysis result comprises mutual information between each independent signal and Pearson correlation coefficient ; The mutual information is calculated by the following formula: ; Wherein, is a preset entropy function, is the separated independent signal; The Pearson correlation coefficient is calculated by the following formula: ; Wherein, is a covariance, is a standard deviation, is the separated independent signal.

[0012] In some preferred embodiments, the learning rate and the objective function of the improved FastICA algorithm are iteratively adjusted according to the analysis result until the analysis result meets a preset threshold, comprising: Determining whether the mutual information and the Pearson correlation coefficient in the analysis result meet the preset threshold; If the mutual information and the Pearson correlation coefficient do not meet the threshold, it is determined that each independent signal is not completely separated; If it is determined that each independent signal is not completely separated, the learning rate and the objective function of the improved FastICA algorithm are iteratively adjusted, and the improved FastICA algorithm is repeatedly executed until the mutual information and the Pearson correlation coefficient meet the threshold.

[0013] In some preferred embodiments, the method further comprises: Calculating the energy of the independent signal of each SPION : ; Wherein, is the independent signal of the i-th SPION, is time, , is the signal sampling time of the i-th SPION; The independent signal of each SPION is respectively subjected to Fourier transform to extract frequency characteristics, and the formula of the Fourier transform is: ; Wherein, is the frequency domain signal of the i-th SPION, is a time domain signal of the ith SPIONs, is a time, is a kernel function of Fourier transform; determines whether to re-separate the target signal according to the energy of each independent signal and the frequency characteristics.

[0014] Advantages of the present application: (1) The improved FastICA algorithm (hereinafter referred to as AF-ICA algorithm, namely Adaptive Fast Independent Component Analysis Signal Separation, AF-ICA) in the present application combines the fast convergence characteristics of the classic FastICA with the dynamic adjustment capability of adaptive signal processing, so as to dynamically adjust the related parameters of the blind source separation process, significantly improve the separation accuracy of different SPIONs signals, ensure the accuracy of each separated signal, and enhance the robustness and flexibility of the overall system.

[0015] (2) The present application combines adaptive signal processing technology to dynamically adjust the filter bandwidth and the learning rate, target function in the AF-ICA algorithm, so as to ensure that the algorithm can run efficiently under different experimental conditions, greatly enhance the adaptability of the system, and still maintain good separation effect in complex signal aliasing scene.

[0016] (3) The present application can effectively deal with the signal aliasing problem in multi-color MPI through the improved signal separation method and efficient adaptive optimization technology, significantly improve the real-time performance and accuracy of multi-color imaging, so that the present application has broad application prospects in the fields of multi-functional molecular labeling, drug delivery monitoring and complex biological tissue imaging. BRIEF DESCRIPTION OF DRAWINGS

[0017] Other features, objects and advantages of the present application will become more apparent from the following detailed description of non-limiting embodiments made with reference to the accompanying drawings: Figure 1 is a flowchart of a multi-color magnetic nanoparticle aliasing signal separation method based on adaptive signal processing according to an embodiment of the present application; Figure 2 is a detailed flowchart of a multi-color magnetic nanoparticle aliasing signal separation method based on adaptive signal processing according to an embodiment of the present application; Figure 3 is a schematic diagram of a similar frequency SPIONs particle aliasing signal separation according to an embodiment of the present application; Figure 4is a schematic diagram of mixed signal separation of different frequency SPIONs particles proposed by the embodiment of the present application. Figure 5 is a structural schematic diagram of a computer system proposed by the embodiment of the present application. DETAILED DESCRIPTION

[0018] The present application will be further described in detail below with reference to the accompanying drawings and embodiments. It can be understood that the specific embodiments described herein are only used to explain the related application, and not to limit the application. In addition, it should be noted that, for the convenience of description, only the parts related to the application are shown in the drawings.

[0019] It should be noted that the embodiments in the present application and the features in the embodiments can be combined with each other without conflict. The present application will be described in detail below with reference to the accompanying drawings and embodiments.

[0020] Reference Figures 1-2 As Figure 1 indicated, the present application provides a multi-color magnetic nanoparticle mixed signal separation method based on adaptive signal processing, comprising: Step S10, acquiring an initial signal to be separated, the initial signal being composed of mixed signals of multiple SPIONs; It is easy to understand that SPIONs exhibit nonlinear magnetization response in an alternating magnetic field, and the signal characteristics thereof depend on the physical and chemical properties such as particle size, relaxation time, and surface modification. Therefore, different types of SPIONs (such as nanoprobe targeting different biomarkers) will generate unique harmonic signals under the same excitation, and these signals can be further captured by a magnetic particle imaging device through a receiving coil.

[0021] The present embodiment can collect mixed signals including multiple superparamagnetic iron oxide nanoparticles (SPIONs) through a magnetic particle imaging device, that is, an external magnetic field is generated by a magnetic particle imaging (MPI) device, and a sample containing n SPIONs is scanned using a known gradient field. Thus, under the action of the external magnetic field, the magnetization response of the n SPIONs can be collected through an induction coil, and the SPIONs will generate a magnetization intensity under the action of the external magnetic field, and the signal change rule over time can be described by the following formula: ; wherein, is the particle magnetization intensity, is the magnetic susceptibility of each particle, is the external magnetic field.

[0022] When a magnetic particle is passed through a point or a line without a magnetic field, the magnetization response changes, so that the signal changes in the time domain voltage The form is saved, and it is easy to understand that the mixed signal contains the responses of n different SPIONs at the same time, so there may be overlaps in the frequency spectrum and time of each signal.

[0023] Finally, the initial signal formed The mixed signal signal vector should satisfy: ; In the formula, is the time, is the initial signal, is an unknown mixing matrix, is the source signal of multiple SPIONs.

[0024] In step S20, the initial signal is preprocessed to obtain a target signal; the preprocessing is: using a preset adaptive filter to perform denoising processing on the initial signal, and performing normalization processing on the denoised initial signal to obtain the target signal, and the filter coefficient of the adaptive filter is dynamically adjusted in the denoising processing process to reduce the filter residual error; 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.

[0025] It is easy to understand that the collected mixed signal x(t) is usually accompanied by the influence of system noise and environmental noise, and the interference signal needs to be eliminated through denoising processing. For this purpose, the adaptive filter processor is constructed in advance in this embodiment, and the adaptive signal processing technology is combined in the filtering process to dynamically adjust the filter parameters, so as to reduce the noise to the greatest extent, and at the same time, the key features of the signal are preserved as much as possible.

[0026] 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 amount of calculation, and is suitable for offline analysis; it can also be a frequency domain adaptive filter, etc., which accelerates the frequency domain filtering through FFT and is more suitable for wideband noise suppression.

[0027] On this basis, combined with adaptive signal processing technology, the real-time change of the response signal is dynamically filtered, so as to achieve the ideal filtering effect.

[0028] Step S30, using the improved FastICA algorithm, blind source separation is performed on the target signal to obtain independent signals of various SPIONs; the learning rate of the improved FastICA algorithm and the separation matrix are dynamically adjusted in the process of blind source separation to respond to the characteristic changes of the target signal. To facilitate understanding of the improved FastICA algorithm of the present application, the classical FastICA algorithm in the art is first introduced.

[0029] As can be understood by those skilled in the art, the classical FastICA, 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 the dynamic changes of signals in complex environments, therefore, the classical FastICA algorithm is improved by introducing adaptive signal processing technology in this embodiment, the purpose is to dynamically adjust the algorithm parameters according to the characteristics of the real-time signals processed by the algorithm, to adapt to the dynamic changes of the signals, so as to improve the precision and convergence speed of signal separation.

[0030] For convenience of distinction, the improved algorithm is named as adaptive fast ICA signal separation algorithm (i.e. AF-ICA, Adaptive Fast Independent Component Analysis Signal Separation) in this application. Please refer to Figures 3-4 As shown in Figure 3 is a schematic diagram of signal separation of SPIONs particle mixed signals of similar frequencies using AF-ICA algorithm for blind source separation, and Figure 4 is a schematic diagram of signal separation of SPIONs particle mixed signals of different frequencies using AF-ICA algorithm for blind source separation.

[0031] In this embodiment, the learning rate and the non-gaussianity objective function in AF-ICA are dynamically adjusted through the pre-constructed adaptive signal processing module , so as to optimize the separation effect in different signal environments.

[0032] In one aspect, based on the introduced adaptive signal processing module, the learning rate is adjusted in time by detecting the change characteristics of the current signal , when the signal changes sharply, the learning rate is increased to speed up the convergence; when the signal changes slowly, the learning rate is reduced to avoid overfitting: In another aspect, 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 selected as: ; When the signal strength is weak, the target function is selected as: ; In the formula, y is the target signal.

[0033] Based on this, the embodiment combines the adaptive signal processing module to constantly update the learning rate and the target function of the algorithm, so that the separation matrix of the AF-ICA algorithm is dynamically updated to adapt to the characteristics of the target signal, until the final obtained separation matrix converges.

[0034] After the separation matrix converges, the value of the estimated source signal 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.

[0035] In step S40, the independent signals of various SPIONs are analyzed to obtain an analysis result, and the learning rate and the target function of the improved FastICA algorithm are iteratively adjusted according to the analysis result until the analysis result meets a preset threshold.

[0036] It is easy to understand that the purpose of signal analysis is to quantitatively analyze the result of this signal separation, so that the process of signal separation can be adjusted in feedback combined with the preset threshold, so that the final independent signal meets the preset threshold. The preset threshold can be set based on statistical data of historical signal separation processes, or can be set according to performance analysis indicators or industry standard specifications, and the embodiment does not make too many limitations.

[0037] Specifically, the analysis result of the embodiment includes but is not limited to the detection results of the energy and power of each independent signal, the independence and consistency detection results between each independent signal, and the signal quality detection results of each independent signal. The analysis results generated based on multiple dimensions can be analyzed.

[0038] More specifically, in the embodiment, the above-mentioned preprocessing process of the initial signal includes: ; ; ; In the formula, is the time, is the initial signal, is the noise of the initial signal, is the initial signal after denoising processing, is the result of normalizing , and is the target signal after preprocessing.

[0039] More specifically, in the embodiment, the filter coefficient of the adaptive filter is adjusted adaptively during the denoising process, and the adjustment satisfies: ; ; In the formula, is the adjusted filter coefficient, is the filter coefficient before adjustment, is the learning rate of the adaptive filter, is the time, is the residual error, is the initial signal after denoising, is the initial signal before denoising.

[0040] More specifically, in the embodiment, 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 changes in the characteristics of the target signal after being initialized; The target signal is separated using the initialized separation matrix to obtain a first signal, and the Gaussian type of the first signal is calculated; According to the Gaussian type of the first signal, the target function is updated, and the current separation matrix is iteratively updated according to the current learning rate and target function until the updated separation matrix converges, and a converged separation matrix is obtained; The independent signals of various SPIONs are calculated using the converged separation matrix.

[0041] More specifically, in the embodiment, the learning rate of the improved FastICA algorithm satisfies: ; In the formula, is the updated learning rate, is the learning rate before updating, is an adaptive adjustment factor, is the target function; When the non-Gaussianity of the target signal is greater than a first threshold, the target function of the improved FastICA algorithm is: ; When the non-Gaussianity of the target signal is greater than a first threshold, the target function of the improved FastICA algorithm is: Wherein, y is the target signal.

[0042] More specifically, in the embodiment, the updating the separation matrix by the target function includes: Wherein, is a correction vector for maintaining the orthogonality constraint, is the target function; The separation matrix satisfies: Wherein, is the updated separation matrix, is the separation matrix before updating, is a preset convergence threshold.

[0043] More specifically, in the embodiment, the analysis result includes mutual information between each independent signal and Pearson correlation coefficient . Wherein, the mutual information is calculated by the following formula: Wherein, is a preset entropy function, is the separated independent signal; The Pearson correlation coefficient is calculated by the following formula: Wherein, is a covariance, is a standard deviation, is the separated independent signal.

[0044] More specifically, in the embodiment, the iterative adjustment of the learning rate and the target function of the improved FastICA algorithm according to the analysis result until the analysis result meets the preset threshold includes: Determining whether the mutual information and the Pearson correlation coefficient in the analysis result meet the preset threshold; If the mutual information and the Pearson correlation coefficient do not meet the threshold, it is determined that each independent signal is not completely separated; If it is determined that each independent signal is not completely separated, the learning rate and the target function of the improved FastICA algorithm are iteratively adjusted, and the improved FastICA algorithm is repeatedly executed until the mutual information and the Pearson correlation coefficient meet the threshold.

[0045] Further, it also includes:​​​​​ calculating the energy of the individual signals of various SPIONs wherein, is the individual signal of the i-th SPION, is time, is the sampling time of the signal of the i-th SPION; performing Fourier transform on the individual signals of various SPIONs respectively, and extracting frequency features, the formula of the Fourier transform being: wherein, is the frequency domain signal of the i-th SPION, is the time domain signal of the i-th SPION, is time, is the kernel function of the Fourier transform; determining whether to re-separate the target signal according to the energy of the individual signals

[0046] In the embodiment, the effectiveness of the obtained individual signals is preliminarily judged by counting the energy and frequency features of each individual signal. Specifically, the frequency features of the individual signals include but are not limited to mean, variance and peak value, etc. Meanwhile, multiple threshold values can be set for independent comparison of the above indicators, and a preliminary judgment is made according to the overall comparison result, i.e., whether the current signal is preliminarily effective and whether the target signal needs to be re-separated.

[0047] Further, the application also provides a multi-color magnetic nanoparticle aliasing signal separation system based on adaptive signal processing, comprising: a data acquisition module, configured to acquire an initial signal to be separated, wherein the initial signal is composed of individual signals of various SPIONs; a preprocessing module, configured to pre-process the initial signal to obtain a target signal; the preprocessing is: using a preset adaptive filter to perform denoising processing on the initial signal, and performing normalization processing on the denoised initial signal to obtain the target signal, wherein the filter coefficient of the adaptive filter is adaptively adjusted in the process of denoising processing to reduce filter residual error; a signal separation module, configured to use an improved FastICA algorithm to perform blind source separation on the target signal to obtain individual signals of various SPIONs; the learning rate and separation matrix of the improved FastICA algorithm are adaptively adjusted in the process of blind source separation to correspond to the feature change of the target signal.​​​​​ a signal analysis module, configured to analyze independent signals of various SPIONs, obtain an analysis result, and iteratively adjust a learning rate and an objective function of the improved FastICA algorithm according to the analysis result until the analysis result meets a preset threshold.

[0048] Reference will now be made to the following description Figure 5 which shows a structural schematic diagram of a computer system of a server suitable for implementing the embodiments of the method, system and device of the present application. Figure 5 The server shown is merely an example and should not bring any limitation to the functions and use range of the embodiments of the present application.

[0049] As shown in Figure 5 the computer system includes a central processing unit (CPU) 301 which can perform various appropriate actions and processes according to programs stored in a read only memory (ROM) 302 or loaded from a storage portion 308 into a random access memory (RAM) 303. Various programs and data required for system operation are also stored in the RAM 303. The CPU 301, the ROM 302 and the RAM 303 are connected to each other through a bus 304. An input / output (I / O) interface 305 is also connected to the bus 304.

[0050] The following components are connected to the I / O interface 305: an input portion 306 including a keyboard, a mouse, etc.; an output portion 307 including a display such as a cathode ray tube (CRT), a liquid crystal display (LCD), etc., and a speaker, etc.; a storage portion 308 including a hard disk, etc.; and a communication portion 309 including a network interface card such as a LAN (Local Area Network) card, a modem, etc. The communication portion 309 performs communication processing via a network such as the Internet. A drive 310 is also connected to the I / O interface 305 as necessary. A removable recording medium 311 such as a magnetic disk, an optical disk, a magneto-optical disk, a semiconductor memory, etc. is attached to the drive 310 as necessary, so that a computer program read therefrom is installed in the storage portion 308 as necessary.

[0051] In particular, the processes described above with reference to the flowcharts can be implemented as a computer software program in accordance with embodiments of the present application. For example, embodiments of the present application include a computer program product comprising a computer program carried on a computer readable medium, the computer program comprising program code for performing the methods illustrated by the flowcharts. In such embodiments, the computer program can be downloaded and installed from a network via the communication section 309, and / or installed from the removable media 311. When the computer program is executed by the central processing unit (CPU) 301, the above-described functions defined in the methods of the present application are performed. Note that the computer readable medium described above in the present application can be either a computer readable signal medium or a computer readable storage medium or any combination of the two. The computer readable storage medium may, for example, be, but is not limited to, an electronic, magnetic, optical, electromagnetic, infrared, or semiconductor system, apparatus or device, or any suitable combination of the foregoing.

[0052] More specific examples of the computer readable storage medium can include, but are not limited to, an electrical connection having one or more wires, a portable computer diskette, a hard disk, a random access memory (RAM), a read-only memory (ROM), an erasable programmable read-only memory (EPROM or Flash memory), an optical fiber, a portable compact disc read-only memory (CD-ROM), an optical storage device, a magnetic storage device, or any suitable combination of the foregoing. In the present application, a computer readable storage medium can be any tangible medium that can contain or store a program for use by or in connection with an instruction execution system, apparatus or device. In the present application, a computer readable signal medium can include a computer readable program code carried by a data signal in a baseband or as part of a carrier wave. Such a propagated data signal can take any of a variety of forms, including but not limited to electro-magnetic, optical, or any suitable combination thereof. Computer readable signal media can be any computer readable medium that is not a computer readable storage medium and that can communicate, propagate or transport a program for use by or in connection with an instruction execution system, apparatus or device. Program code embodied on a computer readable medium can be transmitted using any appropriate medium, including but not limited to wireless, wire line, optical fiber cable, RF, etc., or any suitable combination of the foregoing.

[0053] Computer program code for carrying out operations of the present application can be written in any combination of one or more programming languages, including an object oriented programming language such as Java, Smalltalk, C++ or the like and conventional procedural programming languages, such as the "C" programming language or similar programming languages. The program code can execute entirely on the user's computer, partly on the user's computer, as a stand-alone software package, partly on the user's computer and partly on a remote computer or entirely on the remote computer or server. In the latter scenario, the remote computer can be connected to the user's computer through any type of network, including a local area network (LAN) or a wide area network (WAN), or the connection can be made to an external computer (for example, through the Internet using an Internet Service Provider).

[0054] The flow diagrams and the block diagrams in the drawings are illustrations of architectures, functionalities, and operations of possible implementations of systems, methods, and computer program products according to various embodiments of the present application. In this regard, each block in the flow diagrams or block diagrams can represent a module, a segment, or a portion of code, which comprises one or more executable instructions for implementing the specified logical function(s). It should also be noted that in some alternative implementations, the functions noted in the block can occur out of the order noted in the figures. For example, two blocks shown in succession may, in fact, be executed substantially concurrently or the blocks can sometimes be executed in the reverse order, depending upon the functionality involved. It will also be noted that each block of the block diagrams and / or flow diagrams, and combinations thereof, can be implemented by special purpose hardware-based systems that perform the specified functions or operations, or combinations of special purpose hardware and computer instructions.

[0055] The terms "first", "second", etc. are used to distinguish similar objects, not to describe or indicate a particular order or sequence.

[0056] The term "comprising" or any other similar term is intended to encompass the inclusion of one or more elements, steps, or components, but not to the exclusion of any other elements, steps, or components. It is intended to mean that the process, method, article, or apparatus / assembly includes the listed elements, but not excluding other elements.

[0057] So far, the technical solutions of the present application have been described in combination with the preferred embodiments shown in the drawings.

[0058] The above merely provides an example of the present application, but is not intended to limit the present application. Any modification, equivalent replacement, improvement, etc. within the spirit and principle of the present application should be included in the scope of claims of the present application.

Claims

1. A method for separating multi-color magnetic nanoparticle aliased signals based on adaptive signal processing, characterized in that: The method comprises: Acquiring an initial signal to be separated, wherein the initial signal is composed of a mixture of independent signals of multiple SPIONs; Preprocessing the initial signal to obtain a target signal; the preprocessing comprises: performing denoising processing on the initial signal using a preset adaptive filter, and normalizing the denoised initial signal to obtain the target signal, wherein the filter coefficient of the adaptive filter is adaptively adjusted during the denoising process to reduce filtering residuals; 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 characteristic changes of the target signal; The independent signals of various SPIONs are analyzed to obtain analysis results, and based on the analysis results, the learning rate and objective function of the improved FastICA algorithm are iteratively adjusted to re-perform signal separation until the analysis results meet a preset threshold.

2. The method for separating multi-color magnetic nanoparticle aliased signals based on adaptive signal processing according to claim 1, characterized in that: The initial signal is: ； Where, For time, is the initial signal, is the unknown mixing matrix, are the source signals of various SPIONs.

3. The method according to claim 1, characterized in that The preprocessing of the initial signal includes: ； ； ； Where, For time, is the initial signal, is the noise of the initial signal, is the initial signal for denoising, For The result of normalization is is the target signal after preprocessing.

4. The method according to claim 1, wherein The filter coefficients of the adaptive filter satisfy the following when adaptively adjusted: ； ； Where, is the adjusted filter coefficient, is the filter coefficient before adjustment, is the learning rate of the adaptive filter, For time, is the residual, is the initial signal after denoising, is the initial signal before denoising.

5. The method according to claim 1, wherein The improved FastICA algorithm is used to perform blind source separation on the target signal to obtain independent signals of various SPIONs, including: Initializing a separation matrix, a learning rate, and an objective function of the improved FastICA algorithm, wherein the learning rate and the objective function are adaptively adjusted in response to characteristic changes of the target signal after being initialized; Separating the target signal using the initialized separation matrix to obtain a first signal, and calculating a Gaussian shape of the first signal; updating the objective function according to the Gaussian shape of the first signal, and iteratively updating the current separation matrix according to the current learning rate and the objective function until the updated separation matrix converges to obtain a converged separation matrix; Using the converged separation matrix, the independent signals of various SPIONs are calculated.

6. The method according to claim 5, characterized in that The learning rate of the improved FastICA algorithm satisfies the following when adaptively adjusted: ； Where, is the updated learning rate, is the learning rate before updating, is the adaptive adjustment factor, is the objective function; 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: ； Where y is the target signal.

7. The method according to claim 5, characterized in that When the separation matrix is ​​iteratively updated, it satisfies: ； Where, is the correction vector used to maintain the orthogonality constraint, is the objective function; The separating matrix satisfies when converged: ； Where, is the updated separation matrix, is the separation matrix before updating, is the preset convergence threshold.

8. The method according to claim 1, characterized in that The analysis results include the mutual information between each independent signal and Pearson correlation coefficient ; The mutual information The calculation formula is: ； Where, is the preset entropy function, It is an independent signal after separation; The Pearson correlation coefficient The calculation formula is: ； Where, is the covariance, is the standard deviation, It is an independent signal after separation.

9. The method according to claim 1, characterized in that The iteratively adjusting the learning rate and the objective function of the improved FastICA algorithm according to the analysis result until the analysis result meets a preset threshold comprises: Determining whether the mutual information and the Pearson correlation coefficient in the analysis results both meet preset thresholds; If both the mutual information and the Pearson correlation coefficient do not meet the threshold, it is determined that the independent signals are not completely separated; If it is determined that the independent signals cannot be completely separated, the learning rate and the objective function of the improved FastICA algorithm are iteratively adjusted, and the improved FastICA algorithm is repeatedly executed until the mutual information and the Pearson correlation coefficient both meet the threshold.

10. The method according to claim 1, characterized in that The method further comprises: Calculate the energy of the independent signals of various SPIONs : ； Where, is the independent signal of the i-th SPIONs, For time, 、 is the signal sampling time of the i-th SPIONs; Fourier transform is performed on the independent signals of various SPIONs to extract the frequency characteristics. The formula of the Fourier transform is: ； Where, is the frequency domain signal of the i-th SPIONs, is the time domain signal of the i-th SPIONs, For time, is the kernel function of Fourier transform; According to the energy of each independent signal and the frequency characteristics to determine whether to re-separate the target signal.

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