A broad spectrum reconstruction method based on singular value decomposition

Abstract

The application discloses a wide spectrum reconstruction method based on singular value decomposition. The method comprises the following steps: firstly, acquiring multiple spectrum signals by a spectrum instrument, and performing coil combination on the spectrum time domain signals; then, performing spectrum registration by using a singular value decomposition method, and completing frequency and phase alignment of different acquired spectrum signals; finally, performing average processing on a target spectrum signal matrix, and then completing spectrum signal reconstruction. The singular value decomposition method is applied to perform spectrum registration for the first time, frequency and phase alignment of different acquired spectrum signals is completed, the time domain coil combination method is combined, spectrum reconstruction is realized under low signal-to-noise ratio, the signal-to-noise ratio of the reconstructed spectrum signal is improved, and thus, spectrum signal underestimation is reduced.

Description

Technical Field

[0001] This invention belongs to the field of spectral technology, and in particular relates to a broad spectral reconstruction method based on singular value decomposition. Background Technology

[0002] Magnetic resonance spectroscopy can be used to measure unique information about the concentration of brain metabolites in the body. Some metabolites are thought to be highly specific to glial cells, such as glutamine or inositol; some metabolites are specific to neurons, such as N-acetylaspartate or glutamate; while others are present in all cell types, such as various forms of creatine.

[0003] However, magnetic resonance spectroscopy is inherently a low signal-to-noise ratio (SNR) technique because the concentration of metabolites is much lower than that of water, thus requiring extensive spectral acquisition and averaging. This is especially problematic when precise spatial localization is needed to study minute structures, as large voxel volumes cannot compensate for the low SNR. Furthermore, some derivative techniques of magnetic resonance spectroscopy, such as diffusion-weighted spectroscopy, edited spectroscopy, and spectral imaging, significantly reduce the final SNR due to complications such as increased acquisition sequences, reduced individual voxel volumes, increased echo times, or further signal attenuation. Therefore, post-processing methods that minimize noise variance and its impact on the quantization of magnetic resonance spectroscopy signals are necessary.

[0004] Furthermore, phase or frequency drift cannot be ignored during multiple spectral acquisitions. Spectral registration can typically increase the signal-to-noise ratio (SNR) of the final average signal and reduce signal artifacts. Spectral registration methods are crucial for avoiding artifacts from spectral subtraction during editing, SNR loss, and underestimation / overestimation of metabolite levels. To achieve better SNR during coil assembly and spectral registration, significant efforts have been made to improve magnetic resonance spectral post-processing. Magnetic resonance equipment manufacturers and popular magnetic resonance spectral data processing toolkits such as FID-A employ time-domain coil assembly methods, using the first time point data of the freely decaying signal to calculate phase and amplitude weights. Singular value decomposition-based coil assembly methods, however, do not require reference to any specific time point. In terms of spectral registration, some researchers have proposed robust spectral registration methods that use the best reference spectrum and nonlinear least squares optimization algorithms to align individual acquired spectra. However, the reconstruction effect deteriorates when the spectral signal-to-noise ratio is poor, and the optimization algorithms used have low time efficiency. Other researchers have proposed time-domain spectral registration methods that use optimization methods to align the frequencies and phases of different acquired spectra, but these methods still suffer from insufficient robustness and other signal contamination issues. Summary of the Invention

[0005] To address the problems existing in the background art, the present invention aims to provide a broad spectrum reconstruction method based on singular value decomposition. This invention utilizes singular value decomposition for spectrum registration, aligning the frequencies and phases of different acquired spectral signals. Combined with a time-domain coil combination method, it achieves spectrum reconstruction under low signal-to-noise ratio (SNR) conditions and improves the SNR of the reconstructed spectral signal, thereby reducing the underestimation of spectral signal intensity.

[0006] To achieve the above objectives, the present invention adopts the following solution, which includes the following steps:

[0007] S1. First, acquire M spectral signals using a spectral instrument;

[0008] S2. Then, the spectral signal of each wave spectrum is weighted and averaged according to the receiving coil to obtain the weighted average coil wave spectrum signal.

[0009] S3. Next, the M coil spectrum signals are combined to form an unaligned coil spectrum matrix, and the singular value decomposition method is used to align the coil spectrum matrix to obtain an aligned spectrum signal matrix.

[0010] S4. Correct the phase and frequency of the aligned spectral signal matrix to obtain the corrected target spectral signal matrix;

[0011] S5. Remove the damaged spectrum and average the target spectrum signal matrix to complete the reconstruction of the spectrum signal.

[0012] The specific steps for weighted average processing in S2 are as follows:

[0013] S2.1. Based on the amplitude and phase of the spectral signal, the amplitude weight γf of each channel in the receiving coil is obtained according to the following formula. i and receiving coil phase weight γx i :

[0014]

[0015] γx i =γX i

[0016] Where, γf i γF represents the amplitude weight of the receiving coil in the i-th channel. i Z represents the amplitude at the first time-domain point in the spectral signal received by the i-th channel. i γx represents the noise of the spectral signal received by the i-th channel. i γX represents the phase weight of the receiving coil in the i-th channel. i This represents the phase of the first time-domain point in the spectral signal received by the i-th channel, where i represents the channel number of the receiving coil;

[0017] S2.2, Amplitude weighting γf of the receiving coils for all channels i Normalization is performed to obtain the normalized amplitude weight γg for each channel. i The spectral signals in each channel are weighted and averaged using the following formula to obtain the weighted averaged coil spectral signal:

[0018]

[0019]

[0020] Where A is the amplitude of the coil spectrum signal, Ф is the phase of the coil spectrum signal, and L is the total number of channels of the receiving coil.

[0021] The specific steps of S3 are as follows:

[0022] S3.1, Each weighted average coil spectral signal is composed of a column vector a with N elements. m This means that M column vectors a m The unaligned coil spectral matrix S unaligned :

[0023] S unaligned =[a1,a2,…,a m ,…,a M ]

[0024] Where m represents the ordinal number of the spectrum acquisition, M represents the total number of acquisitions, and N is the total number of complex points of the coil spectrum signal;

[0025] S3.2. Using singular value decomposition to analyze the coil spectral matrix S unaligned The decomposition yields three unitary matrices, specifically decomposed according to the following formula:

[0026] S unaligned =UYV H

[0027] Where U is an N*N unitary matrix, Y is a positive semi-definite N*M unitary matrix, V is an M*M unitary matrix, and H represents the conjugate transpose.

[0028] S3.3 Select R singular values ​​Q of the coil spectral matrices in the unitary matrix Y. r Determine the singular value Q r The corresponding left singular vector u r and the right singular vector v r The aligned spectral signal matrix S is obtained by processing it according to the following formula. aligned :

[0029]

[0030]

[0031] U N,R =[u1,u2,…,u r ,...,u R ]

[0032]

[0033]

[0034]

[0035] Where, Σ R,R It represents R singular values ​​Q r The diagonal matrix formed, U N,R Represents R left singular vectors u r The matrix formed Let |v| represent the magnitude of R right singular vectors. r | The matrix formed by The `median()` function represents the median phase; `angle()` represents the phase angle function. Represents the right singular vector v r The phase; e represents a natural number, and r represents the ordinal number of the singular value.

[0036] The specific steps of S4 are as follows:

[0037] S4.1 First, the power spectrum and signal peak of the signal within the preset frequency are obtained according to the aligned spectral signal matrix. The power spectrum and signal peak are cross-correlated, and the cross-correlation results are nonlinearly fitted to obtain the frequency drift Aq.

[0038] S4.2 Select a signal peak within a given frequency range based on the aligned spectral signal matrix, and then select a target peak based on the signal peak. The frequency of the target peak is in the range of ff-0.42 to ff+0.58, where ff is the given frequency. Fit the target peak to obtain the phase drift Фq.

[0039] S4.3. Align the spectral signal matrix S according to the frequency drift Aq and phase drift Фq. aligned After correction, the corrected target spectral signal matrix S is obtained. p :

[0040] S p =S aligned ×e -(2πAqt+φq)

[0041] Where t represents the time domain of the spectral signal, and e represents a natural number.

[0042] The specific steps of S5 are as follows:

[0043] S5.1, Based on the corrected target spectral signal matrix S p The spectrum with the largest signal is selected as the target spectrum; 60% of the maximum value of the target spectrum signal is used as a reference threshold, and spectra with maximum values ​​below this reference threshold are discarded, resulting in the updated target spectrum signal matrix S. r ;

[0044] S5.2, Regarding the target spectral signal matrix S r The average of each row in the array is performed to obtain a target spectral signal column vector with N elements. This target spectral signal column vector is then used as the reconstructed spectral signal.

[0045] An electronic device includes a memory and a processor, as well as computer instructions stored in the memory and running on the processor, wherein the computer instructions, when executed by the processor, perform the steps in the method described above.

[0046] The method of this invention can be applied to magnetic resonance fields or non-magnetic resonance fields, including other fields such as optics.

[0047] This invention utilizes the singular value decomposition method for spectral registration, completing the frequency and phase alignment of different acquired spectral signals. Combined with the time-domain coil combination method, spectral reconstruction is achieved under low signal-to-noise ratio.

[0048] Compared with the prior art, the beneficial effects of the present invention are as follows:

[0049] This invention is the first to apply singular value decomposition (SVD) for spectral registration, aligning the frequencies and phases of different acquired spectral signals. Combined with a time-domain coil combination method, it achieves spectral reconstruction under low signal-to-noise ratio (SNR) conditions and improves the SNR of the reconstructed spectral signal, thereby reducing the underestimation of spectral signal concentration. Simultaneously, it boasts high time efficiency, enabling simultaneous spectral denoising and registration, and can be applied to a wide range of spectral data acquisition techniques (diffusion-weighted spectroscopy, spectral editing, spectral imaging, etc.). Attached Figure Description

[0050] Figure 1 This is an overall flowchart of the present invention;

[0051] Figure 2 This is a diagram showing the experimental setup for the present invention;

[0052] Figure 3 This is a schematic diagram of the reconstructed spectrum of the present invention;

[0053] Figure 4 This is a performance comparison chart of the algorithm of this invention. Detailed Implementation

[0054] The following embodiments will help those skilled in the art to further understand the present invention, but do not limit the invention in any way. It should be noted that those skilled in the art can make various modifications and improvements without departing from the concept of the present invention. These all fall within the scope of protection of the present invention.

[0055] The embodiments of the present invention take the human brain as an example. Specific embodiments are as follows:

[0056] S1. Recruit 5 normal subjects (aged 24±1.4 years).

[0057] S2. Select the voxel location. Data acquisition is performed deep within the left upper frontal cortex, around the ventricles. Specific locations are as follows: Figure 2 As shown in b in the figure.

[0058] S3. Acquiring human brain spectral signals using monomer diffusion-weighted stimulated echo sequences, the steps include:

[0059] S3.1. Place the normal subject in the magnetic resonance scanner with the head first, in a supine position.

[0060] S3.2. Preparation of rapid gradient echo sequence for scanning positioning images and 3D T1-weighted magnetization (imaging field of view: 187*240*247mm) 3 The repeat time is 2300ms, the echo time is 3ms, the flip angle is 9°, and the resolution is 0.96mm*0.96mm*1.06mm) is used to locate the position of the spectral voxels.

[0061] S3.3. Set the repetition time of the spectral sequence to 1500ms, the echo time to 62ms, the mixing time to 45.6ms, and the voxel size to 60*24*25mm. 3 The bandwidth is 4000Hz, the diffusion time is 80ms, the diffusion gradient duration is 20ms, and it is applied at a speed of 0–5000s / mm. 2 Seven b-values ​​within the range (0, 833, 1667, 2500, 3334, 4167, 5000) were selected, with three orthogonal directions. With water suppression enabled, 20 spectra were acquired for each b-value condition. A shimming frame was selected to cover the voxel locations for shimming.

[0062] S4. Reconstructing the human brain spectral signal acquired from the spectral sequence, including the following steps: Figure 1 As shown:

[0063] S4.1 First, acquire M spectral signals using a spectral instrument;

[0064] It can import raw data from different equipment manufacturers into MATLAB data format, and perform spectral registration, averaging, correction and other processing, and finally export it for quantitative processing.

[0065] S4.2 Then, the spectral signal of each wave is weighted and averaged according to the receiving coil to obtain the weighted average coil wave spectrum signal:

[0066] S4.2.1 Based on the amplitude and phase of the spectral signal, the amplitude weight γf of each channel in the receiving coil is obtained according to the following formula. i and receiving coil phase weight γx i :

[0067]

[0068] γx i =γX i

[0069] Where, γf i γF represents the amplitude weight of the receiving coil in the i-th channel. i Z represents the amplitude at the first time-domain point in the spectral signal received by the i-th channel. i γx represents the noise of the spectral signal received by the i-th channel. i γX represents the phase weight of the receiving coil in the i-th channel. i This represents the phase of the first time-domain point in the spectral signal received by the i-th channel, where i represents the channel number of the receiving coil;

[0070] S4.2.2, Amplitude weighting γf of the receiving coils for all channels i Normalization is performed to obtain the normalized amplitude weight γg for each channel. i The spectral signals in each channel are weighted and averaged using the following formula to obtain the weighted averaged coil spectral signal:

[0071]

[0072]

[0073] Where A is the amplitude of the coil spectrum signal, Ф is the phase of the coil spectrum signal, and L is the total number of channels of the receiving coil.

[0074] S4.3 Next, the M coil spectral signals are combined to form an unaligned coil spectral matrix, and the singular value decomposition method is used to align the coil spectral matrix to obtain an aligned spectral signal matrix:

[0075] S4.3.1, Each weighted average coil spectral signal is composed of a column vector a with N elements. mThis means that M column vectors a m The unaligned coil spectral matrix S unaligned :

[0076] S unaligned =[a1,a2,...,a m ,...,a M ]

[0077] Where m represents the ordinal number of the spectrum acquisition, M represents the total number of acquisitions, and N is the total number of complex points of the coil spectrum signal;

[0078] S4.3.2. Using singular value decomposition to analyze the coil spectral matrix S unaligned The decomposition yields three unitary matrices, specifically decomposed according to the following formula:

[0079] S unaligned =UYV H

[0080] Where U is an N*N unitary matrix, Y is a positive semi-definite N*M unitary matrix, V is an M*M unitary matrix, and H represents the conjugate transpose.

[0081] S4.3.3 Select R singular values ​​Q of the coil spectral matrices in the unitary matrix Y. r Determine the singular value Q r The corresponding left singular vector u r and the right singular vector v r And obtain the magnitude matrix of the right singular vector. and phase The aligned spectral signal matrix S is obtained by processing it according to the following formula. aligned :

[0082]

[0083]

[0084] U N,R =[u1,u2,…,u r ,...,u R ]

[0085]

[0086]

[0087]

[0088] Where, Σ R,R It represents R singular values ​​Q r The diagonal matrix formed, U N,R Represents R left singular vectors ur The matrix formed Let |v| represent the magnitude of R right singular vectors. r | The matrix formed by The `median()` function represents the median phase; `angle()` represents the phase angle function. Represents the right singular vector v r The phase; e represents a natural number, and r represents the ordinal number of the singular value.

[0089] S4.4. Perform phase and frequency correction on the aligned spectral signal matrix to obtain the target spectral signal matrix:

[0090] S4.4.1 First, based on the aligned spectral signal matrix, the power spectrum of the signal in the frequency range of 1.85-4.2ppm and the signal peaks of 3.03ppm creatine-3.22ppm choline are obtained. The power spectrum and the signal peaks of 3.03ppm creatine-3.22ppm choline are cross-correlated, and the cross-correlation results are nonlinearly fitted by a single Lorentz curve to obtain the frequency drift Aq.

[0091] Among them, the metabolites of the power spectrum of the signal in the frequency range of 1.85-4.2ppm are N-acetylaspartic acid and creatine.

[0092] S4.4.2 Select the creatine metabolism peak based on the aligned spectral signal matrix, and then select the target metabolism peak based on the creatine metabolism peak. The frequency of the target metabolism peak is in the range of ff-0.42 to ff+0.58, where ff is the frequency of the creatine metabolism peak. Use the double Lorentz curve to fit the target metabolism peak to obtain the phase drift Фq.

[0093] S4.4.3 Align the spectral signal matrix S according to the frequency drift Aq and phase drift Фq. aligned After correction, the corrected target spectral signal matrix S is obtained. p :

[0094] S p =S aligned ×e -(2πAqt+φq)

[0095] Where t represents the time domain of the spectral signal, and e represents a natural number.

[0096] S4.5. Remove the damaged spectrum and average the target spectrum signal matrix, then remove the water signal to complete the reconstruction of the spectrum signal:

[0097] S4.5.1, Based on the corrected target spectral signal matrix S pThe spectrum with the largest signal value is selected as the target spectrum. Spectrum values ​​below 60% of the target spectrum's maximum value are used as a reference threshold. Spectrum values ​​below this threshold are discarded and updated, resulting in the updated target spectrum signal matrix S. r ;

[0098] S4.5.2. After the spectrum has been processed including coil assembly, abnormal signal removal, spectrum registration, frequency and phase correction, the target spectrum signal matrix S... r The average of each row in the array is used to obtain a target spectral signal column vector with N elements.

[0099] S4.5.3, Based on the target spectral signal matrix S r A water signal is selected, and a singular value decomposition method based on the Hankel matrix is ​​used to model the water signal, resulting in a water signal model. This water signal model is then removed from the target spectral signal column vector, and the removed vector is used as the final water-suppressed signal to complete the spectral signal reconstruction. Figure 3 As shown, at b0 = 0 s / mm 2 and b5 = 4167s / mm 2 The diagram shows the reconstructed spectrum of the in vivo spectral data after time-domain coil assembly, obtained through singular value decomposition spectral registration and robust spectral registration methods. Please note that spectra with poor acquisition quality have not yet been deleted (they will be deleted in subsequent steps according to the invention process).

[0100] S5. Replace steps S4.2 and S4.3 with the singular value decomposition coil combination method and the robust spectral registration method, respectively, to reconstruct the human brain spectral signal acquired from the spectral sequence, and compare it with the S4 method. The steps include:

[0101] S5.1 Replace step S4.2 with a coil combination method based on singular value decomposition. No specific time point needs to be referenced. All coil combination signals can be obtained based on singular value decomposition.

[0102] S5.2 Replace step S4.3 with a robust spectral registration method, calculate the similarity matrix of free decay time-domain signal points acquired from different sources (obtained through mean square error), select the corresponding minimum mean square error as the reference free decay signal, then align all acquired free decay time-domain signals, and obtain the optimal solution through the nonlinear least squares method, that is, obtain the frequency phase drift to align different acquired signals.

[0103] S6. Perform correlation quantification on the reconstructed spectrum. The steps include:

[0104] S6.1 The signal-to-noise ratio (SNR) is calculated by dividing the area under the peak of N-acetylaspartic acid by the standard deviation of the corresponding metabolite's spectral frequency domain signal-to-noise range. The result is as follows: Figure 4As shown in a:

[0105] As the b-value increases, the signal-to-noise ratio (SNR) decreases overall. Different coil combination methods (time-domain coil combination and singular value decomposition coil combination) exhibit similar SNRs, while different spectral registration methods show slightly different SNRs. After a paired-sample t-test, the differences are significant, indicating that at higher b-values, the singular value decomposition spectral registration method has a better SNR than robust spectral registration, especially when b > 3000 s / mm. 2 hour.

[0106] This verifies that the signal-to-noise ratio obtained by the spectral reconstruction method based on singular value decomposition developed in this invention is superior to that of existing advanced spectral reconstruction methods.

[0107] S6.2. Quantify the relative concentrations of each metabolite molecule using jMRUI software, and calculate the apparent diffusion coefficient of each metabolite molecule according to the following formula. Figure 2 a represents the spectral signal reconstructed by the invention method with 7 b values, and... Figure 2 c is a schematic diagram of fitting after quantifying the relative concentration:

[0108]

[0109] Where S0 is the signal received without a diffusion gradient, S(b) is the signal received with a diffusion gradient, and D is the apparent diffusion coefficient. Apparent diffusion coefficients of major metabolite molecules (unit: μm). 2 / ms), the average apparent diffusion coefficient is obtained by the arithmetic mean of the apparent diffusion coefficients in three directions, and the result is as follows: Figure 4 b and Figure 4 As shown in c; Figure 4 Figures b and c show the single-exponential model from five volunteers. Figure 4 b, the maximum b value is 3334 s / mm 2 (within the range) and ( Figure 4 c, the maximum b value is 5000s / mm 2 Apparent diffusion coefficients of three metabolites (within the specified range). Different processing methods (procedures) are labeled as: time-domain coil combination - robust spectral registration (black); singular value decomposition coil combination - robust spectral registration (gray); time-domain coil combination - singular value decomposition spectral registration (light gray); singular value decomposition coil combination - singular value decomposition spectral registration (white). (*, p < 0.05; **, p < 0.01):

[0110] The maximum b-values ​​of the three metabolites from the five volunteers were 3334 s / mm. 2 and 5000s / mm 2The average apparent diffusion coefficient was obtained within the specified range. Among the different methods compared, the average apparent diffusion coefficient calculated using post-processing with time-domain coil combination and singular value decomposition spectral registration was the lowest.

[0111] Therefore, the extensive spectrum reconstruction method based on singular value decomposition proposed in this invention can complete spectrum reconstruction under low signal-to-noise ratio and improve the signal-to-noise ratio of the reconstructed spectrum signal, thereby reducing the underestimation of spectrum signal intensity. Thus, it can help to reconstruct spectrum data in the common situation where "the signal-to-noise ratio is too low to successfully reconstruct the spectrum in the application of various spectrum acquisition methods".

[0112] The method of this invention first uses the time-domain signal of the spectrum for coil combination; then, it uses the singular value decomposition method to perform spectrum registration, completing the frequency and phase alignment of different acquired spectrum signals. This invention can complete spectrum reconstruction under low signal-to-noise ratio and improve the signal-to-noise ratio of the reconstructed spectrum signal, thereby reducing the underestimation of spectrum signal intensity, and can achieve spectrum reconstruction even in the common situation of excessively low signal-to-noise ratio in spectrum acquisition.

Claims

1. A method for extensive spectral reconstruction based on singular value decomposition, characterized in that: S1. First, acquire M spectral signals using a spectral instrument; S2. Then, the spectral signal of each wave spectrum is weighted and averaged according to the receiving coil to obtain the weighted average coil wave spectrum signal. The specific steps for weighted average processing in S2 are as follows: S2.

1. Based on the amplitude and phase of the spectral signal, the amplitude weight γ of each channel in the receiving coil is obtained according to the following formula. f i and receiving coil phase weight γ x i : ； ； Where, γ f i Indicates the first i The amplitude weights of the receiving coils for each channel, γ F i Indicates the first i The amplitude of the first time-domain point in the spectral signal received by each channel, Z i Indicates the first i The noise of the spectral signal received by each channel, γ x i Indicates the first i Phase weights of the receiving coils for each channel, γX i Indicates the first i The phase of the first time-domain point in the spectral signal received by each channel. i Indicates the channel number of the receiving coil; S2.2, Amplitude weighting γ of the receiving coils for all channels f i Normalization is performed to obtain the normalized amplitude weight γ for each channel. g i The spectral signals in each channel are weighted and averaged using the following formula to obtain the weighted averaged coil spectral signal: ； ； Where A is the amplitude of the coil spectral signal. Ф L represents the phase of the coil spectrum signal, and L is the total number of channels in the receiving coil. S3. Next, the M coil spectrum signals are combined to form an unaligned coil spectrum matrix, and the singular value decomposition method is used to align the coil spectrum matrix to obtain an aligned spectrum signal matrix. S4. Correct the phase and frequency of the aligned spectral signal matrix to obtain the corrected target spectral signal matrix; S5. Remove the damaged spectrum and average the target spectrum signal matrix to complete the reconstruction of the spectrum signal.

2. The extensive spectral reconstruction method based on singular value decomposition according to claim 1, characterized in that: The specific steps of S3 are as follows: S3.1, Each weighted average coil spectral signal is composed of a column vector a with N elements. m This means that M column vectors a m Composing an unaligned coil spectral matrix : ； Where m represents the ordinal number of the spectrum acquisition, M represents the total number of acquisitions, and N is the total number of complex points of the coil spectrum signal; S3.

2. Using singular value decomposition to analyze the coil spectral matrix. The decomposition yields three unitary matrices, specifically decomposed according to the following formula: ； Where U is an N*N unitary matrix, Y is a positive semi-definite N*M unitary matrix, V is an M*M unitary matrix, and H represents the conjugate transpose. S3.3, Select from unitary matrix Y R The singular values ​​Q of the spectral matrix of each coil r Determine the singular value Q r The corresponding left singular vector u r and the right singular vector v r The aligned spectral signal matrix is ​​obtained by processing it according to the following formula. : ； ； ； ； ； φ r =angle(in r ); in, Indicates by R A singular value Q r The diagonal matrix formed Indicates by R A left singular vector u r The matrix formed Indicates by R The magnitude of a right singular vector The matrix formed Indicates the median of the phase. The `angle()` function calculates the median; `angle()` calculates the phase angle, φ. r Represents the right singular vector v r The phase; e represents a natural number, and r represents the ordinal number of the singular value.

3. The extensive spectral reconstruction method based on singular value decomposition according to claim 1, characterized in that: The specific steps of S4 are as follows: S4.1 First, the power spectrum and signal peak of the signal within the preset frequency are obtained according to the aligned spectral signal matrix. The power spectrum and signal peak are cross-correlated, and the cross-correlation results are nonlinearly fitted to obtain the frequency drift Aq. S4.2 Select a signal peak within a given frequency range based on the aligned spectral signal matrix, and then select a target peak based on the signal peak. The frequency of the target peak is in the range of ff-0.42~ff+0.58, where ff is the given frequency. Fit the target peak to obtain the phase drift Фq. S4.3 Align the spectral signal matrix according to the frequency drift Aq and phase drift Фq. The correction is performed to obtain the corrected target spectral signal matrix. : ； Where t represents the time domain of the spectral signal, and e represents a natural number.

4. The extensive spectral reconstruction method based on singular value decomposition according to claim 1, characterized in that: The specific steps of S5 are as follows: S5.1, Based on the corrected target spectral signal matrix The spectrum with the largest signal is selected as the target spectrum; Using 60% of the maximum value of the target spectral signal as a reference threshold, and discarding spectra with maximum values ​​below this reference threshold, we obtain the updated target spectral signal matrix. ; S5.2, Target Spectral Signal Matrix The average of each row in the array is performed to obtain a target spectral signal column vector with N elements. This target spectral signal column vector is then used as the reconstructed spectral signal.

5. An electronic device, characterized in that: It includes a memory and a processor, as well as computer instructions stored in the memory and running on the processor, which, when executed by the processor, perform the steps of the method according to any one of claims 1-4.

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