Magnetic resonance spectrum water peak modeling and post-processing method based on Hankel singular value decomposition
By combining Hankel singular value decomposition and asymmetric least squares method, the problem of residual water peak interference in magnetic resonance spectroscopy was solved, achieving efficient water peak modeling and removal, and improving spectral quality and the distinguishability of metabolic peaks.
Patent Information
- Authority / Receiving Office
- CN · China
- Patent Type
- Applications(China)
- Current Assignee / Owner
- Filing Date
- 2025-12-16
- Publication Date
- 2026-03-13
AI Technical Summary
In existing magnetic resonance spectroscopy techniques, residual water peak signals cause severe interference, affecting the dynamic range and quantitative accuracy of the spectrum. Furthermore, existing methods suffer from insufficient water peak modeling accuracy, strong baseline dependence, and poor repeatability.
The Hankel singular value decomposition method is adopted. By constructing the Hankel structure matrix and performing singular value decomposition, residual water peak signals are screened out. Combined with channel weighted merging, frequency and eddy current correction, and baseline correction using the asymmetric least squares method, residual water peaks are removed and the spectrum quality is improved.
It effectively reduces residual water peak interference, improves spectrum baseline smoothness and metabolic peak distinguishability, significantly improves signal-to-noise ratio and metabolic peak resolution, and is computationally stable without increasing sequence complexity.
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Figure CN121656931A_ABST
Abstract
Description
Technical Field
[0001] This invention belongs to the field of magnetic resonance imaging signal processing technology, specifically relating to a magnetic resonance spectral image post-processing method based on Hankel singular value decomposition to achieve water peak modeling and removal. Background Technology
[0002] Magnetic resonance spectroscopy (MRS) is a non-invasive detection method that obtains tissue metabolic information based on the magnetic resonance phenomenon. It can be used to analyze the metabolic status of brain tissue, myocardium, liver and skeletal muscle, and has important clinical value in the fields of neurodegenerative diseases, tumor diagnosis and metabolic research.
[0003] The main metabolites analyzed quantitatively include N-acetylaspartic acid (NAA), choline (Cho), creatine (Cr), lactate (Lac), and inositol (mI).
[0004] Although MRS typically employs water suppression techniques, the residual water peak signal remains significantly higher than the metabolite signal. This residual signal not only affects the dynamic range of the spectrum but also easily introduces ringing artifacts, baseline drift, and sideband noise after Fourier transform, thereby interfering with the accuracy of metabolic peak quantification.
[0005] Furthermore, magnetic field drift, eddy current effects, and phase inconsistencies during the scanning process can further degrade spectral quality. Existing methods based on frequency domain window filtering, manual parameter adjustment, or empirical modeling all suffer from insufficient accuracy in water peak modeling, strong baseline dependence, and poor repeatability; while deep learning methods, although effective, lack interpretability and have limited standardization capabilities.
[0006] Therefore, there is a market demand for a magnetic resonance spectral water peak modeling and post-processing method based on Hankel singular value decomposition that can effectively reduce residual water peak interference and improve the smoothness of the spectrum baseline and the distinguishability of metabolic peaks. Summary of the Invention
[0007] The technical problem to be solved by the present invention is to provide a method for modeling and post-processing water peaks in magnetic resonance spectroscopy based on Hankel singular value decomposition.
[0008] To solve the above-mentioned technical problems, the technical solution adopted by this invention is: a magnetic resonance spectral water peak modeling and post-processing method based on Hankel singular value decomposition, comprising the following steps: Step S1, acquiring multi-channel time-domain spectral signals and water reference signals using a PRESS sequence, and simultaneously performing singular value decomposition on the water reference signal, calculating the channel weights based on the eigenvectors obtained from the decomposition; Step S2, merging the multi-channel spectral signals using the channel weights to obtain a merged time-domain spectral signal, and performing frequency correction and eddy current correction on the time-domain spectral signal; Step S3, based on the corrected time-domain signal... A Hankel structure matrix is constructed, and singular value decomposition is performed on the Hankel structure matrix. Based on the singular value energy distribution, corresponding frequency characteristics, and attenuation characteristics, the exponentially decaying component corresponding to the residual water peak is selected from the singular value decomposition results to reconstruct the time-domain water peak model. In step S4, the time-domain water peak model is subtracted from the corrected time-domain spectral signal to obtain the net metabolite time-domain signal after removing the water peak, and exponential filtering is performed. In step S5, the filtered time-domain signal is frequency-domain transformed to obtain a frequency-domain spectrum. In the frequency domain, the baseline is corrected using the asymmetric least squares method to obtain the final spectrum.
[0009] In some embodiments, in step S1, the multi-channel raw time-domain signal acquired by the PRESS sequence includes a water-suppressed raw FID signal and a water reference signal without water suppression. The water reference signal has the characteristics of high signal-to-noise ratio, strong inter-channel phase consistency, and is unaffected by metabolite shape changes; singular value decomposition formula. ,in It is a left singular matrix. It is a diagonal matrix of singular values. It is a right singular matrix, extracted from the matrix. The first column of singular vectors is processed by phase consistency correction and normalization to generate channel weights.
[0010] In some implementations, in step S2, frequency and phase correction employs a spectral registration method, using the first average signal as a reference, based on a model. Estimated frequency offset and phase offset Signal correction is achieved by minimizing the complex residual; eddy current correction is achieved by utilizing the phase information of the merged water reference signal.
[0011] In some implementations, in step S3, the Hankel structure matrix expression is: Perform singular value decomposition on it. Then, the exponentially decaying parameter and frequency components are estimated from the first singular vectors, passing through the poles. and formula Reconstructing the time-domain water peak model, in which The damping coefficient is... For the corresponding frequency, For complex amplitude parameters.
[0012] In some embodiments, in step S3, residual water peak components are screened based on frequency distribution characteristics, and exponentially decaying components falling within the range of the center frequency of the water peak are determined as residual water peak signals.
[0013] In some implementations, in step S4, the exponential filtering adopts a time-domain weighted form, and the filter expression is: Noise is suppressed by exponential decay weighting, thus improving the peak shape quality of the spectrum.
[0014] In some implementations, in step S5, the cost function of the asymmetric least squares method is: ,in The original signal, The signal to be estimated, These are asymmetric weighting coefficients. It is a second-order difference operator. For smoothness, the baseline is estimated by iterative fitting and subtracted from the spectrum.
[0015] In some implementations, the generation process of the channel weights includes singular value decomposition of the water reference signal, extraction of the first column of singular vectors, phase consistency correction, and normalization processing, which are used for weighted merging of multi-channel signals to improve signal-to-noise ratio and phase consistency.
[0016] In some implementations, the spectral registration method compensates for the frequency and phase shifts of each signal relative to the reference signal by fitting multiple averaged time-domain signals one by one, thereby achieving signal alignment and averaging.
[0017] In some implementations, the asymmetric weighting coefficient Based on spectral line morphology settings, smoothness Adjustments are made based on the degree of baseline drift to achieve adaptive baseline correction.
[0018] The scope of this invention is not limited to technical solutions formed by specific combinations of the above-described technical features, but also includes other technical solutions formed by arbitrary combinations of the above-described technical features or their equivalents. For example, technical solutions formed by substituting the above-described features with (but not limited to) technical features with similar functions disclosed in this application.
[0019] Due to the application of the above technical solutions, this invention has the following advantages compared with the prior art: This invention provides a magnetic resonance spectrum water peak modeling and post-processing method based on Hankel singular value decomposition. It utilizes Hankel structure matrix singular value decomposition to achieve accurate modeling and removal of residual water peaks, introduces asymmetric least squares method for adaptive baseline correction, effectively reduces residual water peak interference, improves spectrum baseline smoothness and metabolic peak resolvability, and can achieve accurate modeling and removal of residual water peaks by performing structured matrix decomposition on time domain signals without relying on additional modulation at the acquisition end or increasing sequence complexity. This significantly improves the signal-to-noise ratio and metabolic peak resolution of the spectrum. Combined with channel weighted merging, frequency and eddy current correction, Hankel-SVD modeling, and asymmetric least squares baseline fitting, residual water peaks are effectively suppressed, while avoiding metabolic peak damage and spectral distortion caused by traditional frequency domain filtering methods. The method is computationally stable and robust, and the final MRS spectrum obtained can meet clinical needs. Attached Figure Description
[0020] Figure 1 This is a schematic diagram of the method flow of the present invention; Figure 2 This is the time-domain modulus diagram of the spectrum acquired in the first sampling of this invention; Figure 3 This is the time-domain modulus diagram of the spectrum after frequency and phase correction according to the present invention; Figure 4 This is the time-domain modulus diagram of the spectrum after eddy current correction according to the present invention; Figure 5 This is a time-domain modulus diagram of the water peak model of the present invention; Figure 6 This is the final MRS spectrum of the present invention. Detailed Implementation
[0021] like Figure 1 The method for water peak modeling and post-processing in magnetic resonance spectroscopy based on Hankel singular value decomposition is illustrated with a detailed flowchart. Following this flowchart, the final MRS spectrum can be obtained. The method includes the following steps.
[0022] Step S1: Acquire multi-channel time-domain spectral signals and water reference signals using PRESS sequences, and simultaneously perform singular value decomposition on the water reference signals. Calculate the weights of each channel based on the eigenvectors obtained from the decomposition.
[0023] In this embodiment, a set of human brain occipital lobe signals acquired by PRESS sequence is used as an example. This set of signals includes two parts: a multi-channel water reference signal without water suppression pulse and a multi-channel spectral signal with water suppression pulse.
[0024] Singular value decomposition was performed on the water reference signal (2048 sampling points, 16 channels, 1 average frequency). The first singular vector was extracted as the channel weight, and this weight was used to weight and merge the acquired multi-channel spectral signals (2048 sampling points, 16 channels, 96 average frequencies) to obtain a set of merged spectral signals (2048 sampling points, 96 average frequencies). Taking the first acquisition as an example, the time-domain modulus plot is shown below. Figure 2 As shown.
[0025] The multi-channel raw time-domain signals acquired by the PRESS sequence include water-suppressed raw FID signals and unsuppressed water reference signals. The water reference signals have the characteristics of high signal-to-noise ratio, strong inter-channel phase consistency, and are not affected by metabolite pattern changes.
[0026] Singular Value Decomposition Formula ,in It is a left singular matrix. It is a diagonal matrix of singular values. It is a right singular matrix, extracted from the matrix. The first column of singular vectors is processed by phase consistency correction and normalization to generate channel weights.
[0027] The process of generating channel weights includes singular value decomposition of the water reference signal, extraction of the first column of singular vectors, phase consistency correction, and normalization, which are used for weighted merging of multi-channel signals to improve signal-to-noise ratio and phase consistency.
[0028] Step S2: Use the channel weights to merge the multi-channel spectral signals to obtain the merged time-domain spectral signal, and perform frequency correction and eddy current correction on the time-domain spectral signal.
[0029] Frequency and phase correction employs a spectral registration method, using the first average signal. For reference, based on the model Estimated frequency offset and phase offset , The target signal after spectral registration correction is corrected by minimizing the complex residual; eddy current correction is achieved using the phase information of the merged water reference signal.
[0030] The spectral registration method compensates for the frequency and phase shifts of each signal relative to the reference signal by fitting the time-domain signals acquired multiple times on an average basis, thereby achieving signal alignment and averaging.
[0031] Frequency and phase corrections were performed on the merged time-domain spectral signals. Specifically, using the first acquired spectral signal as a reference signal, the remaining 95 sets of spectral signals were aligned using spectral registration to obtain frequency and eddy current corrected data. Then, the aligned data were averaged to obtain an averaged spectral signal (2048 sampling points). Its time-domain magnitude plot is shown below. Figure 3 As shown.
[0032] The water reference signal is channel-merged, and then the spectral signal is eddy current corrected using the water reference signal. Specifically, the channel weighting is the same as in step S2. After weighting and merging, a set of water reference signals (2048 sampling points) is obtained. The phase of this water reference signal is used to perform eddy current correction on the spectral signal, resulting in the eddy current corrected spectral signal. Its time-domain magnitude plot is shown below. Figure 4 As shown.
[0033] Step S3: Construct a Hankel structure matrix based on the corrected time-domain signal, and perform singular value decomposition on the Hankel structure matrix. Based on the singular value energy distribution, corresponding frequency characteristics and attenuation characteristics, select the exponentially decaying component corresponding to the residual water peak from the singular value decomposition results, and reconstruct the time-domain water peak model.
[0034] The Hankel structure matrix expression is: Perform singular value decomposition on it. Then, the exponentially decaying parameter and frequency components are estimated from the first singular vectors, passing through the poles. and formula Reconstructing the time-domain water peak model, in which The damping coefficient is... For the corresponding frequency, For complex amplitude parameters.
[0035] The residual water peak components are screened based on frequency distribution characteristics, and the exponentially decaying components falling within the range of the center frequency of the water peak are identified as residual water peak signals.
[0036] The water peak is modeled using the corrected time-domain signal. Specifically, the corrected time-domain signal is decomposed using HSVD, with a truncation rank of 30, and only the exponentially decaying components corresponding to the first 30 singular values are extracted for reconstructing the signal model.
[0037] Subsequently, components falling within ±60Hz of the center frequency of the water peak were selected based on frequency characteristics and treated as residual water peak signals. These components were then used to reconstruct the time-domain water peak model, as shown in the time-domain modulus diagram. Figure 5 As shown.
[0038] Step S4: Subtract the time-domain water peak model from the corrected time-domain spectral signal to obtain the net metabolite time-domain signal after removing the water peak, and perform exponential filtering.
[0039] Exponential filtering uses a time-domain weighted form, and the filter expression is: Noise is suppressed by exponential decay weighting, thus improving the peak shape quality of the spectrum.
[0040] The water peak signal is subtracted from the spectral signal to obtain a clean spectral signal. Then, the signal is transformed to the frequency domain for baseline correction to obtain the final spectrum. Specifically, the asymmetric weighting coefficients... Smoothness is 0.01. The baseline is set to 3. Subtracting the baseline from the spectral lines yields the final spectrum as shown below. Figure 6 As shown, Figure 6 In the middle, MRS Spectrum represents MRS spectrum, X-axis represents chemical shift in ppm (per ten thousand percent), and Y-axis represents spectral signal.
[0041] Step S5: The filtered time-domain signal is transformed into a frequency-domain spectrum. The baseline is corrected using the asymmetric least squares method in the frequency domain to obtain the final spectrum.
[0042] The cost function of the asymmetric least squares method is: ,in The original signal, The signal to be estimated, These are asymmetric weighting coefficients. It is a second-order difference operator. For smoothness, the baseline is estimated through iterative fitting and subtracted from the spectrum. Asymmetric weighting coefficients. Based on spectral line morphology settings, smoothness Adjustments are made based on the degree of baseline drift to achieve adaptive baseline correction.
[0043] This method utilizes Hankel structural matrix singular value decomposition to achieve accurate modeling and removal of residual water peaks. It introduces asymmetric least squares for adaptive baseline correction, effectively reducing residual water peak interference and improving spectral baseline smoothness and metabolic peak resolution. It can achieve accurate modeling and removal of residual water peaks through structured matrix decomposition of the time-domain signal without relying on additional modulation at the acquisition end or increasing sequence complexity. This significantly improves the signal-to-noise ratio and metabolic peak resolution of the spectrum. Combining channel weighted merging, frequency and eddy current correction, Hankel-SVD modeling, and asymmetric least squares baseline fitting effectively suppresses residual water peaks while avoiding metabolic peak damage and spectral distortion caused by traditional frequency domain filtering methods. The method is computationally stable and robust, and the resulting MRS spectrum meets clinical needs.
[0044] The above embodiments are only for illustrating the technical concept and features of the present invention, and are intended to enable those skilled in the art to understand the content of the present invention and implement it accordingly. They should not be construed as limiting the scope of protection of the present invention. All equivalent changes or modifications made in accordance with the spirit and essence of the present invention should be covered within the scope of protection of the present invention.
Claims
1. A method for modeling and post-processing water peaks in magnetic resonance spectra based on Hankel singular value decomposition, characterized in that: Includes the following steps: Step S1: Acquire multi-channel time-domain spectral signals and water reference signals using PRESS sequences, and simultaneously perform singular value decomposition on the water reference signals, and calculate the weights of each channel based on the eigenvectors obtained from the decomposition. Step S2: Use the channel weights to merge the multi-channel spectral signals to obtain the merged time-domain spectral signal, and perform frequency correction and eddy current correction on the time-domain spectral signal. Step S3: Construct a Hankel structure matrix based on the corrected time-domain signal, and perform singular value decomposition on the Hankel structure matrix. Based on the singular value energy distribution, corresponding frequency characteristics, and attenuation characteristics, select the exponentially decaying component corresponding to the residual water peak from the singular value decomposition results, and reconstruct the time-domain water peak model. Step S4: Subtract the time-domain water peak model from the corrected time-domain spectral signal to obtain the net metabolite time-domain signal after removing the water peak, and perform exponential filtering processing. Step S5: The filtered time-domain signal is transformed into a frequency-domain spectrum. The baseline is corrected using the asymmetric least squares method in the frequency domain to obtain the final spectrum.
2. The method for modeling and post-processing water peaks in magnetic resonance spectroscopy based on Hankel singular value decomposition according to claim 1, characterized in that: In step S1, the multi-channel raw time-domain signals acquired by the PRESS sequence include water-suppressed raw FID signals and unsuppressed water reference signals. The water reference signals possess high signal-to-noise ratios, strong inter-channel phase consistency, and are unaffected by metabolite shape changes. Singular value decomposition formula... ,in It is a left singular matrix. It is a diagonal matrix of singular values. It is a right singular matrix, extracted by matrix... The first column of singular vectors is processed by phase consistency correction and normalization to generate channel weights.
3. The method for modeling and post-processing water peaks in magnetic resonance spectroscopy based on Hankel singular value decomposition according to claim 1, characterized in that: In step S2, frequency and phase correction employ a spectral registration method, using the first average signal as a reference, based on a model. Estimated frequency offset and phase offset Signal correction is achieved by minimizing the complex residual; eddy current correction is achieved by utilizing the phase information of the merged water reference signal.
4. The method for modeling and post-processing water peaks in magnetic resonance spectroscopy based on Hankel singular value decomposition according to claim 1, characterized in that: In step S3, the Hankel structure matrix expression is given, and singular value decomposition is performed on it. Then, the exponential decay parameter and frequency components are estimated from the first singular vectors, passing through the poles. and formula Reconstructing the time-domain water peak model, in which The damping coefficient is... For the corresponding frequency, This is the complex amplitude parameter.
5. The method for modeling and post-processing water peaks in magnetic resonance spectroscopy based on Hankel singular value decomposition according to claim 1, characterized in that: In step S3, residual water peak components are screened based on frequency distribution characteristics, and exponentially decaying components falling within the range of the center frequency of the water peak are identified as residual water peak signals.
6. The method for modeling and post-processing water peaks in magnetic resonance spectroscopy based on Hankel singular value decomposition according to claim 1, characterized in that: In step S4, the exponential filtering adopts a time-domain weighted form, and the filter expression is: Noise is suppressed by exponential decay weighting, thus improving the peak shape quality of the spectrum.
7. The method for modeling and post-processing water peaks in magnetic resonance spectroscopy based on Hankel singular value decomposition according to claim 1, characterized in that: In step S5, the cost function of the asymmetric least squares method is: ,in The original signal, The signal to be estimated, These are asymmetric weighting coefficients. It is a second-order difference operator. For smoothness, the baseline is estimated by iterative fitting and subtracted from the spectrum.
8. The method for modeling and post-processing water peaks in magnetic resonance spectroscopy based on Hankel singular value decomposition according to claim 2, characterized in that: The process of generating the channel weights includes singular value decomposition of the water reference signal, extraction of the first column of singular vectors, phase consistency correction, and normalization processing, which are used for weighted merging of multi-channel signals to improve signal-to-noise ratio and phase consistency.
9. The method for modeling and post-processing water peaks in magnetic resonance spectroscopy based on Hankel singular value decomposition according to claim 3, characterized in that: The spectral registration method compensates for the frequency and phase shifts of each signal relative to the reference signal by fitting the time-domain signals acquired multiple times on an average basis, thereby achieving signal alignment and averaging.
10. The method for modeling and post-processing water peaks in magnetic resonance spectroscopy based on Hankel singular value decomposition according to claim 7, characterized in that: The asymmetric weighting coefficient Based on spectral line morphology settings, smoothness Adjustments are made based on the degree of baseline drift to achieve adaptive baseline correction.