CN110503060B - Spectral signal denoising method and system - Google Patents
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Abstract
The invention discloses a spectral signal denoising method and a system thereof, wherein, singular value decomposition is carried out on a one-dimensional discrete spectral signal, fast Fourier transform is carried out on signal components obtained by reconstructing each singular value, a frequency value corresponding to the maximum amplitude in the fast Fourier transform result of each singular value component signal is obtained, first-order lag difference is carried out on the frequency value of the corresponding component signal according to a singular value decreasing mode, a main frequency difference spectrum is obtained, finally, a difference threshold value is set, the position which is not less than the difference threshold value in the main frequency difference spectrum is selected as a singular value effective order, the rest singular values are set to be zero, a reconstruction matrix is obtained by utilizing the inverse process of singular value decomposition, and a denoised signal is obtained by inversion. According to the method, the odd-value order reconstruction signal can be accurately selected, and the denoising effect is improved.
Description
Technical Field
The invention belongs to the technical field of spectral signal denoising, and particularly relates to a spectral signal denoising method and a system thereof.
Background
In the ultraviolet and visible spectrum quantitative analysis, random noise is generated due to factors such as a light source, a detector, electronic components, dark current, external environment interference and the like in the micro spectrometer, and the accuracy of the spectrum quantitative analysis result is greatly influenced. Therefore, preprocessing of the spectral data is an essential step before the concentration model is established. The reasonable preprocessing method can retain useful chemical information of a sample to be detected in the spectrum signal, filter out noise information and redundant information, and improve the robustness and the prediction capability of the model. At present, a plurality of methods for processing data of a spectrum signal are available, and the methods mainly comprise wavelet transformation, empirical mode decomposition, local curve fitting and the like, but the optimal decomposition layer number and threshold value in the wavelet transformation are difficult to determine, the number of times of local curve fitting needs to be further researched, and the methods mostly depend on experiments and experience determination of researchers at present.
The singular value denoising algorithm does not need to depend on the performance of a wavelet filter very much like time domain averaging, does not need to input signals to a standard like adaptive filtering, and can realize denoising on variable frequency signals, so the singular value denoising algorithm is also applied to signal denoising, but if too many singular values are reserved, even if the signals are preprocessed, a lot of noises are still mixed, and the signal-to-noise ratio is still very small; if the number of the reserved singular values is too small, although the noise is removed, some detail features of the original signal are lost, even the original signal is severely distorted, and the signal reconstruction accuracy is affected. Therefore, how to accurately select the odd-value order needs to be considered and perfected. The existing singular value differential spectrum method can effectively select the number of reconstructed singular values to a certain extent, but when the frequency components of real signals are complex, after the signals are decomposed by the singular values, because each singular value corresponds to a component signal, the maximum spectrum peak of the differential spectrum can only represent that the two component signals have great difference, but the maximum difference is not always the boundary of the signals and noise, therefore, the singular value differential spectrum method which directly carries out the difference by using the singular values is greatly interfered by the trend term of the real signals under certain conditions, the original selection means can be violated, and the accuracy of the order of the obtained singular values is also required to be improved.
Disclosure of Invention
The invention aims to provide a spectral signal denoising method and a system thereof, which can automatically and accurately select singular value orders so as to improve the reconstruction precision and the signal-to-noise ratio of signals.
The invention provides a spectral signal denoising method, which comprises the following steps:
s1: singular value decomposition is carried out on the spectral signal to be denoised to obtain an orthogonal matrix U, VTAnd a singular value matrix Σ;
wherein the singular value matrix
Λ is r singular values σiR is the rank of Hankel matrix, and 0 represents zero matrix;
s2: performing for r singular values respectively: preserving a single singular value sigma in the diagonal matrix lambdaiAnd setting the rest singular values to zero to obtain a new diagonal matrix Lambda′ iRespectively carrying out inversion reconstruction to obtain new spectral signal components;
s3: respectively carrying out fast Fourier transform on the r new spectral signal components in the step S2, respectively obtaining frequency values corresponding to the maximum amplitude from the transform results, and carrying out first-order lag difference on the corresponding frequency values according to a singular value decreasing method to obtain a main frequency difference spectrum;
bi＝fi+1-fi
in the formula, biIs the ith main frequency differential value, f in the main frequency differential spectrumi、fi+1Respectively, i-th singular value σ arranged in descending order according to singular valueiI +1 th singular value σi+1The frequency value corresponding to the maximum amplitude in the transformation result of the corresponding new spectral signal component;
s4: identifying a first main frequency difference value b not less than a preset difference threshold value in a main frequency difference spectrumjAnd reserving the first j singular values according to a singular value decreasing mode, setting the rest singular values to zero to obtain a new diagonal matrix, and performing inversion reconstruction to obtain the denoised spectral signal.
Further preferably, the step S1 is performed as follows:
reconstructing the spectral signal to be denoised into a Hankel matrix;
then, singular value decomposition is carried out on the Hankel matrix to obtain an orthogonal matrix U, VTAnd a singular value matrix Σ.
Wherein the singular value matrix
Λ＝diag(σ1，σ2，…，σr)，σ1≥σ2≥…≥σr，σiIs a matrix Hm×nThe singular value of (a).
Further preferably, the spectral signal to be denoised is reconstructed into a Hankel matrix with a size of mxn, where m is equal to or less than n, and the Hankel matrix is as follows:
where m is the embedding dimension and m + N-1 ═ N.
Further preferably, the preset differential threshold is in the range of [30,50 ].
The invention also provides a system based on the method, which comprises a singular value decomposition module, a reconstruction module and a main frequency difference spectrum acquisition module;
the singular value decomposition module is used for performing singular value decomposition on the spectral signal to be denoised to obtain an orthogonal matrix U, VTAnd a singular value matrix Σ;
the reconstruction module is used for respectively carrying out a new diagonal matrix A based on r singular values′ iUpdating and inverting reconstruction to obtain a new spectrum signal component;
the main frequency difference spectrum acquisition module is used for respectively carrying out fast Fourier transform on r new spectral signal components, respectively acquiring frequency values corresponding to the maximum amplitude from the transform results, and then carrying out first-order lag difference on the corresponding frequency values according to a singular value decreasing method to obtain a main frequency difference spectrum;
the reconstruction module is used for identifying a first main frequency difference value b which is not less than a preset difference threshold value in a main frequency difference spectrumjAnd reserving the first j singular values according to a singular value decreasing mode, setting the rest singular values to zero to obtain a new diagonal matrix, and performing inversion reconstruction to obtain the denoised spectral signal.
Advantageous effects
The invention researches and discovers that after a signal is decomposed by a singular value, a component signal of a singular value with a larger numerical value represents a real signal, a singular value component signal with a smaller numerical value represents noise, and simultaneously discovers that the frequency of the noise signal is larger than that of the real signal, namely the noise signal and the real signal have obvious difference in the frequency domain, and the main frequency can generate a large mutation after the fast Fourier transform is carried out on the boundary of the singular value component signal corresponding to the real signal and the singular value component signal corresponding to the noise signal. Compared with the method for selecting the singular value order by the singular value difference spectrum algorithm, the method has stronger universality on signal preprocessing, does not need manual intervention in the data preprocessing process, can automatically select the singular value order, can meet the requirement of on-line preprocessing of the spectrum signal, and can greatly improve the reconstruction precision and the signal-to-noise ratio of the signal.
Drawings
FIG. 1 is a graph of the UV-Vis spectral signal of the 480nm to 800nm wavelength band of an embodiment of the present invention;
FIG. 2 is a graph of the first 50 singular value dominant frequency difference spectra according to an embodiment of the present invention;
fig. 3 is a diagram illustrating noise reduction effects on measured spectrum data according to an embodiment of the present invention.
Detailed Description
The present invention will be further described with reference to the following examples.
According to the spectral signal denoising method and system provided by the invention, the singular value denoising algorithm is utilized to denoise the original spectrum, the order of the singular value can be accurately selected, and the denoising effect is improved. The sampling integration time of the micro spectrometer is 9ms, the sampling integration interval is 500ms, wherein as shown in fig. 1, the ultraviolet visible spectrum signal with the wavelength range of 480nm to 800nm is collected as the spectrum signal to be denoised. The method of the embodiment is implemented as follows:
the method comprises the following steps: the spectral signal X to be denoised is (X)1，x2，…，xN) And reconstructing into a Hankel matrix. The reconstructed Hankel matrix in the embodiment has the size of m multiplied by n, m is less than or equal to n, and is as follows:
wherein Hm×nFor the Hankel matrix, 1 < N <, m is the embedding dimension and satisfies m + N-1 ═ N.
Step two: carrying out singular value decomposition on the Hankel matrix to obtain Hm×n＝UΣVT。
Wherein, U = (U)1，u2，…，um)∈Rm×m、V=(v1，v2，…，vn)∈Rn×nAre all orthogonal matrices, u1Representing the first column, v, of an orthogonal matrix U1Represents the first column of the orthogonal matrix V,
is an m × n dimensional matrix, and Λ ═ diag (σ)1，σ2，…，σr) And σ1≥σ2≥…≥σr，σiIs a matrix Hm×nR is the rank of the Hankel matrix, and 0 is a zero matrix. In other possible embodiments, the positions of the elements in the matrix may be adapted
Step three: performing for r singular values respectively: preserving a single singular value sigma in the diagonal matrix lambdaiAnd setting the rest singular values to zero to obtain a new diagonal matrix Lambda′ iAnd respectively carrying out inversion reconstruction to obtain new spectral signal components.
Such as: retention Λ ═ diag (σ)1，σ2，…，σr) A single singular value ofiWill divide by σiAll the other singular values are set to zero, namely the lambda is obtained′ i＝diag(0，…,σi,…，0)，
i＝1,2，3，…,r。
Obtaining r new diagonal matrixes Lambda′ iThereafter, orthogonal matrix U, V is reusedTSequentially calculating new Hankel matrix H'i(H′i＝UΣ′ iVT) And performing inversion according to a construction method of a Hankel matrix to obtain r spectral signal components Xi(i＝1,2，3,…,r)。
Step four: respectively carrying out fast Fourier transform on r new spectral signal components, respectively obtaining frequency values corresponding to the maximum amplitude from the transform results, and carrying out first-order lag difference on the corresponding frequency values according to a singular value decreasing method to obtain a main frequency difference spectrum B, wherein B = [ B ]1,b2,…，br-1]；
bi＝fi+1-fi
In the formula, biIs the ith main frequency differential value, f in the main frequency differential spectrumi、fi+1Respectively, i-th singular value σ arranged in descending order according to singular valueiI +1 th singular value σi+1The frequency value corresponding to the maximum amplitude in the transformation result of the corresponding new spectral signal component.
Step five: identifying a first main frequency difference value b not less than a preset difference threshold value in a main frequency difference spectrumjAnd reserving the first j singular values according to a singular value decreasing mode, setting the rest singular values to zero to obtain a new diagonal matrix, and performing inversion reconstruction to obtain the denoised spectral signal.
In the present embodiment, Λ ═ diag (σ)1，σ2，…，σr)，σ1≥σ2≥…≥σrIf b is recognizedjIf the condition exists, the first j singular values in the diagonal matrix Lambda are reserved, and the rest singular values are set to zero; and reconstructing a Hankel matrix and inverting to obtain a denoised spectrum signal.
Because the main frequencies of the singular value component signal of the real signal and the singular value component signal of the noise signal are greatly different, and the frequency has a large mutation, the invention finds and sets a differential threshold value through research to be used for identifying the mutation condition. As shown in fig. 2, in this embodiment, the preset differential threshold is 50, and it is recognized that the first position not smaller than the differential threshold is the 12 th point, that is, the effective order of singular values is 12, the first 12 singular values are retained, the remaining singular values are set to zero, a reconstruction matrix is obtained by using an inverse process of singular value decomposition, and a signal after noise reduction is obtained through inversion.
Based on the method, the system provided by the invention comprises the following steps: the system comprises a singular value decomposition module, a reconstruction module and a main frequency difference spectrum acquisition module;
the singular value decomposition module is used for performing singular value decomposition on the spectral signal to be denoised to obtain an orthogonal matrix U, VTAnd a singular value matrix Σ;
a reconstruction module for performing new diagonal matrix Lambda based on r singular values′ iUpdating and inverting reconstruction to obtain a new spectrum signal component;
a dominant frequency difference spectrum obtaining module, configured to perform fast fourier transform on the r new spectral signal components, obtain frequency values corresponding to the largest amplitudes from the transform results, and perform first-order lag difference on the corresponding frequency values according to a singular value decreasing method to obtain a dominant frequency difference spectrum;
a reconstruction module for identifying a first main frequency difference value b not less than a preset difference threshold in the main frequency difference spectrumjAnd reserving the first j singular values according to a singular value decreasing mode, setting the rest singular values to zero to obtain a new diagonal matrix, and performing inversion reconstruction to obtain the denoised spectral signal.
It should be understood that the invention can automatically and accurately select the order of the singular value by considering the frequency domain characteristics of the singular value component signal, has no special requirements on signal stationarity and noise characteristics, and can meet the requirements on-line preprocessing of the spectrum signal.
It should be emphasized that the examples described herein are illustrative and not restrictive, and thus the invention is not to be limited to the examples described herein, but rather to other embodiments that may be devised by those skilled in the art based on the teachings herein, and that various modifications, alterations, and substitutions are possible without departing from the spirit and scope of the present invention.
Claims (5)
1. A spectral signal denoising method is characterized in that: the method comprises the following steps:
s1: reconstructing the spectral signals to be denoised into a Hankel matrix, and performing singular value decomposition on the Hankel matrix to obtain an orthogonal matrix U, VTAnd a singular value matrix Σ;
wherein the singular value matrix
Λ is r singular values σiR is the rank of Hankel matrix, and 0 represents zero matrix;
s2: performing for r singular values respectively: preserving a single singular value sigma in the diagonal matrix lambdaiAnd setting the residual singular values to zero to obtain a new diagonal matrix Lambda'iReuse of orthogonal matrix U, VTSequentially calculating a new Hankel matrix and carrying out inversion reconstruction to obtain a new spectrum signal component;
s3: respectively carrying out fast Fourier transform on the r new spectral signal components in the step S2, respectively obtaining frequency values corresponding to the maximum amplitude from the transform results, and carrying out first-order lag difference on the corresponding frequency values according to a singular value decreasing method to obtain a main frequency difference spectrum;
bi＝fi+1-fi
in the formula, biIs the ith main frequency differential value, f in the main frequency differential spectrumi、fi+1Respectively, i-th singular value σ arranged in descending order according to singular valueiI +1 th singular value σi+1The frequency value corresponding to the maximum amplitude in the transformation result of the corresponding new spectral signal component;
s4: identifying a first main frequency difference value b not less than a preset difference threshold value in a main frequency difference spectrumjAnd reserving the first j singular values according to a singular value decreasing mode, setting the rest singular values to zero to obtain a new diagonal matrix, and performing inversion reconstruction to obtain the denoised spectral signal.
2. The method of claim 1, wherein: the step S1 is performed as follows:
reconstructing the spectral signal to be denoised into a Hankel matrix;
then, singular value decomposition is carried out on the Hankel matrix to obtain an orthogonal matrix U, VTAnd a singular value matrix Σ;
wherein the singular value matrix
Λ＝diag(σ1,σ2,…,σr)，σ1≥σ2≥…≥σr，σiAre the singular values of the Hankel matrix.
3. The method of claim 2, wherein: reconstructing the spectral signal to be denoised into a Hankel matrix with the size of mxn, wherein m is less than or equal to n, and the Hankel matrix is as follows:
in the formula, Hm×nRepresenting a Hankel matrix, m is the embedding dimension, and m + N-1 ═ N.
4. The method of claim 1, wherein: the preset differential threshold range is [30,50 ].
5. A system based on the method of any one of claims 1-4, characterized by: the system comprises a singular value decomposition module, a reconstruction module and a main frequency difference spectrum acquisition module;
the singular value decomposition module is used for reconstructing the spectral signal to be denoised into a Hankel matrix, and then performing singular value decomposition on the Hankel matrix to obtain an orthogonal matrix U, VTAnd a singular value matrix Σ;
the reconstruction module is used for respectively carrying out new diagonal matrix Lambda 'on the diagonal matrix Lambda in the singular value matrix Sigma based on r singular values'iUpdating and inverting reconstruction to obtain a new spectrum signal component;
the main frequency difference spectrum acquisition module is used for respectively carrying out fast Fourier transform on r new spectral signal components, respectively acquiring frequency values corresponding to the maximum amplitude from the transform results, and then carrying out first-order lag difference on the corresponding frequency values according to a singular value decreasing method to obtain a main frequency difference spectrum;
the reconstruction module is used for identifying a first main frequency difference value b which is not less than a preset difference threshold value in a main frequency difference spectrumjReserving the first j singular values according to a singular value decreasing mode, setting the rest singular values to zero to obtain a new diagonal matrix, and then utilizing an orthogonal matrix U, VTAnd sequentially calculating a new Hankel matrix and carrying out inversion reconstruction to obtain the denoised spectral signal.
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