CN113592743B - Spectral high-frequency information and low-frequency information separation and coupling method based on complex wavelet transformation - Google Patents
Spectral high-frequency information and low-frequency information separation and coupling method based on complex wavelet transformation Download PDFInfo
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Abstract
The invention discloses a method for separating and reconstructing spectrum high-frequency information and low-frequency information based on complex wavelet transformation, which comprises the following steps: acquiring a spectrum of a sample to be detected; decomposing the spectrum of the sample to be detected on a plurality of scales by adopting complex wavelet transformation to obtain complex wavelet coefficients of different positions and different scales, wherein the real part coefficients of the complex wavelet coefficients correspond to low-frequency information, and the imaginary part coefficients of the complex wavelet coefficients correspond to high-frequency information; the real part and the imaginary part of the complex wavelet coefficient are separated, and modeling, argument, ratio and difference parameters are constructed by using the real part and the imaginary part of the complex wavelet coefficient. According to the method for separating and reconstructing the spectrum high-frequency information and the spectrum low-frequency information based on complex wavelet transformation, the advantages of the spectrum low-frequency information and the spectrum high-frequency information are combined complementarily, and the spectrum sensitivity is improved.
Description
Technical Field
The invention relates to the technical field of spectrum analysis, in particular to a method for separating and reconstructing spectrum high-frequency information and spectrum low-frequency information based on complex wavelet transformation.
Background
Along with the continuous improvement of the spectrum resolution, the development process of optical remote sensing can be divided into full color, multispectral and hyperspectral. The hyperspectral imaging technology and the spectroscopic technology are combined together, and when the target space features are imaged, tens or even hundreds of narrow wave bands are formed on each space pixel through dispersion so as to carry out continuous spectrum coverage. Currently, hyperspectral technology is widely applied and greatly advanced in the fields of agriculture, forestry, homeland, food, industry and the like, and meanwhile, the technical progress of the related fields is promoted.
The spectrum is the comprehensive response of physical and chemical components of substances in the visual field and the interaction of light, the high-frequency information in the spectrum is mainly detail information, contains more available information, is easily interfered by other factors, and has stronger instability; the low-frequency information in the spectrum is mainly macroscopic information, contains less available information, and has stronger stability; the high-frequency information and the low-frequency information of the spectrum have strong complementarity, so that the advantages of the high-frequency information and the low-frequency information need to be complementarily combined. In the prior art, the research of separating a spectrum into high-frequency information and low-frequency information by adopting a wavelet transformation algorithm is more, but the research of reconstructing the high-frequency information and the low-frequency information of the spectrum is less.
Disclosure of Invention
The invention aims to provide a spectrum high-frequency and low-frequency information separation and coupling method based on complex wavelet transformation, which complementarily combines the advantages of spectrum low-frequency information and high-frequency information and improves spectrum sensitivity.
In order to achieve the above object, the present invention provides the following solutions:
a method for separating and reconstructing spectrum high-frequency information and low-frequency information based on complex wavelet transformation comprises the following steps:
s1, acquiring a spectrum of a sample to be detected;
s2, decomposing the spectrum of the sample to be detected on multiple scales by adopting complex wavelet transformation to obtain complex wavelet coefficients of different positions and different scales, wherein the real part coefficient of the complex wavelet coefficients corresponds to low-frequency information, and the imaginary part coefficient of the complex wavelet coefficients corresponds to high-frequency information;
s3, separating the real part and the imaginary part of the complex wavelet coefficient, and constructing a model, a argument, a ratio and a difference parameter by utilizing the real part and the imaginary part of the complex wavelet coefficient.
Optionally, step S1 further includes: and smoothing and denoising the spectrum by adopting a Hamming window low-pass filter with the length of 9.
Optionally, in step S2, the wavelet basis of the complex wavelet transformation is cmor1-1.8, and the decomposition scale of the wavelet basis is 80 scale.
Optionally, in step S3, the constructional model, the argument, the ratio and the difference parameter are based on the inherent characteristics of the complex number; wherein the ratio is divided by the real part of the complex wavelet coefficient using the imaginary part of the complex wavelet coefficient and the difference is subtracted by the real part of the complex wavelet coefficient using the imaginary part of the complex wavelet coefficient.
According to the specific embodiment provided by the invention, the invention discloses the following technical effects: the invention provides a method for separating and reconstructing spectrum high-frequency information and low-frequency information based on complex wavelet transformation, which comprises the following steps: acquiring a spectrum of a sample to be detected; decomposing the spectrum of the sample to be detected on multiple scales by adopting complex wavelet transformation to obtain complex wavelet coefficients of different positions and different scales, wherein the real part coefficient of the complex wavelet coefficients corresponds to low-frequency information, and the imaginary part coefficient of the complex wavelet coefficients corresponds to high-frequency information; and separating the real part and the imaginary part of the complex wavelet coefficient, and constructing modeling, argument, ratio and difference parameters by utilizing the real part and the imaginary part of the complex wavelet coefficient. The method complementarily combines the advantages of the spectrum low-frequency information and the high-frequency information, improves spectrum sensitivity, has the characteristics of simplicity and easiness in operation, is applied to soil organic matter content monitoring for verification, and shows that the method is high in accuracy, good in robustness and strong in universality.
Drawings
In order to more clearly illustrate the embodiments of the present invention or the technical solutions of the prior art, the drawings that are needed in the embodiments will be briefly described below, it being obvious that the drawings in the following description are only some embodiments of the present invention, and that other drawings may be obtained according to these drawings without inventive effort for a person skilled in the art.
FIG. 1 is a flow chart of a method for separating and reconstructing spectral high-frequency information and low-frequency information based on complex wavelet transform according to an embodiment of the present invention;
FIG. 2 is a matrix of coefficients for determining parameters and organic matter content of soil for complex wavelet transformation in accordance with an embodiment of the present invention.
Detailed Description
The following description of the embodiments of the present invention will be made clearly and completely with reference to the accompanying drawings, in which it is apparent that the embodiments described are only some embodiments of the present invention, but not all embodiments. All other embodiments, which can be made by those skilled in the art based on the embodiments of the invention without making any inventive effort, are intended to be within the scope of the invention.
The invention aims to provide a method for separating and reconstructing spectrum high-frequency information and low-frequency information based on complex wavelet transformation, which complementarily combines the advantages of the spectrum low-frequency information and the spectrum high-frequency information and improves spectrum sensitivity.
In order that the above-recited objects, features and advantages of the present invention will become more readily apparent, a more particular description of the invention will be rendered by reference to the appended drawings and appended detailed description.
As shown in fig. 1, the method for separating and reconstructing spectral high-frequency information and low-frequency information based on complex wavelet transformation provided by the embodiment of the invention comprises the following steps:
s1, acquiring a spectrum of a sample to be detected;
s2, decomposing the spectrum of the sample to be detected on multiple scales by adopting complex wavelet transformation to obtain complex wavelet coefficients of different positions and different scales, wherein the real part coefficients of the complex wavelet coefficients correspond to low-frequency information, and the imaginary part coefficients of the complex wavelet coefficients correspond to high-frequency information;
s3, separating the real part (low-frequency information) and the imaginary part (high-frequency information) of the complex wavelet coefficient, and modeling, argument, ratio and difference parameters by utilizing the real part and the imaginary part of the complex wavelet coefficient.
In this embodiment, acquiring spectral data of a sample to be measured refers to acquiring spectral data of soil.
Because the measured spectrum of the ground object contains high-frequency noise and low-frequency noise under the influence of external uncontrollable factors, response errors of the instrument or dark current, the measured spectrum needs to be subjected to smooth denoising treatment to weaken the influence of non-information noise on the spectrum and improve the signal to noise ratio, and the step S1 further comprises the following steps: denoising the spectrum by using a Hamming window low-pass filter with the length of 9 to obtain standard soil spectrum data. The Hamming window low-pass filter sets corresponding coefficients according to the influence of corresponding wave bands on the central wave band of the filter, so that the original information in the spectrum of the ground object can be maintained to the greatest extent, and the influence of noise on the spectrum information can be weakened.
The complex wavelet transformation can decompose functions or signals on multiple scales through operations such as expansion and translation, and the like, so that the defect that the Fourier transformation cannot analyze the time domain and the frequency domain at the same time is well overcome. In the step S2, the wavelet base of the complex wavelet transformation is cmor1-1.8, and the decomposition scale of the wavelet base is 80 scale. The complex wavelet transform method decomposes spectral reflectance f (λ) (λ=1, 2,., n, n is the number of bands) into complex wavelet coefficients of different scales by using one complex wavelet basis function, which employs a wavelet basis function:
wherein λ is the number of bands of the spectral curve, a and b are both positive real numbers, wherein a represents a scaling factor for defining the width of the wavelet, and b is a panning factor for determining the position of the wavelet. When a > 1, the wavelength range of ψ (λ/a) is larger than that of ψ (λ), and the increasing amplitude of the wavelength range of ψ (λ/a) than that of ψ (λ) becomes larger with the gradual increase of the value of a, at which time the wavelet transform is relatively rough in wavelength reflection and relatively fine in frequency reflection, which corresponds exactly to the low frequency information; when a < 1, the wavelength range of ψ (λ/a) is smaller than the wavelength range of ψ (λ), and the amplitude by which the wavelength range of ψ (λ/a) is smaller than the wavelength range of ψ (λ) with the gradual decrease of the value of a becomes smaller, at which time the wavelet transform reflects relatively coarser on frequency and relatively finer on wavelength, which corresponds exactly to the high frequency information.
In the step S3, modeling, argument, ratio and difference parameters are based on the inherent characteristics of the complex number.
A plurality of modes: the positive square root of the sum of the squares of the real and imaginary parts of a complex number is referred to as the modulus of the complex number, denoted as |z|, i.e. for complex number z=a+bi, its modulus:
plural argument: any one of the plural angles Z which are not zero has an infinite number of values, and these values differ by an integer multiple of 2 pi, and a value suitable for the angle θ of-pi.ltoreq.θ < pi is called the principal value of the angle, denoted argZ, the principal value of the angle being unique, its angle:
Z＝R(cosθ+i*sinθ)。
ratio of: dividing the imaginary part of the complex wavelet coefficient by the real part of the complex wavelet coefficient, ratio=b/a.
Difference value: the real part of the complex wavelet coefficient is subtracted from the imaginary part of the complex wavelet coefficient, difference=b-a.
As shown in fig. 2, the reconstructed spectral model has a degree of correlation R compared to the measured spectral model 2 The spectral sensitivity is improved.
Taking cultivated land soil in Beijing city as a study object, collecting soil samples, carrying out 10 months in 2011 and 2012, collecting 96 soil samples in total, wherein the soil sample collecting method is a four-point mixing method, collecting soil layers are 0-20cm of cultivated layers, and a scientific and objective construction and evaluation prediction model is realized, 2/3 samples are selected for construction of the prediction model by a random method, 1/3 samples are used for checking the estimation precision of the model, the soil organic matter content estimation model is constructed by adopting a partial least square algorithm (Partial Least Squares Regression, PLS for short), and a soil organic matter content prediction model list is constructed based on complex wavelet transformation, wherein the table 1 is as follows:
TABLE 1 construction of a soil organic matter content prediction model List based on Complex wavelet transform
Note that: i_j is the wavelet coefficient in the i scale, jnm band.
As can be found from Table 1, the soil organic matter content prediction spectrum model constructed based on complex wavelet transformation is verified, and the prediction result shows that the correlation degree R 2 The method has the advantages that the method is large, the Root Mean Square Error (RMSE) is small, the requirement of rapid identification of the content information of the chemical components of the ground object can be met, the detection precision is obviously improved, and the method is high in precision, good in robustness and strong in universality.
The invention provides a method for separating and reconstructing spectrum high-frequency information and low-frequency information based on complex wavelet transformation, which comprises the following steps: acquiring a spectrum of a sample to be detected; decomposing the spectrum of the sample to be detected on multiple scales by adopting complex wavelet transformation to obtain complex wavelet coefficients of different positions and different scales, wherein the real part coefficient of the complex wavelet coefficients corresponds to low-frequency information, and the imaginary part coefficient of the complex wavelet coefficients corresponds to high-frequency information; and separating the real part and the imaginary part of the complex wavelet coefficient, and constructing modeling, argument, ratio and difference parameters by utilizing the real part and the imaginary part of the complex wavelet coefficient. The method complementarily combines the advantages of the spectrum low-frequency information and the high-frequency information, improves spectrum sensitivity, has the characteristics of simplicity and easiness in operation, is applied to soil organic matter content monitoring for verification, and shows that the method is high in accuracy, good in robustness and strong in universality.
The principles and embodiments of the present invention have been described herein with reference to specific examples, the description of which is intended only to assist in understanding the methods of the present invention and the core ideas thereof; also, it is within the scope of the present invention to be modified by those of ordinary skill in the art in light of the present teachings. In view of the foregoing, this description should not be construed as limiting the invention.
Claims (2)
1. The method for separating and reconstructing the spectrum high-frequency information and the spectrum low-frequency information based on complex wavelet transformation is characterized by comprising the following steps:
s1, acquiring a spectrum of a sample to be detected;
s2, decomposing the spectrum of the sample to be detected on multiple scales by adopting complex wavelet transformation to obtain complex wavelet coefficients of different positions and different scales, wherein the real part coefficient of the complex wavelet coefficients corresponds to low-frequency information, and the imaginary part coefficient of the complex wavelet coefficients corresponds to high-frequency information;
the wavelet basis of the complex wavelet transformation in the step S2 is cmor1-1.8, the decomposition scale of the wavelet basis is 80 scale, the complex wavelet transformation method decomposes the spectral reflectance f (λ) (λ=1, 2..and n, n is the band number) into complex wavelet coefficients of different scales by using a complex wavelet basis function, and the complex wavelet basis function is adopted:
wherein lambda is the band number of the spectrum curve, a and b are positive real numbers, wherein a represents a stretching factor for defining the width of the wavelet, and b is a translation factor for determining the position of the wavelet;
s3, separating the real part and the imaginary part of the complex wavelet coefficient, and constructing a model, a argument, a ratio and a difference parameter by utilizing the real part and the imaginary part of the complex wavelet coefficient;
the construction model, the argument, the ratio and the difference parameter in the step S3 are based on the inherent characteristics of the complex number;
a plurality of modes: the positive square root of the sum of the squares of the real and imaginary parts of a complex number is referred to as the modulus of the complex number, denoted as |z|, i.e. for complex number z=a+bi, its modulus:
plural argument: any one of the plural angles Z which are not zero has an infinite number of values, and these values differ by an integer multiple of 2 pi, and a value suitable for the angle θ of-pi.ltoreq.θ < pi is called the principal value of the angle, denoted argZ, the principal value of the angle being unique, its angle:
Z＝R(cosθ+i*sinθ)；
ratio of: dividing the imaginary part of the complex wavelet coefficient by the real part of the complex wavelet coefficient, ratio=b/a;
difference value: the real part of the complex wavelet coefficient is subtracted from the imaginary part of the complex wavelet coefficient, difference=b-a.
2. The method for separating and reconstructing spectral high-frequency information from low-frequency information based on complex wavelet transform according to claim 1, wherein step S1 further comprises: and smoothing and denoising the spectrum by adopting a Hamming window low-pass filter with the length of 9.
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