CN113239751A - Wavelet threshold denoising method based on weighting factor - Google Patents
Wavelet threshold denoising method based on weighting factor Download PDFInfo
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Abstract
The invention belongs to the technical field of communication, and particularly relates to a wavelet threshold denoising method based on a weighting factor. The method mainly comprises the steps of performing wavelet decomposition on the collected signals, extracting high-frequency wavelet coefficients of each layer, calculating a threshold value according to the wavelet coefficients, processing the wavelet coefficients according to the threshold value and weighting factors, and reconstructing the signals according to the processed wavelet coefficients. Compared with the traditional common method, the method has the advantages that the method effectively solves the problems that the soft/hard threshold function is discontinuous at the critical point and has fixed errors, and enables the wavelet threshold denoising to have better effect.
Description
Technical Field
The invention belongs to the technical field of communication, and particularly relates to a wavelet threshold denoising method based on a weighting factor.
Background
Identification of signals has been an important research direction in the field of communications. In general, different signals are mixed in a large number of noise signals, the types of noise in the communication process are more various, and how to reduce the noise in the noise-containing signals is a research hotspot at present. Taking the threshold denoising algorithm proposed by Donoho as an example, the threshold functions calculated by the common soft and hard threshold rules are all discontinuous at the threshold points and have fixed errors and the like. The traditional method has the problem that the calculated soft threshold function and the calculated hard threshold function are not continuous at the threshold point, and the traditional soft threshold always has the problem of fixed error.
Disclosure of Invention
The invention aims to provide a wavelet threshold denoising method based on a weighting factor aiming at the problems.
The technical scheme of the invention is as follows:
a wavelet threshold denoising method based on weighting factors is characterized by comprising the following steps:
s1, collecting an input signal S (t) containing noise;
s2, performing N-layer wavelet decomposition on S (t);
s3, extracting the high-frequency wavelet coefficient of each layer;
s4, calculating a threshold lambda corresponding to each layer of wavelet coefficient:
where j denotes the current decomposition scale, i.e. the current number of decomposition levels, n denotes the total number of wavelet decompositions, and δ ═ mid (W)j,k,0≤k≤m)/0.6745，Wj,kM represents the number of wavelet coefficients when the scale of the wavelet coefficients is j, and mid () represents taking the absolute value and then the median value of the wavelet coefficients of the first layer.
S5, processing the wavelet coefficient based on the weighting factor alpha:
wherein the content of the first and second substances,
is the wavelet coefficient after processing;
and S6, reconstructing the processed wavelet coefficient to obtain a reconstructed signal.
The invention has the beneficial effects that: compared with the traditional common method, the method effectively solves the problems of discontinuity of the soft/hard threshold function at the critical point and the existence of fixed errors, and ensures that the wavelet threshold denoising has better effect.
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FIG. 1 is a logic schematic block diagram of wavelet decomposition and reconstruction in accordance with the present invention.
Detailed Description
The technical scheme of the invention is described in detail below with reference to the accompanying drawings:
as shown in fig. 1, the method of the present invention performs wavelet decomposition on an input signal, which is shown as decomposition into 4 layers, extracts a high-frequency wavelet coefficient CDi of each layer, obtains a wavelet coefficient CDi 'after the processing by the method of the present invention, and performs wavelet reconstruction on the processed wavelet coefficient CDi' to obtain a reconstructed signal.
The method comprises the following specific steps:
s1, collecting input signal S (t) containing noise, wherein S (t) can be pure signal superimposed Gaussian white noise or underwater sound signal containing background noise.
S2, performing N-layer wavelet decomposition on S (t).
And S3, extracting the high-frequency wavelet coefficient of each layer.
S4, calculating corresponding threshold values for the wavelet decomposition of each layer, wherein the specific expression is as follows:
where j denotes the current decomposition scale, the threshold λ is added with a decomposition scale in a common fixed rule, n denotes the total number of wavelet decompositions, and δ -mid (W) is because the noise is mainly concentrated in the first layer after wavelet decomposition of the signalj,k,0≤k≤m)/0.6745，Wj,kM represents the number of wavelet coefficients when the scale of the wavelet coefficients is j, and mid () represents taking the absolute value and then the median value of the wavelet coefficients of the first layer. The threshold gives a standard deviation for each layer of wavelet coefficient, and meets the self-adaptive characteristics required by the wavelet threshold method.
And S5, processing the high-frequency wavelet coefficient in the wavelet decomposition of the N layers of the wavelet domain. The invention provides a new threshold processing method based on the traditional soft threshold processing method. The specific processing function is shown as follows:
Wj,krepresenting the kth wavelet coefficient of the jth layer before processing,
the wavelet coefficient is represented by the value after threshold processing, and lambda represents the adopted threshold.
As the resolution scale increases, the threshold decreases. After adding the weighting factor, because
So that after treatment
Is a value between the soft and hard threshold methods. When | Wj,kWhen | approaches to the threshold λ, the weighting factor α approaches to 1, and the processed wavelet coefficient
Approaches 0 and at the same time
Is continuous at the lambda point, which solves the problem that the soft and hard threshold functions calculated by the traditional method are discontinuous at the lambda point, when the lambda point is continuousj,kWhen the l is large, the number of the columns,
approaches to Wj,kAnd the problem that the traditional soft threshold always has fixed errors is solved.
And S6, reconstructing the processed wavelet coefficient to obtain a reconstructed signal.
Claims (1)
1. A wavelet threshold denoising method based on weighting factors is characterized by comprising the following steps:
s1, collecting an input signal S (t) containing noise;
s2, performing N-layer wavelet decomposition on S (t);
s3, extracting the high-frequency wavelet coefficient of each layer;
s4, calculating a threshold lambda corresponding to each layer of wavelet coefficient:
where j denotes the current decomposition scale, n denotes the total number of wavelet decompositions, and δ ═ mid (W)j,k,0≤k≤m)/0.6745，Wj,kM represents the number of wavelet coefficients when the scale of the wavelet coefficients is j, and mid () represents that the absolute value and then the median are taken from the wavelet coefficients of the first layer;
s5, processing the wavelet coefficient based on the weighting factor alpha:
wherein the content of the first and second substances,
is the wavelet coefficient after processing;
and S6, reconstructing the processed wavelet coefficient to obtain a reconstructed signal.
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Citations (3)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN108985179A (en) * | 2018-06-22 | 2018-12-11 | 福建和盛高科技产业有限公司 | A kind of electric energy quality signal denoising method based on improvement wavelet threshold function |
| CN109242799A (en) * | 2018-09-19 | 2019-01-18 | 安徽理工大学 | A kind of Wavelet noise-eliminating method of variable threshold value |
| CN112395992A (en) * | 2020-11-18 | 2021-02-23 | 云南电网有限责任公司电力科学研究院 | Electric power harmonic signal denoising method based on improved wavelet threshold |
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Patent Citations (3)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN108985179A (en) * | 2018-06-22 | 2018-12-11 | 福建和盛高科技产业有限公司 | A kind of electric energy quality signal denoising method based on improvement wavelet threshold function |
| CN109242799A (en) * | 2018-09-19 | 2019-01-18 | 安徽理工大学 | A kind of Wavelet noise-eliminating method of variable threshold value |
| CN112395992A (en) * | 2020-11-18 | 2021-02-23 | 云南电网有限责任公司电力科学研究院 | Electric power harmonic signal denoising method based on improved wavelet threshold |
Non-Patent Citations (1)
| Title |
|---|
| 李春萌等: ""基于改进阈值函数的分数阶小波图像去噪"" * |
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