CN104462800A - Signal de-noising method based on wavelet frame - Google Patents

Abstract

The invention relates to a signal and image de-noising method based on a wavelet frame, in particular to de-noising of high-frequency dynamic signals. According to the method, a Ron-Shen tight frame is selected to conduct L-layer SFT decomposition on signals, wherein if L judges that the ratio of the entropy of high-frequency coefficients and the entropy of original signals is smaller than 5%, decomposition is stopped, then the high-frequency coefficients obtained by decomposition are subjected to nonlinear threshold value processing, at last, ISFT (SFT inverse transformation) is used for reconstructing signals, and the de-noised signals are obtained.

Description

Based on the signal de-noising method of wavelet frame

Technical field

The present invention relates to a kind of method that can be used for signal and image noise reduction based on wavelet frame, especially the noise reduction of high frequency Dynamic Signal.

Background technology

Noise reduction, as the first step of signal analysis and image procossing, is determine the whether believable key of analysis result.Efficiently strong noise-reduction method is the key determining noise reduction quality.

The method that early stage noise reduction many employings Fourier transform is analyzed and filtering combines, but, Fourier transform all needs complete test data of experiment, can only carry out post-processed to experimental data.The Short Time Fourier Transform occurred afterwards can obtain the information of signal at time-frequency domain simultaneously, but the method can not obtain high resolving power at time-frequency domain simultaneously.The continuous wavelet transform developing out by the window function changing Short Time Fourier Transform can meet Time-Frequency Analysis and high resolving power requirement simultaneously, effectively compensate for the deficiency of Short Time Fourier Transform, but the method calculated amount is large, can not process in real time data.And based on the Threshold Denoising Method of wavelet transform, there is calculated amount little, easy reliable feature.Threshold Denoising has low entropy, multi-resolution characteristics, decorrelation, selects the features such as base dirigibility, the entropy that can effectively overcome after the signal conversion that traditional noise-reduction method has increases, and cannot portray the non-stationary property of signal and cannot obtain the shortcoming of the correlativity of signal.But, basis function due to orthogonal wavelet transformation is by wavelet function coming by flexible and displacement, and displacement sample interval doubly becomes large with the index of 2, therefore, Orthogonal Wavelets can not the local feature of matched signal very well, may cause the distortion of sign mutation part.

Wavelet frame is that the one of small echo is promoted and expansion, reduces the requirement of wavelet basis to orthogonality, introduces redundancy.Redundancy makes the design of rrame filter have larger degree of freedom on the one hand, redundancy can not only provide sparse frame transform coefficient on the other hand, robustness can also be caused, the framework coefficient obtained under low precision can be made reconstruction signal under relatively high precision.This has unique advantage in denoising, image co-registration, encryption and coding etc.

Summary of the invention

The object of the invention is by building rational wavelet frame, Decomposition order decision criteria and realizing the noise reduction to signal and image to the non-linear threshold disposal route of decomposing the high frequency coefficient obtained.Concrete implementation step is:

(1) consider a special tight frame wave filter, be called Ron-Shen tight frame, corresponding, wave filter is expressed as follows:

$H=(\frac{1}{2},1,\frac{1}{2}),G_1=(\frac{\sqrt{\sqrt{2}}}{2},0,\frac{-\sqrt{\sqrt{2}}}{2}),G_2=(\frac{-1}{2},-1,\frac{-1}{2})$

(2) Ron-Shen tight frame is selected, SFT is utilized to carry out the decomposition of L layer to signal, wherein the judgement of L is less than 5% with the entropy of detail coefficients and the ratio of the entropy of original signal: have translation invariance to make conversion, we select suitable wave filter to carry out convolution to signal equally, but lower sampling is not carried out to coefficient, this conversion is called SFT, and the low frequency coefficient of jth layer is resolved into 1 low frequency coefficient and 2 high frequency coefficients of jth+1 layer by the SFT of one dimension.Decomposition algorithm and restructing algorithm as follows:

Decomposition algorithm:

$a_k^j=\underset{n}{\mathrm{\Σ}}{h}_{n-2k}{a}_n^{j-1},$

$a_k^{1,j}=\underset{n}{\mathrm{\Σ}}{g}_{n-2k}^1{a}_n^{j-1},$

$a_k^{2,j}=\underset{n}{\mathrm{\Σ}}{g}_{n-2k}^2{a}_n^{j-}$

Restructing algorithm:

$a_j^{j-1}=\underset{n}{\mathrm{\Σ}}{a}_k^j{h}_{k-2n}+\underset{n}{\mathrm{\Σ}}{d}_n^{1,j}{g}_{k-2n}^1+\underset{n}{\mathrm{\Σ}}{d}_n^{2,j}{g}_{k-2n}^2$

Wherein a ^j, d ^{1, j}and d ^{2, j}be respectively a low frequency and two high frequencies of jth layer.

For Setting signal s={s (k) }, its information entropy is defined as:

$E\left(s\right)=\underset{k}{\mathrm{\Σ}}p\left(k\right)\×\log \frac{1}{p\left(k\right)},p\left(k\right)=\frac{{\left|s\left(k\right)\right|}^2}{{\left|\right|s\left|\right|}^2}$

(3) non-linear threshold process is carried out to high frequency coefficient.

${\tilde{w}}_{j,k}=\left\{\begin{array}{cc}{w}_{j,k}& \left|w_{j,k}\right|\&GreaterEqual;{\mathrm{\&lambda;}}_j\\ 0,& \left|w_{j,k}\right|<{\mathrm{\&lambda;}}_j\end{array}\right.,{\mathrm{\&lambda;}}_j=\frac{\sqrt{2\log N}}{\log (j+1)}$

(4) utilize ISFT (SFT inverse transformation) by signal reconstruction.

Embodiment

(1) Ron-Shen tight frame is created.

(2) select Ron-Shen tight frame, utilize SFT to carry out the decomposition of L layer to signal, wherein the judgement of L is less than 5% with the entropy of high frequency coefficient and the ratio of the entropy of original signal, then stop decomposing.

(3) non-linear threshold process is carried out to high frequency coefficient.

${\tilde{w}}_{j,k}=\left\{\begin{array}{cc}{w}_{j,k}& \left|w_{j,k}\right|\&GreaterEqual;{\mathrm{\&lambda;}}_j\\ 0,& \left|w_{j,k}\right|<{\mathrm{\&lambda;}}_j\end{array}\right.,{\mathrm{\&lambda;}}_j=\frac{\sqrt{2\log N}}{\log (j+1)}$

(4) utilize ISFT (SFT inverse transformation) by signal reconstruction.

Claims (4)

1. the Dynamic Signal noise-reduction method based on wavelet frame can be used for signal and image noise reduction, it is characterized in that:

(1) the present invention is applied to various types of signal and image noise reduction;

(2) the tight frame type selected of the present invention, utilizes SFT to carry out the decomposition of L layer to signal, then carrying out non-linear threshold process to decomposing the high frequency coefficient obtained, finally utilizing ISFT (SFT inverse transformation) by signal reconstruction.

2. a kind of Dynamic Signal noise-reduction method based on wavelet frame as claimed in claim 1, it is characterized in that having used the tight frame wave filter that is special, be called Ron-Shen tight frame, wave filter is expressed as follows:

$H=(\frac{1}{2},1,\frac{1}{2}),G_1=(\frac{\sqrt{\sqrt{2}}}{2},0,\frac{-\sqrt{\sqrt{2}}}{2}),G_2=(\frac{-1}{2},-1,\frac{-1}{2})$

3. a kind of Dynamic Signal noise-reduction method based on wavelet frame as claimed in claim 1, is characterized in that utilizing SFT to carry out the decomposition of L layer to signal.The SFT algorithm of one dimension is as follows: 1 low frequency coefficient and 2 high frequency coefficients that the low frequency coefficient of jth layer are resolved into jth+1 layer.Decomposition algorithm and restructing algorithm as follows:

Decomposition algorithm:

$a_k^j=\underset{n}{\mathrm{\&Sigma;}}{h}_{n-2}{a}_n^{j-1},$

$d_k^{1,j}=\underset{n}{\mathrm{\&Sigma;}}{g}_{n-2k}^1{a}_n^{j-1},$

$d_k^{2,j}=\underset{n}{\mathrm{\&Sigma;}}{g}_{n-2k}^2{a}_n^{j-1},$

Restructing algorithm:

$a_k^{j-1}=\underset{n}{\mathrm{\&Sigma;}}{a}_k^j{h}_{k-2n}+\underset{n}{\mathrm{\&Sigma;}}{d}_n^{1,j}{g}_{k-2n}^1+\underset{n}{\mathrm{\&Sigma;}}{d}_n^{2,j}{g}_{k-2n}^2$

Wherein a ^j, d ^{1, j}and d ^{2, j}be respectively a low frequency coefficient and two high frequency coefficients of jth layer.

Wherein the judgement of L is less than 5% with the entropy of high frequency coefficient and the ratio of the entropy of original signal, then stop decomposing.For Setting signal s={s (k) }, its information entropy is defined as:

$E\left(s\right)=\underset{k}{\mathrm{\&Sigma;}}p\left(k\right)\&times;\log \frac{1}{p\left(k\right)},p\left(k\right)=\frac{{\left|s\left(k\right)\right|}^2}{{\left|\right|s\left|\right|}^2}$

4. a kind of Dynamic Signal noise-reduction method based on wavelet frame as claimed in claim 1, it is characterized in that carrying out non-linear threshold process to high frequency coefficient, disposal route is as follows:

${\tilde{w}}_{j,k}=\left\{\begin{array}{cc}{w}_{j,k},& \left|w_{j,k}\right|\&GreaterEqual;{\mathrm{\&lambda;}}_j\\ 0,& \left|w_{j,k}\right|<{\mathrm{\&lambda;}}_j\end{array}\right.,{\mathrm{\&lambda;}}_j=\frac{\sqrt{2\log N}}{\log (j+1)}$