CN109242806A - A kind of small echo thresholding denoising method based on gaussian kernel function - Google Patents
A kind of small echo thresholding denoising method based on gaussian kernel function Download PDFInfo
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Abstract
The invention belongs to small echo thresholding noise-removed technology fields, more particularly to a kind of small echo thresholding denoising method based on gaussian kernel function, by wavelet coefficient LL, wavelet coefficient LH1, wavelet coefficient HL1 and wavelet coefficient HH1 carries out inverse wavelet transform, the subsignal coefficient LL ' of corresponding horizontal low frequencies and vertical low frequency after being denoised, the subsignal coefficient LH ' of horizontal low frequencies and vertical high frequency, the subsignal coefficient HH ' of the subsignal coefficient HL ' and horizontal high-frequent and vertical high frequency of horizontal high-frequent and vertical low frequency, the present invention solves the prior art and exists for noise signal while retaining original signal, the problem of white Gaussian noise and soiline-alkali plants can also be effectively removed, with not only obvious to Gaussian noise and salt-pepper noise denoising effect, and remain the detailed information of original signal, its filter effect is better than The advantageous effects of the effect of median filtering and wavelet soft thresholding.
Description
Technical field
The invention belongs to small echo thresholding noise-removed technology fields more particularly to a kind of small echo thresholding based on gaussian kernel function to go
Method for de-noising.
Background technique
The basic thought of wavelet threshold denoising is that a threshold limit value λ is first arranged, if wavelet coefficient is less than λ, it is believed that this is
Number is mainly caused by noise, removes this part coefficient；If wavelet coefficient is greater than λ, then it is assumed that this coefficient is mainly caused by signal,
Retain this part coefficient, then wavelet coefficient carries out the signal after wavelet inverse transformation is denoised, the prior art to treated
In the presence of for noise signal while retaining original signal, moreover it is possible to the problem of effectively removing white Gaussian noise and soiline-alkali plants.
Summary of the invention
The present invention provides a kind of small echo thresholding denoising method based on gaussian kernel function, to solve to mention in above-mentioned background technique
Go out the prior art to exist for noise signal while retaining original signal, moreover it is possible to effectively remove white Gaussian noise and salt green pepper
The problem of noise.
Technical problem solved by the invention is realized using following technical scheme: a kind of small echo based on gaussian kernel function
Thresholding denoising method, comprising:
Noise signal is decomposed into horizontal frequency band, vertical frequency band, diagonal line frequency according to the basic function of two-dimensional wavelet transformation
Band and low-frequency band；
The basic function of the two-dimensional wavelet transformation are as follows:
ψ1(x, y)=Φ (x) ψ (y)；
ψ2(x, y)=ψ (x) Φ (y)；
ψ3(x, y)=ψ (x) ψ (y)；
Φ (x, y)=Φ (x) Φ (y)；
Wherein；
The Φ (x) is a unidimensional scale function of noise signal；
The ψ (x) is a corresponding wavelet function of unidimensional scale function of noise signal；
The Φ (y) is another unidimensional scale function of noise signal；
The ψ (y) is another corresponding wavelet function of unidimensional scale function of noise signal；
Noise signal is subjected to Multiresolution Decomposition by one-dimensional wavelet transform, the noise signal after decomposition is pressed into different skies
Between and different frequency a noise signal level low frequency and vertical low frequency subsignal coefficient LL, a noise signal level
The subsignal coefficient LH of low frequency and vertical high frequency, the subsignal coefficient HL of a noise signal level high frequency and vertical low frequency, one
The subsignal coefficient HH of secondary noise signal level high frequency and vertical high frequency；
The wavelet coefficient LL of noise signal noise signal level low frequency and vertical low frequency is kept by two-dimensional wavelet transformation
It is constant, the subsignal coefficient LH to a noise signal level low frequency and vertical high frequency, a noise signal level high frequency respectively
Distinguish with the subsignal coefficient HH of the subsignal coefficient HL of vertical low frequency and a noise signal level high frequency and vertical high frequency
The wavelet coefficient of quadratic noise signal level low frequency and vertical high frequency is filtered and formed using different gaussian kernel functions
Wavelet coefficient HL1, quadratic noise signal level high frequency and the vertical height of LH1, quadratic noise signal level high frequency and vertical low frequency
The wavelet coefficient HH1 of frequency；
Wavelet coefficient LL, wavelet coefficient LH1, wavelet coefficient HL1 and wavelet coefficient HH1 are subjected to inverse wavelet transform, obtained
The subsignal system of the subsignal coefficient LL ' of corresponding horizontal low frequencies and vertical low frequency, horizontal low frequencies and vertical high frequency after to denoising
The subsignal coefficient HH ' of number LH ', the subsignal coefficient HL ' and horizontal high-frequent of horizontal high-frequent and vertical low frequency and vertical high frequency.
Further, the gaussian kernel function is low-pass filtering algorithm.
Further, the low-pass filtering algorithm of the gaussian kernel function is the first step of Canny edge extracting method.
Further, gaussian kernel function G is used to the subsignal coefficient LH of a noise signal level low frequency and vertical high frequency
(x, y, σ) is filtered.
Further, the subsignal coefficient HL to a noise signal level high frequency and vertical low frequency and a noise signal
The subsignal coefficient HH of horizontal high-frequent and vertical high frequency is filtered using gaussian kernel function G (x, y, σ/2).
Further, the root-mean-square deviation σ uses 0.02~0.04.
Further, subsignal after denoising is subjected to denoising effect by normalized mean squared error NMSE and Y-PSNR PSNR
Fruit evaluation.
Further, include: about subsignal coefficient
The subsignal coefficient LL ' is the filtered low scale approximate information of peak low band；
The subsignal coefficient LH ' includes the detailed information after horizontal direction low pass and vertical direction high-pass filtering；
The subsignal coefficient HL ' includes the detailed information after horizontal direction low pass and vertical direction high-pass filtering；
The subsignal coefficient HH ' includes the detailed information after water quadratic sum high pass and vertical direction high-pass filtering；
Further, energy of the noise signal after wavelet transformation is equal with primary energy.
Further, the noise signal after wavelet transformation respectively corresponds to the horizontal, vertical and diagonal of original signal
Line marginal information.
Advantageous effects:
This patent, which is used, is decomposed into horizontal frequency band, vertical frequency according to the basic function of two-dimensional wavelet transformation for noise signal
Band, diagonal line frequency band and low-frequency band；Noise signal is subjected to Multiresolution Decomposition by one-dimensional wavelet transform, after decomposition
Noise signal by a noise signal level low frequency of different spaces and different frequency and the subsignal coefficient of vertical low frequency
The subsignal coefficient LH of LL, a noise signal level low frequency and vertical high frequency, a noise signal level high frequency and vertical low
The subsignal coefficient HH of the subsignal coefficient HL of frequency, a noise signal level high frequency and vertical high frequency；Become by 2-d wavelet
The wavelet coefficient LL of noise signal of changing commanders noise signal level low frequency and vertical low frequency is remained unchanged, respectively to a noise signal
The subsignal coefficient HL of the subsignal coefficient LH of horizontal low frequencies and vertical high frequency, a noise signal level high frequency and vertical low frequency
And the subsignal coefficient HH of a noise signal level high frequency and vertical high frequency is respectively adopted different gaussian kernel functions and carries out
Filter and formed the wavelet coefficient LH1 of quadratic noise signal level low frequency and vertical high frequency, quadratic noise signal level high frequency and
The vertically wavelet coefficient HH1 of the wavelet coefficient HL1 of low frequency, quadratic noise signal level high frequency and vertical high frequency；By wavelet coefficient
LL, wavelet coefficient LH1, wavelet coefficient HL1 and wavelet coefficient HH1 carry out inverse wavelet transform, corresponding horizontal after being denoised
The subsignal coefficient LL ' of low frequency and vertical low frequency, the subsignal coefficient LH ' of horizontal low frequencies and vertical high frequency, horizontal high-frequent and hang down
The straight subsignal coefficient HL ' of the low frequency and subsignal coefficient HH ' of horizontal high-frequent and vertical high frequency, due to by wavelet transformation with
Gaussian kernel function combines the method for carrying out signal denoising and can effectively remove the spiced salt while removing white Gaussian noise and make an uproar
Sound, the method is to carry out Gassian low-pass filter respectively to high-frequency sub-band in the characteristics of wavelet transformation, by filtered wavelet coefficient
The signal after denoising can be obtained after inverse transformation, this method is not only bright to Gaussian noise and salt-pepper noise denoising effect
It is aobvious, and the detailed information of original signal is remained, filter effect is better than the effect of median filtering and wavelet soft thresholding.
Detailed description of the invention
Fig. 1 is a kind of small echo thresholding denoising method general flow chart based on gaussian kernel function of the present invention；
Fig. 2 is a kind of wavelet decomposition figure of the small echo thresholding denoising method based on gaussian kernel function of the present invention；
Fig. 3 is that a kind of three kinds of filtering methods of the small echo thresholding denoising method based on gaussian kernel function of the present invention compare figure；
Specific embodiment
The present invention is described further below in conjunction with attached drawing:
In figure:
Noise signal is decomposed into horizontal frequency band, vertical frequency band, diagonal according to the basic function of two-dimensional wavelet transformation by S101-
Line frequency band and low-frequency band；
Noise signal is carried out Multiresolution Decomposition by one-dimensional wavelet transform by S102-, and the noise signal after decomposition is pressed
The subsignal coefficient LL of the noise signal level low frequency and vertical low frequency of different spaces and different frequency, a noise letter
The subsignal coefficient of the subsignal coefficient LH of number horizontal low frequencies and vertical high frequency, a noise signal level high frequency and vertical low frequency
The subsignal coefficient HH of HL, a noise signal level high frequency and vertical high frequency；
S103- passes through two-dimensional wavelet transformation for the wavelet coefficient LL of noise signal noise signal level low frequency and vertical low frequency
It remains unchanged, respectively the subsignal coefficient LH to a noise signal level low frequency and vertical high frequency, a noise signal level
The subsignal coefficient HL and a noise signal level high frequency of high frequency and vertical low frequency and the subsignal coefficient HH of vertical high frequency
The wavelet systems that different gaussian kernel functions is filtered and forms quadratic noise signal level low frequency and vertical high frequency are respectively adopted
Number LH1, the wavelet coefficient HL1 of quadratic noise signal level high frequency and vertical low frequency, quadratic noise signal level high frequency and vertical
The wavelet coefficient HH1 of high frequency；
Wavelet coefficient LL, wavelet coefficient LH1, wavelet coefficient HL1 and wavelet coefficient HH1 are carried out small echo contravariant by S104-
It changes, the son letter of the subsignal coefficient LL ' of corresponding horizontal low frequencies and vertical low frequency, horizontal low frequencies and vertical high frequency after being denoised
Number the subsignal coefficient HL ' of coefficient LH ', horizontal high-frequent and vertical low frequency and the subsignal coefficient of horizontal high-frequent and vertical high frequency
HH'；
Embodiment:
The present embodiment: as shown in Figure 1, a kind of small echo thresholding denoising method based on gaussian kernel function, comprising:
Noise signal is decomposed into horizontal frequency band, vertical frequency band, diagonal line frequency according to the basic function of two-dimensional wavelet transformation
Band and low-frequency band S101；
The basic function of the two-dimensional wavelet transformation are as follows:
ψ1(x, y)=Φ (x) ψ (y)；
ψ2(x, y)=ψ (x) Φ (y)；
ψ3(x, y)=ψ (x) ψ (y)；
Φ (x, y)=Φ (x) Φ (y)；
Wherein；
The Φ (x) is a unidimensional scale function of noise signal；
The ψ (x) is a corresponding wavelet function of unidimensional scale function of noise signal；
The Φ (y) is another unidimensional scale function of noise signal；
The ψ (y) is another corresponding wavelet function of unidimensional scale function of noise signal；
Since noise signal can be divided into two class of Gaussian noise and salt-pepper noise by its nature, people are according to actually making an uproar at present
The characteristics of sound and statistical property and spectrum distribution rule, have developed many processing methods for eliminating noise, and woodenware use is compared
Common filtering algorithm has median filtering method, faces the domain method of average, wavelet soft-threshold filter method, gaussian filtering, Wiener filtering etc., closely
Nian Lai, wavelet transformation theory are rapidly developed, since wavelet transformation has the locality of spatial domain and frequency domain special simultaneously
Property and multiresolution analysis are specific, so particularly suitable for being applied in noise processed, wherein Wavelet Denoising Method problem
Essence is a function approximation problem, i.e., how to be stretched by wavelet mother function and moved in function space be unfolded, root
According to corresponding criterion, most preferably approaching to original signal is found, to complete the differentiation to original signal and noise signal.
Noise signal is subjected to Multiresolution Decomposition by one-dimensional wavelet transform, the noise signal after decomposition is pressed into different skies
Between and different frequency a noise signal level low frequency and vertical low frequency subsignal coefficient LL, a noise signal level
The subsignal coefficient LH of low frequency and vertical high frequency, the subsignal coefficient HL of a noise signal level high frequency and vertical low frequency, one
The subsignal coefficient HH S102 of secondary noise signal level high frequency and vertical high frequency；
The wavelet coefficient LL of noise signal noise signal level low frequency and vertical low frequency is kept by two-dimensional wavelet transformation
It is constant, the subsignal coefficient LH to a noise signal level low frequency and vertical high frequency, a noise signal level high frequency respectively
Distinguish with the subsignal coefficient HH of the subsignal coefficient HL of vertical low frequency and a noise signal level high frequency and vertical high frequency
The wavelet coefficient of quadratic noise signal level low frequency and vertical high frequency is filtered and formed using different gaussian kernel functions
Wavelet coefficient HL1, quadratic noise signal level high frequency and the vertical height of LH1, quadratic noise signal level high frequency and vertical low frequency
The wavelet coefficient HH1S103 of frequency；
Since noise is 2D signal, one-dimensional small echo signal decomposition can very easily be generalized to two-dimensional space, and small echo becomes
Video signal is exactly carried out Multiresolution Decomposition by the basic thought used instead in noise analysis, and noise signal is decomposed into different skies
Between, the subsignal of different frequency, pass through the basic function of two-dimensional wavelet transformation: ψ1(x, y)=Φ (x) ψ (y)；ψ2(x, y)=ψ
(x)Φ(y)；ψ3(x, y)=ψ (x) ψ (y)；Φ (x, y)=Φ (x) Φ (y)；Noise signal is broken down into after passing through wavelet transformation
Four frequency bands, i.e., horizontal, vertical, diagonal line and low frequency, LL2 are the filtered low scale approximate information of peak low band, same to fraction
Under resolution, HL2 contains the detailed information after horizontal direction high pass, vertical direction low-pass filtering, and what LH2 included is horizontally oriented
Detailed information after low pass, vertical direction high-pass filtering, what HH2 included be horizontally oriented and vertical direction all passes through high-pass filtering
Detailed information afterwards carries out identical treatment process, noise its energy and original shadow after wavelet transformation in resolution layer
As equal, the small echo signal of generation has the characteristic different from original signal, shows that the energy of signal focuses primarily upon low frequency
Part, and horizontal, vertical and diagonal energy is relatively fewer, these parts are believed each corresponding to the edge of original image
Breath, the directionality with ring, low frequency part is usually referred to as approximate signal, and horizontal, vertical and diagonal part is usually referred to as
Detail signal.
Wavelet coefficient LL, wavelet coefficient LH1, wavelet coefficient HL1 and wavelet coefficient HH1 are subjected to inverse wavelet transform, obtained
The subsignal system of the subsignal coefficient LL ' of corresponding horizontal low frequencies and vertical low frequency, horizontal low frequencies and vertical high frequency after to denoising
The subsignal coefficient HH ' of number LH ', the subsignal coefficient HL ' and horizontal high-frequent of horizontal high-frequent and vertical low frequency and vertical high frequency
S104。
Since the image denoising method combined for wavelet transformation and Gaussian function includes: the suitable small echo of selection and small
The Wave Decomposition number of plies, to noise signal carry out wavelet decomposition, obtain low-frequency approximation coefficient LL and three high frequency detail coefficient LH, HL and
HH remains unchanged low frequency LL coefficient, and different Gaussian functions is respectively adopted to LH, HL and HH and is filtered, is after filtering
LH ', HL ' and HH ', to wavelet coefficient LL, LH ', HL ' and HH ' carry out inverse wavelet transform, the signal after denoise, height
This function is low-pass filtering method commonly used in noise processed, such as the first step of classical Canny edge extracting method
Be exactly that Gaussian function low-pass filtering is carried out to handled signal, for signals and associated noises low frequency region noise energy proportion compared with
It is small, and the large percentage shared by high frequency region noise energy, so denoising focuses on high frequency region；
Due to using by noise signal according to the basic function of two-dimensional wavelet transformation be decomposed into horizontal frequency band, vertical frequency band,
Diagonal line frequency band and low-frequency band；Noise signal is subjected to Multiresolution Decomposition by one-dimensional wavelet transform, after decomposition
Noise signal by different spaces and different frequency a noise signal level low frequency and vertical low frequency subsignal coefficient LL,
The subsignal coefficient LH of noise signal level low frequency and vertical high frequency, a noise signal level high frequency and vertical low frequency
The subsignal coefficient HH of subsignal coefficient HL, a noise signal level high frequency and vertical high frequency；It will by two-dimensional wavelet transformation
The wavelet coefficient LL of noise signal noise signal level low frequency and vertical low frequency is remained unchanged, respectively to a noise signal level
The subsignal coefficient LH of low frequency and vertical high frequency, a noise signal level high frequency and vertical low frequency subsignal coefficient HL and
The subsignal coefficient HH of noise signal level high frequency and vertical high frequency is respectively adopted different gaussian kernel functions and is filtered
And form the wavelet coefficient LH1 of quadratic noise signal level low frequency and vertical high frequency, quadratic noise signal level high frequency and vertical
The wavelet coefficient HH1 of the wavelet coefficient HL1 of low frequency, quadratic noise signal level high frequency and vertical high frequency；By wavelet coefficient LL, small
Wave system number LH1, wavelet coefficient HL1 and wavelet coefficient HH1 carry out inverse wavelet transform, after denoise corresponding horizontal low frequencies with
Vertically subsignal coefficient LH ', horizontal high-frequent and the vertical low frequency of the subsignal coefficient LL ' of low frequency, horizontal low frequencies and vertical high frequency
Subsignal coefficient HL ' and horizontal high-frequent and vertical high frequency subsignal coefficient HH ', due to pass through wavelet transformation and Gaussian kernel
Function, which combines the method for carrying out signal denoising, can effectively remove salt-pepper noise while removing white Gaussian noise, this side
Method is to carry out Gassian low-pass filter respectively to high-frequency sub-band in the characteristics of wavelet transformation, and filtered wavelet coefficient is passed through contravariant
The signal after denoising can be obtained after changing, this method is not only obvious to Gaussian noise and salt-pepper noise denoising effect, but also
The detailed information of original signal is remained, filter effect is better than the effect of median filtering and wavelet soft thresholding.
The gaussian kernel function is low-pass filtering algorithm.
The low-pass filtering algorithm of the gaussian kernel function is the first step of Canny edge extracting method.
Gaussian kernel function G (x, y, σ) is used to the subsignal coefficient LH of a noise signal level low frequency and vertical high frequency
It is filtered.
Subsignal coefficient HL and a noise signal level height to a noise signal level high frequency and vertical low frequency
The subsignal coefficient HH of frequency and vertical high frequency is filtered using gaussian kernel function G (x, y, σ/2).
Since (information that HH, HL and LH) include is different, so in this programme for three high frequency coefficients after wavelet transformation
Gaussian function G (x, y, σ) is used to three high frequency coefficients, then Gaussian function G (x, y, σ/2) are used for HL and LH wavelet coefficient
It is filtered.
The root-mean-square deviation σ uses 0.02~0.04.
Subsignal after denoising is subjected to denoising effect assessment by normalized mean squared error NMSE and Y-PSNR PSNR.
As shown in Fig. 2, including: about subsignal coefficient
The subsignal coefficient LL ' is the filtered low scale approximate information of peak low band；
The subsignal coefficient LH ' includes the detailed information after horizontal direction low pass and vertical direction high-pass filtering；
The subsignal coefficient HL ' includes the detailed information after horizontal direction low pass and vertical direction high-pass filtering；
The subsignal coefficient HH ' includes the detailed information after water quadratic sum high pass and vertical direction high-pass filtering；
Since LH is subsignal of the signal after space low pass and column high-pass filtering, it contains noise signal in level side
To the low-frequency information of high-frequency information and vertical direction, HL is subsignal of the noise Jing Guo high pass and column low-pass filtering, it is contained
The high-frequency information of signal low-frequency information in the horizontal direction and vertical direction, HH are signals after space high pass and column high-pass filtering
Subsignal, it contains signal both horizontally and vertically high-frequency information, i.e., focusing direction high-frequency information.
Energy of the noise signal after wavelet transformation is equal with primary energy.
The noise signal after wavelet transformation respectively corresponds to horizontal, the vertical and diagonal edges letter of original signal
Breath.
Working principle:
As shown in figure 3, this patent is by being decomposed into horizontal frequency according to the basic function of two-dimensional wavelet transformation for noise signal
Band, vertical frequency band, diagonal line frequency band and low-frequency band；Noise signal is subjected to multiresolution point by one-dimensional wavelet transform
Solution, by the noise signal after decomposition by the noise signal level low frequency and vertical low frequency of different spaces and different frequency
Subsignal coefficient LH, a noise signal level height of subsignal coefficient LL, a noise signal level low frequency and vertical high frequency
The subsignal coefficient HH of the subsignal coefficient HL of frequency and vertical low frequency, a noise signal level high frequency and vertical high frequency；Pass through
Two-dimensional wavelet transformation remains unchanged the wavelet coefficient LL of noise signal noise signal level low frequency and vertical low frequency, respectively to one
The son of the subsignal coefficient LH of secondary noise signal level low frequency and vertical high frequency, a noise signal level high frequency and vertical low frequency
Different Gausses is respectively adopted in the subsignal coefficient HH of signal coefficient HL and a noise signal level high frequency and vertical high frequency
Kernel function is filtered and is formed the wavelet coefficient LH1 of quadratic noise signal level low frequency and vertical high frequency, quadratic noise signal
The wavelet coefficient HH1 of the wavelet coefficient HL1 of horizontal high-frequent and vertical low frequency, quadratic noise signal level high frequency and vertical high frequency；
Wavelet coefficient LL, wavelet coefficient LH1, wavelet coefficient HL1 and wavelet coefficient HH1 are subjected to inverse wavelet transform, after obtaining denoising
Subsignal coefficient LH ', the water of the subsignal coefficient LL ' of corresponding horizontal low frequencies and vertical low frequency, horizontal low frequencies and vertical high frequency
The subsignal coefficient HH ' of the subsignal coefficient HL ' and horizontal high-frequent and vertical high frequency of flat high frequency and vertical low frequency, due to passing through
The method that wavelet transformation combines progress signal denoising with gaussian kernel function can be effective while removing white Gaussian noise
Salt-pepper noise is removed, the method is to carry out Gassian low-pass filter respectively to high-frequency sub-band in the characteristics of wavelet transformation, after filtering
Wavelet coefficient can be obtained after inverse transformation by denoising after signal, the present invention solve the prior art exist for making an uproar
Acoustical signal is while retaining original signal, moreover it is possible to which the problem of effectively removing white Gaussian noise and soiline-alkali plants, it is not only right to have
Gaussian noise and salt-pepper noise denoising effect are obvious, and remain the detailed information of original signal, during filter effect is better than
The advantageous effects of the effect of value filtering and wavelet soft thresholding.
Using technical solution of the present invention or those skilled in the art under the inspiration of technical solution of the present invention, design
Similar technical solution out, and reach above-mentioned technical effect, it is to fall into protection scope of the present invention.
Claims (10)
1. a kind of small echo thresholding denoising method based on gaussian kernel function characterized by comprising
By noise signal according to the basic function of two-dimensional wavelet transformation be decomposed into horizontal frequency band, vertical frequency band, diagonal line frequency band with
And low-frequency band；
The basic function of the two-dimensional wavelet transformation are as follows:
ψ1(x, y)=Φ (x) ψ (y)；
ψ2(x, y)=ψ (x) Φ (y)；
ψ3(x, y)=ψ (x) ψ (y)；
Φ (x, y)=Φ (x) Φ (y)；
Wherein；
The Φ (x) is a unidimensional scale function of noise signal；
The ψ (x) is a corresponding wavelet function of unidimensional scale function of noise signal；
The Φ (y) is another unidimensional scale function of noise signal；
The ψ (y) is another corresponding wavelet function of unidimensional scale function of noise signal；
Noise signal is subjected to Multiresolution Decomposition by one-dimensional wavelet transform, by the noise signal after decomposition by different spaces with
And different frequency a noise signal level low frequency and vertical low frequency subsignal coefficient LL, a noise signal level low frequency
With the subsignal coefficient LH of vertical high frequency, the subsignal coefficient HL of a noise signal level high frequency and vertical low frequency, once make an uproar
The subsignal coefficient HH of acoustical signal horizontal high-frequent and vertical high frequency；
The wavelet coefficient LL of noise signal noise signal level low frequency and vertical low frequency is remained unchanged by two-dimensional wavelet transformation,
Respectively to the subsignal coefficient LH of a noise signal level low frequency and vertical high frequency, a noise signal level high frequency and vertical
The subsignal coefficient HH of the subsignal coefficient HL of low frequency and a noise signal level high frequency and vertical high frequency is respectively adopted not
With gaussian kernel function be filtered and formed the wavelet coefficient LH1, secondary of quadratic noise signal level low frequency and vertical high frequency
The small echo of the wavelet coefficient HL1 of noise signal level high frequency and vertical low frequency, quadratic noise signal level high frequency and vertical high frequency
Coefficient HH1；
Wavelet coefficient LL, wavelet coefficient LH1, wavelet coefficient HL1 and wavelet coefficient HH1 are subjected to inverse wavelet transform, gone
The subsignal coefficient of the subsignal coefficient LL ' of corresponding horizontal low frequencies and vertical low frequency, horizontal low frequencies and vertical high frequency after making an uproar
The subsignal coefficient HL ' and horizontal high-frequent of LH ', horizontal high-frequent and vertical low frequency and the subsignal coefficient HH ' of vertical high frequency.
2. a kind of small echo thresholding denoising method based on gaussian kernel function according to claim 1, which is characterized in that described
Gaussian kernel function is low-pass filtering algorithm.
3. a kind of small echo thresholding denoising method based on gaussian kernel function according to claim 2, which is characterized in that described
The low-pass filtering algorithm of gaussian kernel function is the first step of Canny edge extracting method.
4. a kind of small echo thresholding denoising method based on gaussian kernel function according to claim 1, which is characterized in that one
The subsignal coefficient LH of secondary noise signal level low frequency and vertical high frequency is filtered using gaussian kernel function G (x, y, σ).
5. a kind of small echo thresholding denoising method based on gaussian kernel function according to claim 4, which is characterized in that one
The subsignal coefficient HL and a noise signal level high frequency and vertical high frequency of secondary noise signal level high frequency and vertical low frequency
Subsignal coefficient HH be filtered using gaussian kernel function G (x, y, σ/2).
6. a kind of small echo thresholding denoising method based on gaussian kernel function according to claim 5, which is characterized in that described
Root-mean-square deviation σ uses 0.02~0.04.
7. a kind of small echo thresholding denoising method based on gaussian kernel function according to claim 1, which is characterized in that will go
Subsignal carries out denoising effect assessment by normalized mean squared error NMSE and Y-PSNR PSNR after making an uproar.
8. a kind of small echo thresholding denoising method based on gaussian kernel function according to claim 1, which is characterized in that about
Subsignal coefficient includes:
The subsignal coefficient LL ' is the filtered low scale approximate information of peak low band；
The subsignal coefficient LH ' includes the detailed information after horizontal direction low pass and vertical direction high-pass filtering；
The subsignal coefficient HL ' includes the detailed information after horizontal direction low pass and vertical direction high-pass filtering；
The subsignal coefficient HH ' includes the detailed information after water quadratic sum high pass and vertical direction high-pass filtering.
9. a kind of small echo thresholding denoising method based on gaussian kernel function according to claim 1, which is characterized in that described
Energy of the noise signal after wavelet transformation is equal with primary energy.
10. a kind of small echo thresholding denoising method based on gaussian kernel function according to claim 9, which is characterized in that institute
State horizontal, vertical and diagonal edges information that the noise signal after wavelet transformation respectively corresponds to original signal.
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