CN104008529A - Cable terminal infrared image denoising method based on improved Fourier and wavelet mixing transformation - Google Patents

Abstract

The invention discloses a cable porcelain shell type terminal infrared image denoising method based on improved Fourier and wavelet mixing transformation. The method includes the following steps of (1) inputting a cable porcelain shell type terminal infrared image to be denoised; (2) estimating the power spectrum density of each Fourier coefficient; (3) carrying out filtering processing on the obtained infrared image, and carrying out inverse Fourier transformation to obtain the denoised infrared image in a Fourier domain; (4) carrying out two-bit wavelet transformation on the infrared image obtained in the Fourier domain to obtain a wavelet coefficient with noise; (5) modeling the wavelet coefficient with the noise through a Laplacian model, and then estimating the wavelet coefficient of a real image; (6) carrying out two-dimensional wavelet reconstruction on the obtained wavelet coefficient to obtain a denoised infrared image in a wavelet domain. The method has the advantages of being capable of effectively removing the noise and completely maintaining details of the image and the like.

Description

Based on improving the cable termination infrared image noise-reduction method that mixes Fourier-small echo

Technical field

The present invention relates to a kind of high-tension cable porcelain bushing type terminal infrared image processing technology, particularly a kind of based on improving the cable termination infrared image noise-reduction method that mixes Fourier-small echo.

Background technology

Infrared diagnosis technology based on infrared image has been widely used in state-detection and the fault diagnosis of electrical equipment, and obtains remarkable effect at aspects such as generator failure diagnosis, the damaged diagnosis of insulator.Infrared image detection method can realize untouchable measurement, have the electromagnetic interference (EMI) of not being subject to, safety, accurately, the feature such as economic and practical, be subject in recent years extensive concern, and be applied in practice the status monitoring of porcelain shell for cable formula terminal.Can whether porcelain shell for cable formula terminal infrared image be clear, and whether image detail is complete, and whether feature is obvious, be to it, carry out the key of correct diagnosis.Because infrared image is subject to the impact of noise of detector, ELECTRONIC NOISE, infrared focal plane array noise and neighbourhood noise in generative process, there is the feature of strong noise, low contrast.Therefore adopting high efficiency filtering method to carry out noise reduction to porcelain shell for cable formula terminal infrared image, promote picture quality, is the prerequisite of carrying out correct diagnosis.In method conventional aspect infrared image noise reduction, it is transform domain method.Wherein Fourier transform effectively has the texture part of certain period of change rule in rarefaction representation image and changes mild part, but the sudden change part effectively in presentation video, as the marginal portion in image; The wavelet transformation signal that rarefaction representation comprises sharp change part effectively, but the texture in rarefaction representation image and the part slowly changing effectively.

Summary of the invention

The shortcoming that the object of the invention is to overcome prior art, with not enough, provides a kind of based on improving the cable termination infrared image noise-reduction method that mixes Fourier-small echo, and this noise-reduction method can be removed noise effectively, and intactly retains the details of infrared image.

Object of the present invention is achieved through the following technical solutions: a kind of based on improving the cable termination infrared image noise-reduction method that mixes Fourier-small echo, comprise the following steps:

(1) the porcelain shell for cable formula terminal infrared image of noise reduction is treated in input;

(2) in Fourier, for noisy infrared image, carry out Fourier transform, and each Fourier coefficient is estimated to its power spectrum density;

(3) utilize S filter to carry out filtering processing to gained infrared image in step (2), and carry out inverse Fourier transform, obtain the infrared image after noise reduction in Fourier;

(4) in Fourier, the infrared image of gained in step (3) is carried out to two wavelet transformations and obtain noisy wavelet coefficient;

(5) adopt laplace model to carry out modeling to the noisy wavelet coefficient of gained, then utilize maximum a posteriori probability to estimate the wavelet coefficient of true picture;

(6) utilize the wavelet coefficient of step (5) gained to carry out 2-d wavelet reconstruct, obtain the infrared image after noise reduction in wavelet field, be the infrared image after final noise reduction;

In described step (2), the power spectrum density estimator of original image is:

$\begin{array}{cc}\hat{S}\left(w\right)=\max (a,\frac{1}{M}\underset{j\∈W}{\mathrm{\Σ}}{\left|Y\left(j\right)\right|}^2-{\mathrm{\σ}}_N^2)& a>0,\end{array}$

In formula, M is the number of Fourier coefficient in square window region W (w), the minimum power spectral density that a is W, and Y (j) represents the Fourier transform of noisy image Y, variance for white Gaussian noise.

The transport function of using S filter to carry out filtering in described step (3) is:

$\begin{array}{cc}H\left(w\right)=\frac{b\·\hat{S}\left(w\right)}{b\·\hat{S}\left(w\right)+{\mathrm{\σ}}_N^2}& b>1,\end{array}$

In formula, b is conservative estimation parameter, for the variance of white Gaussian noise, estimated value for original image power spectrum density.

Described step (5) comprises the following steps:

(a) determine true picture wavelet coefficient and the noisy image wavelet coefficient that need to recover;

(b) consider correlativity between wavelet coefficient yardstick, with laplace model, wavelet coefficient distribution character in infrared image yardstick is described;

(c) utilize the wavelet coefficient probability density function of true picture and noise to carry out maximum a posteriori probability estimation;

(d) each wavelet coefficient is carried out to noise variance and true picture standard deviation parameter estimation, the laplace model standard deviation after being estimated;

In the present invention, in described step (b), the probability density function of laplace model is:

$p_w\left(\stackrel{\→}{w}\right)=\frac{3}{2{\mathrm{\π\σ}}^2}\exp (-\frac{3}{\mathrm{\σ}}\sqrt{w_1^2+w_2^2}),$

In formula, w ₁and w ₂represent respectively wavelet coefficient w _1kand w _2k(for convenience of narration, removing subscript k).Wavelet coefficient w wherein _2kfor wavelet coefficient w _1kpaternal number, i.e. w _2kfor on next yardstick with k wavelet coefficient w _1kat the wavelet coefficient of same position, σ is w ₁and w ₂variance.

In the present invention, in described step (c), maximum a posteriori probability is estimated as:

$\hat{w}\left(y\right)=\arg \max p_{w|y}\left(w\right|y),$

In formula, w is by the image wavelet coefficient of the not Noise of slight distortion, and y is actual measurement wavelet coefficient, p _w|y(w|y) be posterior probability density.

In the present invention, in described step (d), being estimated as of laplace model standard deviation sigma:

$\widehat{\mathrm{\σ}}=\sqrt{{({\widehat{\mathrm{\σ}}}_y^2+{\widehat{\mathrm{\σ}}}_n^2)}_{+}},$

In formula, for observed reading y ₁and y ₂local variance, for noise variance.

The probability density function of described noise wavelet coefficient is:

$p_n\left(\stackrel{\→}{n}\right)=\frac{1}{2\mathrm{\π}{\mathrm{\σ}}_n^2}\·\exp (-\frac{n_1^2+n_2^2}{2{\mathrm{\σ}}_n^2}),$

In formula, n ₁and n ₂for wavelet coefficient, variance for white Gaussian noise.

Bayes's expression formula of described posterior probability density is:

$p_{w|y}\left(w\right|y)=\frac{p_n(y-w)p_w\left(w\right)}{p_y\left(y\right)},$

Described noise variance expression formula is:

${\widehat{\mathrm{\σ}}}_n^2{=\left(\frac{\mathrm{median}\left(\right|y_i\left|\right)}{0.6745}\right)}^2,y_i\∈\mathrm{HH},$

In formula, y _ifor actual measurement wavelet coefficient values.

Described experience be estimated as;

${\widehat{\mathrm{\σ}}}_y^2=\frac{1}{M}\underset{y_i\∈N\left(k\right)}{\mathrm{\Σ}}{y}_i^2,$

In formula, M is the size of rectangular window area N (k), y _ifor surveying little wave number.

The equivalent expression of described maximum a posteriori probability is:

$\hat{w}\left(y\right)=\arg \underset{w}{\max }[\log p_n(y-w)+\log p_w\left(w\right)],$

Described wavelet coefficient w ₁estimation expression formula be:

${\hat{w}}_1=\frac{{(\sqrt{y_1^2+y_2^2}-\frac{\sqrt{3}{\mathrm{\σ}}_n^2}{\mathrm{\σ}})}_{+}}{\sqrt{y_1^2+y_2^2}}{y}_1,$

In formula, (g) ₊be defined as: w ₁represent wavelet coefficient.

Principle of work of the present invention: first the present invention adopts S filter to carry out preliminary noise reduction in Fourier, then in wavelet field, consider correlativity between wavelet coefficient yardstick, introduce laplace model and describe wavelet coefficient, and use maximum a posteriori probability to estimate relevant wavelet coefficient, the method, in to porcelain shell for cable formula terminal infrared image noise reduction, can intactly retain the details of image.

The present invention has following advantage and effect with respect to prior art:

1, the invention solves while utilizing infrared image to carry out fault diagnosis to high-tension cable porcelain bushing type terminal containing noisy problem, the mixing noise reduction algorithm that the method is used Fourier transform and wavelet transformation to combine, consider correlativity between wavelet coefficient yardstick, introduce laplace model and describe wavelet coefficient; The method can more effectively be removed noise, and complete reservation image detail.

2, the present invention uses maximum a posteriori probability to estimate each wavelet coefficient and parameter, has avoided irrationality and the randomness of direct application correlation parameter, use mathematics probability ideological guarantee reached the noise reduction of expection when result validity.

Accompanying drawing explanation

Fig. 1 is the general frame based on mixing the porcelain shell for cable formula terminal infrared image noise-reduction method of Fourier-small echo of the present invention.

Fig. 2 is wavelet coefficient joint probability distribution figure.

Fig. 3 is containing noisy porcelain shell for cable formula terminal infrared image.

Fig. 4 is with the porcelain shell for cable formula terminal infrared image obtaining after the inventive method noise reduction.

Embodiment

Below in conjunction with embodiment and accompanying drawing, the present invention is described in further detail, but embodiments of the present invention are not limited to this.

Embodiment

A kind of based on improving the cable termination infrared image noise-reduction method that mixes Fourier-small echo:

1, wavelet transformation adopts sym4 small echo, and decomposing the number of plies is 4, and the square window size in Fourier and wavelet field is respectively 7*7 and 3*3, minimum power spectral density parameter b=5.

2, in Fourier, for noisy infrared image, carry out Fourier transform, and each Fourier coefficient is estimated to its power spectrum density;

3, utilize S filter to carry out filtering processing to gained infrared image in step (2), and carry out inverse Fourier transform, obtain the infrared image after noise reduction in Fourier;

4, in Fourier, the infrared image of gained in step (3) is carried out to two wavelet transformations and obtain noisy wavelet coefficient;

5, adopt laplace model to carry out modeling to the noisy wavelet coefficient of gained, then utilize maximum a posteriori probability to estimate the wavelet coefficient of true picture;

6, utilize the wavelet coefficient of step (5) gained to carry out 2-d wavelet reconstruct, obtain the infrared image after noise reduction in wavelet field, be the infrared image after final noise reduction;

Below in conjunction with accompanying drawing, the present invention is described in further detail:

The present invention proposes a kind of based on improving the porcelain shell for cable formula terminal infrared image noise-reduction method that mixes Fourier-small echo, the method adopts elder generation Vienna wave filter to carry out filtering to image in Fourier, then in wavelet field noise reduction process, consider correlativity between wavelet coefficient yardstick, and use laplace model to describe wavelet coefficient, adopt maximum a posteriori probability to estimate relevant wavelet coefficient, finally the wavelet coefficient after estimating is reconstructed, obtains the final infrared image of noise reduction in wavelet field.The method has not only been removed the noise in porcelain shell for cable formula terminal infrared image, and also the complete details that retains image, has good effect.

As shown in Figure 1, be a kind of the general frame based on mixing the porcelain shell for cable formula terminal infrared image noise-reduction method of Fourier-small echo.

1. in Fourier, for noisy infrared image, carry out Fourier transform, and each Fourier coefficient is estimated to its power spectrum density;

The power spectrum density estimator of Fourier coefficient is:

$\begin{array}{cc}\hat{S}\left(w\right)=\max (a,\frac{1}{M}\underset{j\∈W}{\mathrm{\Σ}}{\left|Y\left(j\right)\right|}^2-{\mathrm{\σ}}_N^2)& a>0,\end{array}$

In formula, M is the number of Fourier coefficient in square window region W (w), the minimum power spectral density that a is W, and Y (j) represents the Fourier transform of noisy image Y, variance for white Gaussian noise.

2. utilize S filter to carry out filtering processing to gained infrared image, and carry out inverse Fourier transform, obtain the infrared image after noise reduction in Fourier;

The transport function that S filter carries out filtering is:

$\begin{array}{cc}H\left(w\right)=\frac{b\·\hat{S}\left(w\right)}{b\·\hat{S}\left(w\right)+{\mathrm{\σ}}_N^2}& b>1,\end{array}$

In formula, b is conservative estimation parameter, for the variance of white Gaussian noise, estimated value for original image power spectrum density.

3. in Fourier, the infrared image of gained is carried out to two wavelet transformations and obtain noisy wavelet coefficient;

4. adopt laplace model to carry out modeling to the noisy wavelet coefficient of gained, then utilize maximum a posteriori probability to estimate the wavelet coefficient of true picture;

The probability density function of laplace model is:

$p_w\left(\stackrel{\→}{w}\right)=\frac{3}{2{\mathrm{\π\σ}}^2}\exp (-\frac{3}{\mathrm{\σ}}\sqrt{w_1^2+w_2^2}),$

In formula, w ₁and w ₂represent respectively wavelet coefficient w _1kand w _2k(for convenience of narration, removing subscript k).Wavelet coefficient w wherein _2kfor wavelet coefficient w _1kpaternal number, i.e. w _2kfor on next yardstick with k wavelet coefficient w _1kat the wavelet coefficient of same position, σ is w ₁and w ₂variance.

As shown in Figure 2, be the three-dimensional function figure of wavelet coefficient statistical model

Noise variance expression formula is:

${\widehat{\mathrm{\σ}}}_n^2{=\left(\frac{\mathrm{median}\left(\right|y_i\left|\right)}{0.6745}\right)}^2,y_i\∈\mathrm{HH},$

In formula, y _ifor actual measurement wavelet coefficient values.

Described experience be estimated as;

${\widehat{\mathrm{\σ}}}_y^2=\frac{1}{M}\underset{y_i\∈N\left(k\right)}{\mathrm{\Σ}}{y}_i^2,$

In formula, M is the size of rectangular window area N (k), y _ifor surveying little wave number.

5. utilize the wavelet coefficient of gained to carry out 2-d wavelet reconstruct, obtain the infrared image after noise reduction in wavelet field, be the infrared image after final noise reduction;

As shown in Figure 3, be noisy porcelain shell for cable formula terminal infrared image, as shown in Figure 4, be the porcelain shell for cable formula terminal infrared image with obtaining after the inventive method noise reduction.Known through contrasting, the method that the present invention adopts can be removed noise effectively, and can retain to greatest extent the details of original image.

Above-described embodiment is preferably embodiment of the present invention; but embodiments of the present invention are not restricted to the described embodiments; other any do not deviate from change, the modification done under Spirit Essence of the present invention and principle, substitutes, combination, simplify; all should be equivalent substitute mode, within being included in protection scope of the present invention.

Claims (10)

1. based on improving a cable termination infrared image noise-reduction method that mixes Fourier-small echo, it is characterized in that, comprise the following steps:

(1) the porcelain shell for cable formula terminal infrared image of noise reduction is treated in input;

(2) in Fourier, for noisy infrared image, carry out Fourier transform, and each Fourier coefficient is estimated to its power spectrum density;

(3) utilize S filter to carry out filtering processing to the infrared image obtaining in step (2), and carry out inverse Fourier transform, obtain the infrared image after noise reduction in Fourier;

(4) in Fourier, the infrared image of gained in step (3) is carried out to two wavelet transformations and obtain noise wavelet coefficient;

(5) adopt laplace model to carry out modeling to the noisy wavelet coefficient of gained, recycling maximum a posteriori probability is estimated the wavelet coefficient of true picture;

(6) utilize the wavelet coefficient of step (5) gained to carry out 2-d wavelet reconstruct, obtain the infrared image after noise reduction in wavelet field, the infrared image in described wavelet field after noise reduction is the infrared image after final noise reduction.

2. the cable termination infrared image noise-reduction method based on improving mixing Fourier-small echo according to claim 1, is characterized in that, in described step (2), the power spectrum density estimator of original image is:

$\begin{array}{cc}\hat{S}\left(w\right)=\max (a,\frac{1}{M}\underset{j\∈W}{\mathrm{\Σ}}{\left|Y\left(j\right)\right|}^2-{\mathrm{\σ}}_N^2)& a>0,\end{array}$

In formula, M is the number of Fourier coefficient in square window region W (w), the minimum power spectral density that a is W, and Y (j) represents the Fourier transform of noisy image Y, variance for white Gaussian noise.

3. the cable termination infrared image noise-reduction method based on improving mixing Fourier-small echo according to claim 1, is characterized in that,

In step (3), describedly utilize the transport function that S filter carries out filtering to be:

$\begin{array}{cc}H\left(w\right)=\frac{b\·\hat{S}\left(w\right)}{b\·\hat{S}\left(w\right)+{\mathrm{\σ}}_N^2}& b>1,\end{array}$

In formula, b is conservative estimation parameter, for the variance of white Gaussian noise, estimated value for original image power spectrum density;

In step (5), the equivalent expression of described maximum a posteriori probability is:

$\hat{w}\left(y\right)=\arg \underset{w}{\max }[\log p_n(y-w)+\log p_w\left(w\right)],$

Described wavelet coefficient w ₁estimation expression formula be:

${\hat{w}}_1=\frac{{(\sqrt{y_1^2+y_2^2}-\frac{\sqrt{3}{\mathrm{\σ}}_n^2}{\mathrm{\σ}})}_{+}}{\sqrt{y_1^2+y_2^2}}{y}_1,$

In formula, (g) ₊be defined as: w ₁represent wavelet coefficient;

In step (4), the probability density function of described noise wavelet coefficient is:

$p_n\left(\stackrel{\→}{n}\right)=\frac{1}{2\mathrm{\π}{\mathrm{\σ}}_n^2}\·\exp (-\frac{n_1^2+n_2^2}{2{\mathrm{\σ}}_n^2}),$

In formula, n ₁and n ₂for wavelet coefficient, variance for white Gaussian noise.

4. the cable termination infrared image noise-reduction method based on improving mixing Fourier-small echo according to claim 1, is characterized in that, described step (5) comprises the following steps:

(a) determine true picture wavelet coefficient and the noisy image wavelet coefficient that need to recover;

(b) consider correlativity between wavelet coefficient yardstick, with laplace model, wavelet coefficient distribution character in infrared image yardstick is described;

(c) utilize the wavelet coefficient probability density function of true picture and noise to carry out maximum a posteriori probability estimation;

(d) each wavelet coefficient is carried out to noise variance and true picture standard deviation parameter estimation, the laplace model standard deviation after being estimated.

5. the cable termination infrared image noise-reduction method based on improving mixing Fourier-small echo according to claim 4, is characterized in that, in described step (b), the probability density function of laplace model is:

$p_w\left(\stackrel{\→}{w}\right)=\frac{3}{2{\mathrm{\π\σ}}^2}\exp (-\frac{3}{\mathrm{\σ}}\sqrt{w_1^2+w_2^2}),$

In formula, w ₁and w ₂represent respectively wavelet coefficient w _1kand w _2k, wherein, wavelet coefficient w _2kfor wavelet coefficient w _1kpaternal number, i.e. w _2kfor on next yardstick with k wavelet coefficient w _1kat the wavelet coefficient of same position, σ is w ₁and w ₂variance.

6. the cable termination infrared image noise-reduction method based on improving mixing Fourier-small echo according to claim 4, is characterized in that, in step (c), described maximum a posteriori probability is estimated as:

$\hat{w}\left(y\right)=\arg \max p_{w|y}\left(w\right|y),$

In formula, w is the image wavelet coefficient of Noise not, and y is actual measurement wavelet coefficient, p _w|y(w|y) be posterior probability density.

7. the cable termination infrared image noise-reduction method based on improve mixing Fourier-small echo according to claim 4, is characterized in that, in step (d), and being estimated as of described laplace model standard deviation sigma:

$\widehat{\mathrm{\σ}}=\sqrt{{({\widehat{\mathrm{\σ}}}_y^2+{\widehat{\mathrm{\σ}}}_n^2)}_{+}},$

In formula, for observed reading y ₁and y ₂local variance, for noise variance.

8. according to claim 7 based on improving the cable termination infrared image noise-reduction method that mixes Fourier-small echo, it is characterized in that described observed reading y ₁and y ₂local variance experience be estimated as;

${\widehat{\mathrm{\σ}}}_y^2=\frac{1}{M}\underset{y_i\∈N\left(k\right)}{\mathrm{\Σ}}{y}_i^2,$

In formula, M is the size of rectangular window area N (k), y _ifor surveying little wave number.

9. the cable termination infrared image noise-reduction method based on improving mixing Fourier-small echo according to claim 6, is characterized in that, Bayes's expression formula of described posterior probability density is:

$p_{w|y}\left(w\right|y)=\frac{p_n(y-w)p_w\left(w\right)}{p_y\left(y\right)},$

In formula, p _w|y(w|y) represent the Bayes of posterior probability density.

10. the cable termination infrared image noise-reduction method based on improving mixing Fourier-small echo according to claim 4, is characterized in that, in step (d), described noise variance expression formula is:

${\widehat{\mathrm{\σ}}}_n^2{=\left(\frac{\mathrm{median}\left(\right|y_i\left|\right)}{0.6745}\right)}^2,y_i\∈\mathrm{HH},$

In formula, y _ifor actual measurement wavelet coefficient values.