CN1921562A - Method for image noise reduction based on transforming domain mathematics morphology - Google Patents

Abstract

The invention relates to an image noise-reduction method based on transformation domain mathematical morphology. Wherein, it comprises that processing Contourlet rare transformation on the input noise image with multi sizes and multi directions; then using mathematical morphology algorism to process the high-frequency factor at Contourlet domain, to remove the noise with less support domain, and effectively keep the image edge information with continuous support domain; at last, using Contourlet inverse transformation to obtain noise-reduction image, to reduce the noise of image. The invention has wide application.

Description

Based on the morphologic image denoising method of transforming domain mathematics

Technical field

The present invention relates to a kind of based on the morphologic image denoising method of transforming domain mathematics, this method utilizes mathematical morphology operators in the Contourlet territory high frequency coefficient to be handled, remove the noise that has less supporting domain in the image, effectively keep image edge information, to improve picture quality with continuous supporting domain.In systems such as military field and non-military field such as optical imagery, target detection, security monitoring, all be widely used.

Background technology

Usually, image obtain with transmission course in, all can be subjected to noise pollution in various degree, and the purpose of image noise reduction is exactly when removing noise, the principal character information that keeps image to greatest extent, i.e. marginal information in the image is to improve the recovery quality of image.At present, image denoising method mainly is divided into airspace filter and transform domain filtering two big classes.Traditional most of filtering method belongs to the former, as medium filtering etc.And in the transform domain filtering method, the most representative with the collapse threshold noise-reduction method that Donoho and Johnstone propose based on wavelet transformation.Because signal is through behind the wavelet transformation, signal mainly concentrates on the bigger wavelet coefficient of minority absolute amplitude, and noise then is dispersed on the less wavelet coefficient of some absolute amplitude, therefore, can utilize collapse threshold that wavelet coefficient is carried out noise reduction, reach the purpose of noise reduction.

But, because two-dimentional separable wavelets conversion forms by tensor product through the one dimension small echo, it can only represent effectively that the unusual information of one dimension promptly puts unusual information, and two dimension or the unusual information of higher-dimension in the image can not be described effectively, as important informations such as line, profiles, thereby restricted the performance of wavelet de-noising method.The Contourlet conversion is as a kind of new signal analysis instrument, solved wavelet transformation and can not effectively represent the two dimension or the shortcoming of higher-dimension singularity more, can exactly the edge in the image be captured in the subband of different scale, different frequency, different directions.It not only has the multiple dimensioned characteristic of wavelet transformation, also has directivity and anisotropy that wavelet transformation does not have, therefore can be advantageously applied in the image processing that comprises image noise reduction.These methods are determined appropriate threshold by studying the prior information of signal to greatest extent, carry out the threshold value noise reduction, improve the effect of noise reduction.Yet these threshold value noise-reduction methods fail to take into full account the continuous boundary information that keeps image, have restricted the anti-acoustic capability of algorithm.

Summary of the invention

The objective of the invention is to deficiency at the existence of conventional images noise-reduction method, proposed a kind of based on the morphologic image denoising method of transforming domain mathematics, utilize mathematical morphology operators high frequency coefficient to be handled in the Contourlet territory, remove the noise that has less supporting domain in the image, effectively keep image edge information, improve picture quality with continuous supporting domain.

In order to achieve the above object, the present invention adopts following technical proposals:

A kind of based on the morphologic image denoising method of transforming domain mathematics.Its feature is carried out multiple dimensioned, multidirectional sparse decomposition at the noisy image that adopts the input of Contourlet transfer pair, and utilize mathematical morphology operators that high frequency coefficient is handled in the Contourlet territory, remove the noise that has less support region in the image, effectively keep image edge information with continuous support region, obtain the noise reduction image by the Contourlet inverse transformation then, reach the purpose of image noise reduction.

Suppose that the noise image that observes is

I＝f+n (1)

Wherein f is an original image, n be independent identically distributed white Gaussian noise signal N (0, σ ²).

The concrete steps of above-mentioned noise-reduction method are as follows:

1. beginningization setting.Make i=0, j=0 sets the maximal translation amount N on line direction and the column direction ₁And N ₂The middle LP that sets the Contourlet conversion simultaneously decomposes the direction Number of Decomposition L in number of plies K and every layer _k

2. the noisy image I of input is expert at and column direction on carry out the circulation translation of the significance bit amount of moving, obtain the translation image

S _ij＝C _i，j(I)， (2)

Wherein i ∈ (0, N ₁) and j ∈ (0, N ₂) be respectively the translational movement on line direction and the column direction;

3. the translation image S to obtaining _IjCarry out the sparse decomposition of multiple dimensioned, multidirectional Contourlet, promptly

$[S_{\mathrm{lf}},S_{\mathrm{hf}}^{\left(\mathrm{1,1}\right)},\·\·\·,S_{\mathrm{hf}}^{(1,L_1)},S_{\mathrm{hf}}^{\left(\mathrm{2,1}\right)},\·\·\·S_{\mathrm{hf}}^{(K,L_k)}]=T\left(S_{\mathrm{ij}}\right)---\left(3\right)$

Wherein T () is the Contourlet conversion.Thereby obtain a width of cloth low frequency subgraph as S _LfWith a series of high frequency subimage S with different resolution _Hf ^{(k, l)}, wherein k ∈ (1, K) and l ∈ (1, L _k) indicate that subimage is positioned at the l direction of k layer LP (the tower decomposition of Laplce);

4. to each the high frequency subimage S after the Contourlet conversion _Hf ^{(k, l)}, adopt Mathematical Morphology Method to carry out noise reduction process, obtain noise reduction high frequency subimage S _Dhf ^{(k, l)}

5. all noise reduction high frequency subimage S that obtain in going on foot the 4th _Dhf ^{(k, l)}With the low frequency subgraph that obtains in the 3rd step as S _LfImplement the Contourlet inverse transformation, obtain the noise reduction image behind difference translation i and j on line direction and the column direction,

$S_{i,j}^{\mathrm{nf}}=T^{-1}(S_{\mathrm{lf}},S_{\mathrm{Dhf}}^{\left(\mathrm{1,1}\right)},\·\·\·S_{\mathrm{Dhf}}^{(1,L_1)},S_{\mathrm{Dhf}}^{\left(\mathrm{2,1}\right)},\·\·\·S_{\mathrm{Dhf}}^{(K,L_k)}),---\left(4\right)$

Wherein, T ^-1() is the Contourlet inverse transformation;

6. the image S that obtains in going on foot the 5th _{I, j} ^NfCarry out the reverse circulation translation of corresponding translational movement, have

$I_{i,j}^{\mathrm{nf}}=C_{-i,-j}\left(S_{i,j}^{\mathrm{nf}}\right).---\left(5\right)$

7. repeating step 2 to 6, up to i=N ₁And j=N ₂Till, stop repetition;

8. all I to obtaining _{I, j} ^Nf(i=0 ..., N ₁J=0 ..., N ₂) ask average, obtain the noise reduction image:

${\hat{g}}_{\mathrm{CTM}}=\frac{1}{N_1{\mathrm{<figure-callout\; id="2"\; label="N"\; filenames="A20061003074500131.png"\; state="\{\{state\}\}">N</figure-callout>}}_2}\underset{i=0,j=0}{\overset{N_1,N_2}{\mathrm{\&Sigma;}}}{I}_{i,j}^{\mathrm{nf}}.---\left(6\right)$

The step that Mathematical Morphology Method in the 4th above-mentioned step is carried out noise reduction process is as follows:

1. order $S_M=S_{\mathrm{hf}}^{(k,l)};$

2. with S _MIn positive number pixel and negative pixel treat respectively, the order

$P(m,n)=\left\{\begin{array}{cc}{S}_M(m,n),& S_M(m,n)>0;\\ 0& \mathrm{Otherwise}.\end{array}\right.,\mathrm{for}\left\{\begin{array}{c}m=1:N_r\\ n=1:N_c\end{array}\right.---\left(7\right)$

$N(m,n)=\left\{\begin{array}{cc}-S_M(m,n),& S_M(m,n)<0;\\ 0& \mathrm{Otherwise}.\end{array}\right.,\mathrm{for}\left\{\begin{array}{c}m=1:N_r\\ n=1:N_c\end{array}\right.---\left(8\right)$

[N wherein _r, N _c]=size (S _M);

3. utilize threshold value Thr to carry out binaryzation respectively to P and N, obtain P _bAnd N _b

4. to P _bAnd N _bCarry out hit or miss transform, extract the isolated noise pixel in them, have

P _{I_point}＝HMT(P _b，SE1，SE2) (9)

N _{I_point}＝HMT(N _b，SE1，SE2) (10)

Wherein,

$\mathrm{SE}1=\left(\begin{array}{ccc}0& 0& 0\\ 0& 1& 0\\ 0& 0& 0\end{array}\right),\mathrm{<figure-callout\; id="2"\; label="SE"\; filenames="A20061003074500131.png"\; state="\{\{state\}\}">SE</figure-callout>}2=\left(\begin{array}{ccc}1& 1& 1\\ 1& 0& 1\\ 1& 1& 1\end{array}\right);$

5. remove these isolated noise pixels, have

P _b2＝P _b-P _{I_point} (11)

N _b2＝N _b-N _{I_point}； (12)

6. make U _p=or (P _B2, N _B2), with P _B2And N _B2As sign, extract S _MIn corresponding pixel, and adopt the threshold value of front to carry out noise reduction process, have

S _{M_NF}＝(U _p·*S _M)-Thr*P _b2+Thr*N _b2； (13)

7. noise reduction high frequency subimage is

$S_{\mathrm{Dhf}}^{(k,l)}=S_{M\_\mathrm{NF}}.---\left(14\right)$

The inventive method has following conspicuous outstanding substantive distinguishing features and remarkable advantage compared with prior art:

This invention aims to provide a kind of based on the morphologic image denoising method of transforming domain mathematics, this inventive method is at first carried out the sparse conversion of multiple dimensioned, multidirectional Contourlet to the noisy image of input, utilize mathematical morphology operators high frequency coefficient to be handled then in the Contourlet territory, removal has the noise of less supporting domain, effectively keep image edge information with continuous supporting domain, obtain the noise reduction image by the Contourlet inverse transformation at last, reach the purpose of image noise reduction.Concrete characteristics and advantage are:

(1)------be two or higher-dimension singularity in the presentation video effectively at the shortcoming of wavelet transformation in the most representative existing wavelet field threshold value noise-reduction method, the Contourlet conversion is applied in the image noise reduction, carry out multiple dimensioned, multi-direction decomposition, for follow-up noise reduction process provides sparse iamge description coefficient.

(2) conventional images noise reduction technology threshold value noise-reduction method is failed to take into full account the deficiency of the continuous boundary information that keeps image, proposed a kind of based on the morphologic image denoising method of transforming domain mathematics.

(3) the inventive method utilizes mathematical morphology operators that high frequency coefficient is handled at the Contourlet transform domain, removes the noise with less supporting domain, effectively keeps the image edge information with continuous supporting domain.

Image denoising method provided by the invention can improve the noise reduction image quality, target and background information more comprehensively and accurately is provided, reach comparatively ideal noise reduction.In systems such as military field and non-military field such as optical imagery, target detection, security monitoring, all have wide application prospects.

Description of drawings

Fig. 1 is the image denoising method flow chart of one embodiment of the invention.

Fig. 2 is Fig. 1 example noise reduction photo figure as a result.Among the figure, (a) represent σ respectively to (g) _nNoisy image and result under=20,25,30,35,40,45 and 50 situations, wherein first of each row classify noisy image as, second classifies the result that adopts median filter method as, the 3rd classifies the result that adopts Contourlet territory soft-threshold noise-reduction method as, the 4th classifies the result of employing based on the wavelet field noise-reduction method of mathematical morphology as, and the 5th classifies the result who adopts the inventive method noise reduction process as.

Embodiment

A preferred embodiment of the present invention is auspicious in conjunction with the accompanying drawings state as follows:

The present invention aims to provide a kind of method of reducing noise for combined images, as shown in Figure 1.This method is at first carried out the sparse conversion of multiple dimensioned, multidirectional Contourlet to the noisy image of input, utilize mathematical morphology operators high frequency coefficient to be handled then in the Contourlet territory, removal has the noise of less supporting domain, effectively keep image edge information with continuous supporting domain, obtain the noise reduction image by the Contourlet inverse transformation at last, reach the purpose of image noise reduction.

Concrete steps are:

1. initialization setting.Make i=0, j=0 sets the maximal translation amount N on line direction and the column direction ₁And N ₂The middle LP that sets the Contourlet conversion simultaneously decomposes the direction Number of Decomposition L in number of plies K and every layer _k

2. the noisy image I of input is expert at and column direction on carry out the circulation translation of the significance bit amount of moving, obtain the translation image

S _ij＝C _i，j(I)，

Wherein i ∈ (0, N ₁) and j ∈ (0, N ₂) be respectively the translational movement on line direction and the column direction;

3. the translation image S to obtaining _IjCarry out the sparse decomposition of multiple dimensioned, multidirectional Contourlet, promptly

$[S_{\mathrm{lf}},S_{\mathrm{hf}}^{\left(\mathrm{1,1}\right)},\&CenterDot;\&CenterDot;\&CenterDot;,S_{\mathrm{hf}}^{(1,L_1)},S_{\mathrm{hf}}^{\left(\mathrm{2,1}\right)},\&CenterDot;\&CenterDot;\&CenterDot;S_{\mathrm{hf}}^{(K,L_k)}]=T\left(S_{\mathrm{ij}}\right)$

Wherein T () is the Contourlet conversion.Thereby obtain a width of cloth low frequency subgraph as Slf and a series of high frequency subimage S with different resolution _Hf ^{(k, l)}, wherein k ∈ (1, K) and l ∈ (1, L _k) indicate that subimage is positioned at the l direction of k layer LP (the tower decomposition of Laplce).

4. to each the high frequency subimage S after the Contourlet conversion _Hf ^{(k, l)}, adopt following Mathematical Morphology Method to carry out noise reduction process:

1. order $S_M=S_{\mathrm{hf}}^{(k,l)};$

2. with S _MIn positive number pixel and negative pixel treat respectively, the order

$P(m,n)=\left\{\begin{array}{cc}{S}_M(m,n),& S_M(m,n)>0;\\ 0& \mathrm{Otherwise}.\end{array}\right.,\mathrm{for}\left\{\begin{array}{c}m=1:N_r\\ n=1:N_c\end{array}\right.$

$N(m,n)=\left\{\begin{array}{cc}-S_M(m,n),& S_M(m,n)<0;\\ 0& \mathrm{Otherwise}.\end{array}\right.,\mathrm{for}\left\{\begin{array}{c}m=1:N_r\\ n=1:N_c\end{array}\right.$

[N wherein _r, N _c]=size (S _M);

3. utilize threshold value Thr to carry out binaryzation respectively to P and N, obtain P _bAnd N _b

4. to P _bAnd N _bCarry out hit or miss transform, extract the isolated noise pixel in them, have

P _{I_point}＝HMT(P _b，SE1，SE2)

N _{I_point}＝HMT(N _b，SE1，SE2)

Wherein,

$\mathrm{SE}1=\left(\begin{array}{ccc}0& 0& 0\\ 0& 1& 0\\ 0& 0& 0\end{array}\right),\mathrm{<figure-callout\; id="2"\; label="SE"\; filenames="A20061003074500131.png"\; state="\{\{state\}\}">SE</figure-callout>}2=\left(\begin{array}{ccc}1& 1& 1\\ 1& 0& 1\\ 1& 1& 1\end{array}\right);$

5. remove these isolated noise pixels, have

P _b2＝P _b-P _{I_point}，

N _b2＝N _b-N _{I_point}；

6. make U _p=or (P _B2, N _B2), with P _B2And N _B2As sign, extract S _MIn corresponding pixel, and adopt the threshold value of front to carry out noise reduction process, have

S _{M_NF}＝(U _p·*S _M)-Thr*P _b2+Thr*N _b2；

7. the noise reduction subimage is

$S_{\mathrm{Dhf}}^{(k.l)}=S_{M\_\mathrm{NF}};$

5. all noise reduction high frequency subimage S that obtain in going on foot the 4th _Dhf ^{(k, l)}With the low frequency subgraph that obtains in the 3rd step as S _LfImplement the Contourlet inverse transformation, obtain the noise reduction image behind difference translation i and j on line direction and the column direction,

$S_{i,j}^{\mathrm{nf}}=T^{-1}(S_{\mathrm{lf}},S_{\mathrm{Dhf}}^{\left(\mathrm{1,1}\right)},\&CenterDot;\&CenterDot;\&CenterDot;S_{\mathrm{Dhf}}^{(1,L_1)},S_{\mathrm{Dhf}}^{\left(\mathrm{2,1}\right)},\&CenterDot;\&CenterDot;\&CenterDot;S_{\mathrm{Dhf}}^{(K,L_k)}),$

Wherein, T ^-1() is the Contourlet inverse transformation;

6. the image S that obtains in going on foot the 5th _{I, j} ^NfCarry out the reverse circulation translation of corresponding translational movement, have

$I_{i,j}^{\mathrm{nf}}=C_{-i,-j}\left(S_{i,j}^{\mathrm{nf}}\right);$

7. repeating step 2 to 6, up to i=N ₁And j=N ₂Till, stop repetition;

8. all I to obtaining _{I, j} ^Nf(i=0 ..., N ₁J=0 ..., N ₂) ask average, obtain the noise reduction image:

${\hat{g}}_{\mathrm{CTM}}=\frac{1}{N_1{\mathrm{<figure-callout\; id="2"\; label="N"\; filenames="A20061003074500131.png"\; state="\{\{state\}\}">N</figure-callout>}}_2}\underset{i=0,j=0}{\overset{N_1,N_2}{\mathrm{\&Sigma;}}}{I}_{i,j}^{\mathrm{nf}};$

From Fig. 2, be not difficult to find that the inventive method has noise reduction better than other several noise-reduction methods, has better visual effect.

Table 1 has provided noise-reduction method of the present invention and additive method noise reduction result's objective evaluation index.

For the anti-acoustic capability of measure algorithm objectively, table 1 has provided the performance index of weighing with mean square error (MSE) and Y-PSNR (PSNR).In the table, NI (Noised Image) represents noisy image, the result that on behalf of the medium filtering noise-reduction method, MF (MedianFilter) handle, the result that on behalf of Contourlet territory soft-threshold noise-reduction method, CT (Contourlet Threshold) handle, the result that WM (Wavelet Domain Mathematics Morphology) representative is handled based on the wavelet field noise-reduction method of mathematical morphology, PA (the Proposed Approach) the representative result who handles based on the Contourlet transform domain image noise-reduction method of mathematical morphology of the present invention.No matter be PSNR portrayal aspect, or MSE portrayal aspect, the inventive method all obviously is better than Contourlet territory soft-threshold noise-reduction method and based on the wavelet field noise-reduction method of mathematical morphology.And compare with medium filtering, except that noise intensity is 20, the inventive method all is better than medium filtering.In addition, be not difficult to find that the inventive method has remarkable advantages than additive method that Y-PSNR improves about 1～5dB, especially in strong noise intensity, promptly under the low signal-to-noise ratio situation, effect is more obvious, more can embody the advantage of the inventive method.

In a word, no matter be from the human eye vision effect, still from the objective evaluation index, show that all the inventive method reduces the noise signal in the image better, protected the material particular information in the image, improved the quality of image.

Noise reduction result's evaluation index relatively under the different noise levels of table 1

	σ n＝20		σ n＝25		σ n＝30		σ n＝35		σ n＝40		σ n＝45		σ n＝50
															PSNR	MSE	PSNR	MSE	PSNR	MSE	PSNR	MSE	PSNR	MSE	PSNR	MSE	PSNR	MSE
	NI	22.15	396.14	20.28	609.27	18.73	871.26	17.46	1166.30	16.40	1490.85	15.46	1850.72	14.67															2220.43
MF															28.40	94.09	26.89	133.21	25.53	182.18	24.42	235.21	23.34	301.19	22.44	370.61	21.61	448.42
	CT	26.08	160.52	24.66	222.60	23.48	291.95	22.22	390.06	21.36	474.93	20.53	575.64	19.65															704.64
WM															26.53	144.71	25.17	197.88	23.90	265.20	22.87	335.84	21.91	418.40	21.09	505.51	20.30	606.86
	PA	27.77	108.78	27.61	112.79	27.15	125.43	25.32	190.90	25.75	173.17	25.47	184.47	24.42															234.96

Claims (3)

1, a kind of based on the morphologic image denoising method of transforming domain mathematics, it is characterized in that at first the noisy image of importing being carried out the sparse conversion of multiple dimensioned, multidirectional Contourlet, utilize mathematical morphology operators high frequency coefficient to be handled then in the Contourlet territory, removal has the noise of less supporting domain, effectively keep image edge information with continuous supporting domain, obtain the noise reduction image by the Contourlet inverse transformation at last, reach the purpose of image noise reduction.

2, according to claim 1 based on the morphologic image denoising method of transforming domain mathematics, it is characterized in that concrete steps are as follows:

1) initialization setting.Make i=0, j=0 sets the maximal translation amount N on line direction and the column direction ₁And N ₂

The middle LP that sets the Contourlet conversion simultaneously decomposes the direction Number of Decomposition L in number of plies K and every layer _k

2) the noisy image I of input is expert at and column direction on carry out the circulation translation of the significance bit amount of moving, obtain the translation image

S _ij＝C _i，j(I)，

Wherein i ∈ (0, N ₁) and j ∈ (0, N ₂) be respectively the translational movement on line direction and the column direction;

3) the translation image S to obtaining _IjCarry out the sparse decomposition of multiple dimensioned, multidirectional Contourlet, promptly

$[S_{\mathrm{lf}},S_{\mathrm{hf}}^{\left(\mathrm{1,1}\right)},\&CenterDot;\&CenterDot;\&CenterDot;,S_{\mathrm{hf}}^{(1,L_1)},S_{\mathrm{hf}}^{\left(\mathrm{2,1}\right)},\&CenterDot;\&CenterDot;\&CenterDot;,S_{\mathrm{hf}}^{(K,L_k)}]=T\left(S_{\mathrm{ij}}\right),$

Wherein T () is the Contourlet conversion; Thereby obtain a width of cloth low frequency subgraph as S _LfWith a series of high frequency subimage S with different resolution _Hf ^{(k, l)}, wherein k ∈ (1, K) and l ∈ (1, L _k) indicate that subimage is positioned at the l direction of the tower decomposition of k layer Laplce (LP);

4) to each the high frequency subimage S after the Contourlet conversion _Hf ^{(k, l)}, adopt Mathematical Morphology Method to carry out noise reduction process, obtain noise reduction high frequency subimage S _Dhf ^{(k, l)}

5) to the 4th) all noise reduction high frequency subimage S of obtaining in the step _Dhf ^{(k, l)}With the 3rd) low frequency subgraph that obtains in the step is as S _LfImplement the Contourlet inverse transformation, obtain again on line direction and the column direction noise reduction image behind the translation i and j respectively,

$S_{i,j}^{\mathrm{nf}}=T^{-1}(S_{\mathrm{lf}},S_{\mathrm{D\; hf}}^{\left(\mathrm{1,1}\right)},\&CenterDot;\&CenterDot;\&CenterDot;,S_{\mathrm{D\; hf}}^{(1,L_1)},S_{\mathrm{D\; hf}}^{\left(\mathrm{2,1}\right)},\&CenterDot;\&CenterDot;\&CenterDot;,S_{\mathrm{D\; hf}}^{(K,L_k)}),$

Wherein, T ^-1() is the Contourlet inverse transformation;

6) to the 5th) the image S that obtains in the step _{I, j} ^NfCarry out the reverse circulation translation of corresponding translational movement, have

$I_{i,j}^{\mathrm{nf}}=C_{-i,-j}\left(S_{i,j}^{\mathrm{nf}}\right);$

7) repeating step 2) to 6), up to i=N ₁And j=N ₂Till, stop repetition;

8) all I to obtaining _{I, j} ^Nf(i=0, Λ, N ₁J=0, Λ, N ₂) ask average, obtain the noise reduction image:

${\hat{g}}_{\mathrm{CTM}}=\frac{1}{N_1{N}_2}\underset{i=0,j=0}{\overset{N_1,N_2}{\mathrm{\&Sigma;}}}{I}_{i,j}^{\mathrm{nf}}.$

3, according to claim 2 based on the morphologic image denoising method of transforming domain mathematics, it is characterized in that the described the 4th) in the step to each the high frequency subimage S after the Contourlet conversion _Hf ^{(k, l)}, the step that the employing Mathematical Morphology Method is carried out noise reduction process is as follows:

1. order $S_M=S_{\mathrm{hf}}^{(k,l)};$

2. with S _MIn positive number pixel and negative pixel treat respectively, the order

$P(m,n)=\left\{\begin{array}{cc}{S}_M(m,n),& S_M(m,n)>0;\\ 0& \mathrm{Otherwise}.\end{array}\right.\mathrm{for}\left\{\begin{array}{c}m=1:N_r\\ n=1:N_c\end{array}\right.$

$N(m,n)=\left\{\begin{array}{cc}-S_M(m,n),& S_M(m,n)<0;\\ 0& \mathrm{Otherwise}\end{array}\right.,\mathrm{for}\left\{\begin{array}{c}m=1:N_r\\ n=1:N_c\end{array}\right.$

[N wherein _r, N _c]=size (S _M);

3. utilize threshold value Thr to carry out binaryzation respectively to P and N, obtain P _bAnd N _b

4. to P _bAnd N _bCarry out hit or miss transform, extract the isolated noise pixel in them, have

P _{I_point}＝HMT(P _b，SE1，SE2)

N _{I_point}＝HMT(N _b，SE1，SE2)

Wherein,

$\mathrm{SE}1=\left(\begin{array}{ccc}0& 0& 0\\ 0& 1& 0\\ 0& 0& 0\end{array}\right),\mathrm{SE}2=\left(\begin{array}{ccc}1& 1& 1\\ 1& 0& 1\\ 1& 1& 1\end{array}\right);$

5. remove these isolated noise pixels, have

P _b2＝P _b-P _{I_point}

N _b2＝N _b-N _{I_point}；

6. make U _p=or (P _B2, N _B2), with P _B2And N _B2As sign, extract S _MIn corresponding pixel, and adopt the threshold value of front to carry out noise reduction process, have

S _{M_NF}＝(U _p*S _M)-Thr*P _b2+Thr*N _b2；

7. noise reduction high frequency subimage is

$S_{\mathrm{D\; hf}}^{(k,l)}=S_{M\_\mathrm{NF}}.$

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