CN101296312A - Wavelet and small curve fuzzy self-adapting conjoined image denoising method - Google Patents

Abstract

The invention relates to a new method which combines the fuzzy adapting of wavelet transform and curvelet transform in the image noise removal. The noise removal is one of important research programs in the image processing; however, the existing noise removal method can not completely solve the conflict between the noise removal and the edge preserving. The invention aims at providing an image noise removal method with the combination of the wavelet and curvelet fuzzy adapting on the basis of the defect of the prior art. The method of the invention establishes a flatness membership function of a sub-block to fuzzy express the edge information content in the sub-block and takes the membership function as the weight factor to carry out the data fusion to each sub-block by adopting the results from the noise removal with the wavelet transform and the curvelet transform. The method of the invention has the advantages that the data fusion substitutes the compulsory smoothing processing of the adapting combination method to solve the problem of blocking effect more thoroughly and retain more edge details; the advantages of the noise removal with the wavelet and the curvelet are flexibly integrated by the fuzzy data fusion so as to further improve the quality of noise removal.

Description

The image de-noising method of small echo and small curve fuzzy self-adapting associating

Technical field

The present invention relates to a kind of novel associating wavelet transformation and the image de-noising method of little song (Curvelet) conversion, belong to image processing field.

Background technology

Image is subjected to interference of noise inevitably in the process that generates and transmit.The existence of noise has caused the increase of graphical analysis work difficulty such as the reduction of picture quality and later stage target identification.Therefore, how effectively to remove picture noise is one of important subject in the image processing field always.

Classical image de-noising method comprises the airspace filter method, frequency domain filtering method and the denoising method based on wavelet transform (abbreviating the DWT method as) relatively more commonly used in recent years.Though they have obtained denoising effect preferably, can't solve the collision problem between the maintenance at the removal of noise in the denoising process and edge all the time fully.A kind of new signal multi-scale expression---little Qu Bianhuan has been introduced into image processing field in the recent period, it is with line segment rather than put signal primary expression unit, therefore the denoising method (abbreviating the DCT method as) based on discrete little Qu Bianhuan can more effectively keep image edge information (J.L.Starck than DWT method, E.J.Candes, and D.L.Donoho.The Curvelet transform forimage denoising[J] .IEEE Trans.Image Processing, 2002, vol.11:670-684.).But the DWT method can be removed noise better than DCT method when handling less zone, image border simultaneously.Be the advantage of comprehensive both complementations, the image de-noising method of small echo and little Qu Bianhuan associating arises at the historic moment.

The associating denoising method that has occurred at present has two kinds, associating filter method and adaptive combined method.The former adopts mixing steepest gradient algorithm is that each iterative image selects suitable filter operator in order to approach optimal solution (J.L.Starck gradually, M.K.Nguyen, and F.Murtagh.Wavelets andCurvelets for image deconvolution:a combined approach[J] .Signal Processing, 2003, vol.83:2279-2283.).This method can obtain than the DCT method of independent use and the better denoising effect of DWT method, but causes amount of calculation very big because of its iterative process is complicated.The latter then is judged as sub-piece in edge or smooth sub-piece according to the edge pixel distributed intelligence of image subblock with it, in view of the above each sub-piece is selected for use DCT method or the denoising of DWT method, its result is carried out smoothing windows to be handled, handle the result (B.B.Saevarsson of back result the most at last as the adaptive combined denoising of sub-piece, J.R.Sveinsson, and J.A.Benediktsson.Combined Wavelet and Curvelet denoising of SAR images[C] .Geoscience and Remote Sensing Symposium, 2004.IGARSS ' 04.Proceedings.2004 IEEE International, 2004, vol.6:4235-4238.).Compare with the associating filter method, adaptive combined method has further improved the denoising quality and has greatly reduced operand, therefore has more practical value.But it will inevitably bring the fuzzy of edge for the mandatory smoothing processing that solves the blocking effect problem each sub-piece is carried out, and therefore basically, it is that to keep effect be that cost has solved the blocking effect problem to sacrifice to a certain degree edge.

Summary of the invention

The objective of the invention is at the deficiencies in the prior art, propose a kind of with wavelet transformation and little Qu Bianhuan use in conjunction in the new method of image denoising.It can be more comprehensive wavelet transformation and the little Qu Bianhuan advantage when handling image flat site and fringe region respectively, thereby more ideally solve the collision problem between noise remove and edge keep in the denoising process, further improve the quality of denoising image.

For realizing such purpose, the present invention is based on Fuzzy Calculation and image fusion technology, on the basis of adaptive combined method, the image de-noising method of small echo and small curve fuzzy self-adapting associating has been proposed.Different and adaptive combined method is judged as smooth or fringe region piece with imposing uniformity without examining individual cases, the fuzzy self-adaption combination method has been constructed the flatness membership function of sub-piece in order to the marginal information content in the sub-piece of fuzzy expression, and respectively adopts the result of DWT method and DCT method denoising to carry out fusion treatment as weight coefficient to each sub-piece with this membership function.Fuzzy self-adaption combination method proposed by the invention comprises piecemeal, calculates the flatness membership function value of sub-piece, and the fusant piece adopts the result of DWT method and the denoising of DCT method and merges four steps of piece.

1. piecemeal

To add the sub-piece B that the image I of making an uproar is divided into one group of b * b _k, and row, the row adjacent sub-blocks has the overlapping of b/2 * b pixel.

2. calculate the flatness membership function value of sub-piece

At first calculate the flatness index of each sub-piece, it is defined as:

r _k＝V _k/σ ²

V wherein _kBe B _kMiddle b ²The standard deviation of individual grey scale pixel value, σ is the estimated value of I noise criteria difference.By r _kObtain B _kThe flatness membership function mui _k, it is about r _kThe membership function that half mountain range shape distributes falls:

${\mathrm{\&mu;}}_k=\left\{\begin{array}{cc}1& 0<r_k\&le;{\mathrm{\&sigma;}}_1\\ \frac{1}{2}-\frac{1}{2}\sin \frac{\mathrm{\&pi;}}{{\mathrm{\&sigma;}}_2-{\mathrm{\&sigma;}}_1}(r_k-\frac{{\mathrm{\&sigma;}}_2+{\mathrm{\&sigma;}}_1}{2})& {\mathrm{\&sigma;}}_1<r_k\&le;{\mathrm{\&sigma;}}_2\\ 0& r_k\&GreaterEqual;{\mathrm{\&sigma;}}_2\end{array}\right.$

σ wherein ₁And σ ₂Interval be [1,2].

3. the fusant piece adopts the result of DWT method and the denoising of DCT method.

Respectively to the I noise reduction, and obtain corresponding noise reduction result with DWT method and DCT method

With

For any B _k, with

With

The sub-piece of correspondence position Fused data as the result who adopts fuzzy self-adaption combination method noise reduction The interior gray value of pixel arbitrarily

Can be by fusion rule:

${\tilde{B}}_k[i,j]={\mathrm{\&mu;}}_k{\tilde{B}}_{k1}[i,j]+(1-{\mathrm{\&mu;}}_k){\tilde{B}}_{k2}[i,j]$

Calculate, wherein

Representative respectively The gray value of correspondence position pixel.The edge that comprises in the sub-piece is few more, and the flatness membership function value of sub-piece correspondence is more near 1, and then proportion will be high more in fusion results for the denoising result of DWT method; Otherwise it is abundant more to comprise the edge in the sub-piece, and the denoising result of DCT method proportion in fusion results is just high more.

4. merging piece

According to inciting somebody to action with the step of piecemeal contrary

Be incorporated into former figure size.

Beneficial effect of the present invention is: combine both respectively in the advantage of handling image flat site and fringe region by the fusion to the denoising result adaptivity of DWT method and DCT method, can realize better denoising quality than the DWT method and the DCT method of independent use; Mode by the obfuscation data fusion has replaced the mandatory smoothing processing step in the adaptive combined method, therefore when solving the blocking effect problem more up hill and dale, kept the more images marginal information, thereby realized better denoising quality than adaptive combined method than adaptive combined method.

Description of drawings

Fig. 1 is the FB(flow block) of the image de-noising method of small echo of the present invention and small curve fuzzy self-adapting associating.

Fig. 2 is the flatness membership function mui _k(r _k) distribution map.

Fig. 3 adds make an uproar Lena image and its denoising result in the embodiment of the invention.

Embodiment

Concrete implementation step of the present invention is as follows:

1. piecemeal

No din-light to 256 * 256 is learned image Lena, and to add average be 0, and to be 0.02 white Gaussian noise (white Gaussian noise is the most frequently used noise model) add the image I and to its piecemeal of making an uproar with generation to variance, and block size b is taken as 16 * 16.

2. calculate the flatness membership function value of sub-piece

σ ₁And σ ₂ Difference value 1 and 1.5.

3. the fusant piece adopts the result of DWT method and the denoising of DCT method

The realization of DWT method selects wavelet function coif2 that I is carried out three layers of decomposition, adopts the soft-threshold method to handle the DWT coefficient; In the realization of DCT method, the realization of discrete little Qu Bianhuan is undertaken by image being divided into three straton bands, and minimum block size is taken as 16, utilizes the soft-threshold method to handle the DCT coefficient.

4. merging piece

To handle the sub-piece reformation in back and be incorporated into 256 * 256 sizes.

As shown in Figure 3, wherein (1), (2), (3), (4), (5), (6) are followed successively by original Lena image, add to make an uproar the Lena image and adopt the DWT method respectively to adding the Lena that makes an uproar, DCT method, the result of adaptive combined method and the denoising of fuzzy self-adaption combination method.Contrast directly perceived as can be known, the denoising result of adaptive combined method and fuzzy self-adaption combination method obviously more approaches original Lena image, and wherein the denoising result of fuzzy self-adaption combination method is at the hair that keeps image border details such as Lena, aspects such as scrambled eggs obviously are better than adaptive combined method, so visual effect is best.

Simultaneously, we adopt the universal standard---the objective measurement denoising of Y-PSNR (PSNR) quality.The PSNR value of denoising result is big more, and its approaching more desirable denoising result is described, corresponding denoising method is effective more.Table 1 is that variance is 0.01,0.02,0.03 to having added average 0 respectively, and the Lena image of 0.05,0.07 white Gaussian noise and its adopt the DWT method respectively, DCT method, the PSNR value of adaptive combined method and fuzzy self-adaption combination method denoising result.Vertically contrast as can be known, the PSNR of the corresponding denoising result of fuzzy self-adaption combination method generally is higher than the respective value of other three kinds of methods, this has proved that fuzzy self-adaption combination method of the present invention can be than the DWT method of independent use, and DCT method and adaptive combined method are more effectively removed picture noise.

Noise variance	Add the image of making an uproar	The DWT method	The DCT method	Adaptive combined method	The fuzzy self-adaption combination method
						0.01	20.07	25.68	27.39	27.14	28.06
0.02	17.18	24.48	25.42	26.01	26.49
						0.03	15.53	23.87	24.31	25.35	25.65
0.05	13.65	23.02	22.67	24.00	24.40
						0.07	12.46	22.40	21.59	23.16	23.47

Table 1. adds the PSNR value of make an uproar Lena and its denoising result

Claims (4)

1. the image de-noising method of small echo and small curve fuzzy self-adapting associating, it is characterized by constructed sub-piece the flatness membership function in order to the marginal information content in the sub-piece of fuzzy expression, and adopt the result of wavelet transformation and little Qu Bianhuan denoising to carry out data fusion as weight coefficient respectively to each sub-piece with this membership function.

2. the flatness membership function described in the claim 1 is the half mountain range shape distribution function that falls about flatness index, and its expression formula is:

${\mathrm{\&mu;}}_k=\left\{\begin{array}{cc}1& 0<r_k\&le;{\mathrm{\&sigma;}}_1\\ \frac{1}{2}-\frac{1}{2}\sin \frac{\mathrm{\&pi;}}{{\mathrm{\&sigma;}}_2-{\mathrm{\&sigma;}}_1}(r_k-\frac{{\mathrm{\&sigma;}}_2+{\mathrm{\&sigma;}}_1}{2})& {\mathrm{\&sigma;}}_1<r_k{\&le;\mathrm{\&sigma;}}_2\\ 0& r_k\&GreaterEqual;{\mathrm{\&sigma;}}_2\end{array}\right.$

μ wherein _k, r _kBe respectively sub-piece B _kFlatness membership function and flatness index, σ ₁And σ ₂Interval be [1,2].

3. the rule that adopts the result of wavelet transformation and little Qu Bianhuan denoising to carry out data fusion respectively to each sub-piece described in the claim 1 is:

${\tilde{B}}_k[i,j]={\mathrm{\&mu;}}_k{\tilde{B}}_{k1}[i,j]+(1-{\mathrm{\&mu;}}_k){\tilde{B}}_{k2}[i,j]$

Wherein

Be respectively sub-piece B _kAdopt the result of wavelet transformation and little Qu Bianhuan denoising, μ _kBe B _kThe flatness membership function.

4. the flatness index r of the sub-piece described in the claim 2 _kComputing formula be:

r _k＝V _k/σ ²

V wherein _kBe sub-piece B _kThe standard deviation of middle grey scale pixel value, σ is the estimated value that adds the picture noise standard deviation of making an uproar.

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