In the process of denoising color images, it is very important to enhance the edge and texture information of the images. Image quality can usually be improved by eliminating noise and enhancing contrast. Based on the adaptive wavelet threshold shrinkage algorithm and considering structural characteristics on the basis of color image denoising, this paper describes a method that further enhances the edge and texture details of the image using guided filtering. The use of guided filtering allows edge details that cannot be discriminated in grayscale images to be preserved. The noisy image is decomposed into lowfrequency and highfrequency subbands using discrete wavelets, and the contraction function of threshold shrinkage is selected according to the energy in the vicinity of the wavelet coefficients. Finally, the edge and texture information of the denoised color image are enhanced by guided filtering. When the guiding image is the original noiseless image itself, the guided filter can be used as a smoothing operator for preserving edges, resulting in a better effect than bilateral filtering. The proposed method is compared with the adaptive wavelet threshold shrinkage denoising algorithm and the bilateral filtering algorithm. Experimental results show that the proposed method achieves superior color image denoising compared to these conventional techniques.
During their acquisition and transmission, images are adversely affected by noise. Color images contain better visual effects than gray image in terms of visual perception, and the edge information of color images is more abundant than in gray images. Ideally, when removing the additive noise from an image, as many of the important features as possible should be retained. The denoising of color images often results in the loss of some edge and texture information, making the image blurred and creating a poor visual effect.
Denoising methods of color image commonly, Wiener filter and Gaussian filter denoising, have edge blurred situation. Bilateral filtering [
Wavelet threshold denoising [
In recent years, many algorithms have improved and studied the wavelet threshold denoising. Like, Bhandari et al. [
In the process of color image denoising, we compared the proposed method with the algorithms mentioned above (bilateral filter, Wiener filter, Gaussian filter, and wavelet threshold methods). Proposed method achieves superior color image denoising to these conventional algorithms. The reason is that classic algorithms could suppress the Gaussian noise effectively, but, at the same time, these methods fail to maintain the quality of denoised color images (like, texture) and may blur edges in the image. To address these short comings, this paper proposes a method based on image structure using adaptive wavelet threshold and guided filter to maintain edges when denoising. It makes edges continuous and the color of image more brightly. Because guided filter using a local linear model to enhance the image, the edge details remain. In particular, the details in color image, like texture, are more abundant and saturation is more greater.
On this basis, this paper presents a new color image denoising method based on the adaptive wavelet threshold shrinkage algorithm combined with image structurebased guided filtering [
The rest of the paper is organized as follows. Section
Numerous works have been proposed for image denoising. In this part, we review previous and related work about wavelet threshold algorithms and guided filter.
Wavelet threshold denoising is done by Donoho in 1994, which is based on thresholding the discrete wavelet transform (DWT) of the signal. Hard threshold and soft threshold are traditional threshold algorithm. Donoho [
The hard threshold function is expressed in
Normally, hard threshold function can preserve the wavelet coefficients well generated by the useful information from images, but it is discontinuous at
An appropriate threshold
Adaptive wavelet threshold method first assigns zeroes when the wavelet coefficients are smaller than the given threshold. As the threshold increases, the number of coefficients below the threshold will increase rapidly. When the number of nonzero coefficients reaches a certain value, the threshold is further enlarged and the number of nonzero values slowly decreases; this method can remove most of the noise and improve the compression efficiency. Nasri and Nezamabadipour [
The guided filter is based on a dual integral image architecture VLSI [
Guided filter of image is a linear transformable filtering process, where the guidance image
A local linear model (
In this paper, we describe an adaptive wavelet transform method to remove noise from a color image and use the inverse discrete wavelet transform to obtain the denoised image. The guided filter is then applied for edge and texture recovery and enhancement, producing a better color image effect.
The framework of proposed method contains two main stages (Figure
Illustration of the proposed method. It contains two main parts. Left part is denoising by adaptive wavelet threshold algorithm to obtain denoise image
In the ideal case, the wavelet threshold shrinkage algorithm subtracts Gaussian noise from the image, and its denoising effect is obvious. Natural image denoising using the wavelet threshold is very effective because it can capture the energy of the converted images.
Proposed denoising algorithm has the following steps in detail:
Transform the noisy image into the frequency domain using DWT.
Apply the adaptive wavelet threshold shrinkage algorithm to the local window on each subband and then use inverse DWT to obtain preliminary denoising image
Apply guided filter on image
Enhance
The discrete wavelet transform (DWT) applied to image processing has two main components: decomposition and reconstruction. We use DWT to decompose the noisy image into a sequence of images of different spatial resolutions. Twodimensional images can be decomposed in twodegree directions, resulting in different frequency bands: LL (LowFrequency), LH (Horizontal HighFrequency), HL (Vertical HighFrequency), and HH (Diagonal HighFrequency).
In Figure
Twolevel decomposition of the image. Obtaining LowFrequency image (LL) from the noise image and decomposing it resulting in subbands LL2, HL2, LH2, and HH2. The adaptive wavelet shrink algorithm is applied to each subband to denoise the image.
After the twolevel wavelet decomposition of the image (Figure
The structure information of the image can be obtained by calculating the energy of the local area in the wavelet domain. The smoother the image, the lower the energy. A threshold range is determined based on the local energy calculated by the wavelet decomposition, and a different function is used within the corresponding threshold. The specific algorithm takes the average of the square of each pixel value in the local window to calculate the energy of the center pixel of the window. The appropriate shrinkage factor
In practice, we select the local window
This denoising algorithm uses the DWT to calculate the energy near the wavelet coefficients and then applies the adaptive wavelet threshold shrink function to denoise the image. In the experiments, we added Gaussian noise with variances of
Guided filtering is a spatial enhancement technique for the spatial domain, and the filtered output is a linear transformation of the localized image. The filtering algorithm uses a guiding image to process the edges of the noisy image. The guiding image can be the image itself. At this time, their structures are the same; that is, the edges of the original image are the same as the edges of the guiding image. The output pixel values take into account the statistics of the local spatial neighborhood in the guided image. Hence, using guided filtering, the output image is more structured. This can be used for image dehazing and so on. The guided filter adopts an exact linear algorithm. The algorithm is efficient and fast and is considered to be one of the fastest edgepreserving filters.
For both grayscale and color images, the guided filtering algorithm has
Assume that the input image is
Illustration of (
Therefore, the guide filter algorithm proceeds as follows. Traverse the entire image via each local window, implementing the following calculation, where
When
When the guided filter is applied independently to the three color channels of the color image, (
Because the local linear model is more effective in the color space, the edges of gray images cannot be identified but through the color image of the guided filter it can be wellpreserved. Thus, the image edges have a significant effect.
For images with more texture (i.e., Image 5), the above denoising method may cause some regions to appear too smooth. Therefore, it is necessary to further enhance the image texture detail. Using (
We conducted a series of experiments using MATLAB R2015b and images in Figure
Test image: Images 1–12 (from left to right, top to bottom).
Image 1: comparison of various experimental results under noise variance
Bilateral filtering
Adaptive wavelet
Nonlocal means
BM3D
Proposed method
Image 1: comparison of various experimental results under noise variance
Bilateral filtering
Adaptive wavelet
Nonlocal means
BM3D
Proposed method
Image 5: comparison of various experimental results under noise variance
Bilateral filtering
Adaptive wavelet
Nonlocal means
BM3D
Proposed method
Image 5: comparison of various experimental results under noise variance
Bilateral filtering
Adaptive wavelet
Nonlocal means
BM3D
Proposed method
Image 9: comparison of various experimental results under noise variance
Bilateral filtering
Adaptive wavelet
Nonlocal means
BM3D
Proposed method
Image 9: comparison of various experimental results under noise variance
Bilateral filtering
Adaptive wavelet
Nonlocal means
BM3D
Proposed method
Image 10: comparison of various experimental results under noise variance
Bilateral filtering
Adaptive wavelet
Nonlocal means
BM3D
Proposed method
Image 10: comparison of various experimental results under noise variance
Bilateral filtering
Adaptive wavelet
Nonlocal means
BM3D
Proposed method
The guided filter was used to denoise the image
The peak signaltonoise ratio
PSNR of the proposed method, bilateral filtering, and adaptive wavelet.
Noise variance  0.01  0.03  0.01  0.03  0.01  0.03 

Image 1 ( 
Image 2 ( 
Image 3 ( 

Adaptive wavelet  26.7048  25.4507  28.0801  26.4821  27.7967  26.1699 
Bilateral filtering  22.5751  22.0167  23.1551  22.6118  22.7560  22.1802 
Nonlocal means  29.9765  27.4871  30.1415  27.6777  30.1910  27.6823 
BM3D  28.9235  26.9276  30.4215  27.8901  30.9457  28.0957 
Proposed method 






Image 4 ( 
Image 5 ( 
Image 6 ( 

Adaptive wavelet  25.2375  24.2724  23.4663  22.7332  25.6576  24.5766 
Bilateral filtering  22.6074  21.9415  22.1076  21.5494  22.3016  21.7254 
Nonlocal means  26.6512  25.3287  25.3588  24.3120  27.8813  26.2105 
BM3D  25.5157  24.4968  24.0394  23.2556  28.0621  26.3334 
Proposed method 






Image 7 ( 
Image 8 ( 
Image 9 ( 

Adaptive wavelet  27.5706  25.9130  29.0039  26.9908  21.4746  20.8466 
Bilateral filtering  23.2116  22.4080  23.1373  22.4268  21.4834  21.0023 
Nonlocal means  29.4155  27.0736  31.3181  28.2534  23.7273  23.0137 
BM3D  29.1443  26.9120  32.0590  28.6197  21.7645  21.2712 
Proposed method 






Image 10 ( 
Image 11 ( 
Image 12 ( 

Adaptive wavelet  29.4247  27.5268  26.7443  25.4201  15.9075  16.9781 
Bilateral filtering  23.6728  23.0581  22.2984  21.7973  22.7751  22.6673 
Nonlocal means  30.3106  27.9794  28.7439  26.6227  17.4105  17.2673 
BM3D  30.8146  28.3780  31.8744  28.4922  31.0366  30.1990 
Proposed method 






The
Wells [
Image 1: edge comparison of various experimental results under noise variance
Image 1 edge
Bilateral filtering
Adaptive wavelet
Nonlocal means
BM3D
Proposed method
Image 5: edge comparison of various experimental results under noise variance
Image 5 edge
Bilateral filtering
Adaptive wavelet
Nonlocal means
BM3D
Proposed method
Pratt’s figure of merit.
From a subjective point of view, we find that not only can the proposed method preserve edge better, it also reduces noise well when compared with the other four methods. From Figures
To objectively evaluate the results, we use the Pratt’s figure of merit and PSNR for image quality evaluation. Pratt’s figure of merit results are listed in Figure
From the data in Table
In this paper, a new denoising method based on the adaptive wavelet threshold denoising algorithm and edgeguided filtering has been proposed. The image denoising is performed according to the local structure of the image. In comparative experiments against bilateral filtering, the adaptive wavelet denoising method, nonlocal means algorithm, and BM3D algorithm, the proposed method exhibited the best denoising and edge preservation performance. The proposed approach removes Gaussian noise in the frequency domain and then uses linear guided filtering to further enhance the image recovery, resulting in better denoising and edge effects. As color images display more detailed textures, this filtering overcomes the gradient inversion effect in the edge regions. As the linear model (see (
The authors declare that there are no conflicts of interest regarding the publication of this paper.
This work was supported by the National Natural Science Foundation of China (nos. 61370138, 61572077, and U1301251) and the Beijing Municipal Natural Science Foundation (no. 4162027); the Project of Oriented Characteristic Disciplines (no. KYDE40201701); the Project of Construction of Innovative Teams and Teacher Career Development for Universities and Colleges Under Beijing Municipality (no. IDHT20170511).