基于小波变换的不规则邻域的数字图像去噪算法研究
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摘要
图像去噪是图像处理领域中的重要组成部分,其结果对于后续图像分析具有很大的影响。小波图像去噪方法因其具有低熵性、多分辨率、去相关性等良好特性而得到了广泛应用,其中G.Y.Chen等人提出的NeighShrink去噪方法是一种基于邻域系数估计阈值的小波去噪算法,该算法在保留图像细节方面有一定的优势。不过本文通过分析发现,由于NeighShrink在邻域处理中只选择固定窗口中的系数进行阈值处理,而并不考虑窗口中系数与待阈值系数间的相关性强弱,因而会将某些边缘信息过平滑。而此后出现的对NeighShrink改进的方法,也基本限于对阈值的改进或者对固定滑窗形状的改变,并不能够自适应地选择与待阈值系数相关性强的系数进行处理,从而不能很好地解决问题。
由于邻域的合理选择有助于更好地利用小波系数的层内相关性,从而可以达到减轻Gibbs现象、保护边缘的目的。本文正是针对这一问题,提出了采用邻域选取的思路来解决问题的一系列去噪方法。具体如下:
1.在滑动窗口固定的情况下,提出了邻域相关度的概念,并以此来选取合适的待阈值邻域窗口大小,从而更有效地利用了小波系数的邻域相关性。实验结果表明本文提出的基于相关度分析的自适应邻域小波图像去噪算法较好地利用了图像像素点之间的冗余性,较NeighShrink和自适应阈值去噪方法去噪效果更好。
2.根据图像自身的性质,结合脉冲耦合神经网络(Pulse Coupled Neural Networks,PCNN)模型,将图像的低频子带自适应地分割成不同的邻域,并且将此分割信息按照改进的隐马尔可夫树模型映射到各个高频子带。进一步结合小波层内相关性,对各个不规则邻域加上固定的窗口,选择了几何距离更为接近且在同一不规则邻域内的系数,以完善NeighShrink方法。实验结果表明,本文提出的基于PCNN区域分割的邻域小波图像去噪算法在降低了图像噪声的同时又尽可能地保留了图像的边缘信息,是一种有效的去噪方法。
3.为尽量保护图像的边缘特征,将边缘检测结合到小波图像去噪方法中,提出了一种基于边缘检测的邻域加窗的平稳小波图像去噪算法。本算法利用了平稳小波变换的相位不变性,考虑了小波系数的层内和层间相关性,并通过融合边缘,保护图像的边缘信息。并进一步提取出融合后的边缘信息,以此信息对图像进行分割,并在去噪处理时与NeighShrink算法相结合,以避免阈值处理时边缘两侧数据差异太大,而在邻域处理时对边缘造成模糊的现象。实验结果表明,该算法具有较好的边缘保持效果。
Image denoising is an important part of image processing, it has significant effects on further image analysis. NeighShrink algorithm proposed by G.Y.Chen has great advantages in preserving image details. It estimates the coefficients with the neighborhood around them. However, through the research, it’s found that NeighShrink algorithm just chooses the coefficients in a fixed windows around the thresholded one, so the edge informations will be over-smoothed. Choosing a neighborhood reasonably is helpful to make better use of the wavelet coefficients relativity in the same scale, in this way it’s can be achieved to reduce the Gibbs phenomenon and protect the edge of the images. In this paper, sevral algorithms are proposed to select the reasonable neighborhoods to improve the NeighShrink algorithm.
1. An adaptive neighborhood image denoising algorithm based on relativity analysis in wavelet domain is proposed. It chooses neighborhood window by the mean of correlation coefficent in neighborhood with different size, which follows the neighborhood relativity of wavelet coefficients better. The experiments results show that the image can be denoised well while preserving the edge feature.
2. For NeighShrink method used in the image denoising, a new image de-noising algorithm is proposed to keep image edges more effectively, and it mainly improves the domain of NeighShrink which is fixed. This method decomposes noisy images with stationary wavelet transform to keep phase invariance. Then it segments the low frequency sub-band into many domains adaptively using PCNN model, and mapped this segmentation information to all the high frequency subbands. Then it combinates with wavelet intra-scale relativity, gets various irregular neighborhood with a fixed window, selects the data again. And the edge information is protected during the denoising process.
3. An effective denoising method in edge protecting was proposed to overcome the limitation of image denosing methods now, which combines edge detection with image denoising method in wavelet domain. This algorithm decomposes noisy images using stationary wavelet transform to keep phase invariance. Then it detects the edges of low frequency subband and high frequency ones, and gets the approximate information of the edge of origin image by fusion the results of edge detection. The new neighborhood is gotten by the edge information segmentation. Based on intra-scale relativity and inter-scale relativity of wavelet coefficients,the proposed method performs denoising with the new neighborhood weighed. A better restoration of image is demonstrated in the results of experiments, with detail of images kept as well as image noises decreasing.
由于邻域的合理选择有助于更好地利用小波系数的层内相关性,从而可以达到减轻Gibbs现象、保护边缘的目的。本文正是针对这一问题,提出了采用邻域选取的思路来解决问题的一系列去噪方法。具体如下:
1.在滑动窗口固定的情况下,提出了邻域相关度的概念,并以此来选取合适的待阈值邻域窗口大小,从而更有效地利用了小波系数的邻域相关性。实验结果表明本文提出的基于相关度分析的自适应邻域小波图像去噪算法较好地利用了图像像素点之间的冗余性,较NeighShrink和自适应阈值去噪方法去噪效果更好。
2.根据图像自身的性质,结合脉冲耦合神经网络(Pulse Coupled Neural Networks,PCNN)模型,将图像的低频子带自适应地分割成不同的邻域,并且将此分割信息按照改进的隐马尔可夫树模型映射到各个高频子带。进一步结合小波层内相关性,对各个不规则邻域加上固定的窗口,选择了几何距离更为接近且在同一不规则邻域内的系数,以完善NeighShrink方法。实验结果表明,本文提出的基于PCNN区域分割的邻域小波图像去噪算法在降低了图像噪声的同时又尽可能地保留了图像的边缘信息,是一种有效的去噪方法。
3.为尽量保护图像的边缘特征,将边缘检测结合到小波图像去噪方法中,提出了一种基于边缘检测的邻域加窗的平稳小波图像去噪算法。本算法利用了平稳小波变换的相位不变性,考虑了小波系数的层内和层间相关性,并通过融合边缘,保护图像的边缘信息。并进一步提取出融合后的边缘信息,以此信息对图像进行分割,并在去噪处理时与NeighShrink算法相结合,以避免阈值处理时边缘两侧数据差异太大,而在邻域处理时对边缘造成模糊的现象。实验结果表明,该算法具有较好的边缘保持效果。
Image denoising is an important part of image processing, it has significant effects on further image analysis. NeighShrink algorithm proposed by G.Y.Chen has great advantages in preserving image details. It estimates the coefficients with the neighborhood around them. However, through the research, it’s found that NeighShrink algorithm just chooses the coefficients in a fixed windows around the thresholded one, so the edge informations will be over-smoothed. Choosing a neighborhood reasonably is helpful to make better use of the wavelet coefficients relativity in the same scale, in this way it’s can be achieved to reduce the Gibbs phenomenon and protect the edge of the images. In this paper, sevral algorithms are proposed to select the reasonable neighborhoods to improve the NeighShrink algorithm.
1. An adaptive neighborhood image denoising algorithm based on relativity analysis in wavelet domain is proposed. It chooses neighborhood window by the mean of correlation coefficent in neighborhood with different size, which follows the neighborhood relativity of wavelet coefficients better. The experiments results show that the image can be denoised well while preserving the edge feature.
2. For NeighShrink method used in the image denoising, a new image de-noising algorithm is proposed to keep image edges more effectively, and it mainly improves the domain of NeighShrink which is fixed. This method decomposes noisy images with stationary wavelet transform to keep phase invariance. Then it segments the low frequency sub-band into many domains adaptively using PCNN model, and mapped this segmentation information to all the high frequency subbands. Then it combinates with wavelet intra-scale relativity, gets various irregular neighborhood with a fixed window, selects the data again. And the edge information is protected during the denoising process.
3. An effective denoising method in edge protecting was proposed to overcome the limitation of image denosing methods now, which combines edge detection with image denoising method in wavelet domain. This algorithm decomposes noisy images using stationary wavelet transform to keep phase invariance. Then it detects the edges of low frequency subband and high frequency ones, and gets the approximate information of the edge of origin image by fusion the results of edge detection. The new neighborhood is gotten by the edge information segmentation. Based on intra-scale relativity and inter-scale relativity of wavelet coefficients,the proposed method performs denoising with the new neighborhood weighed. A better restoration of image is demonstrated in the results of experiments, with detail of images kept as well as image noises decreasing.
引文
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