基于非局部信息的信号与图像处理算法及其应用研究
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摘要
在信号与图像处理领域,对信号或图像进行有效的表示是一项关键且富有挑战性的研究工作。传统的表示方法一般是依据对信号或图像所做的假设,建立某个函数模型或概率模型。然而,信号与图像的复杂多样性使得构建这样的参数模型成为一项非常困难的工作。通常,这种模型的构建需要大量的先验知识,生成的模型易受假设条件的限制,并且一般只适用于某些特定类型的信号或图像。
当人们还在努力寻求一种通用的参数模型表示方法的时候,海量数据的处理需求以及计算机计算性能的提高催生了一类新的信号及图像分析与处理方法—数据驱动(data driven)的方法,或者称作基于样例(example based)的方法。与传统的基于参数模型的方法不同,数据驱动的方法根据数据本身提供的信息对数据进行表示,适用于处理那些过于复杂而难以准确建模的信号。
图像中的每一个像素点都不是孤立存在的,而是与其邻域内的像素一起构成图像中的几何结构。以像素点为中心的窗口邻域,或者称为图像块,能够很好地体现像素点的结构特征。相应于每一个像素点的图像块的集合可以作为图像的一种过完备表示。同时,图像一般都具有自相似性质,即处于图像中不同位置处的像素点往往表现出很强的相关性,比如自然图像中的长边缘、纹理图像以及具有周期性结构的图像等,都表现出远距离的相关性。基于此,在数据驱动的算法中,可以利用图像自身提供的非局部相似信息来进行有效的图像处理。目前,基于非局部图像块相似性的方法在纹理合成、图像与视频去噪、图像超分辨率分析等诸多领域得到了广泛的应用,并表现出了非常优良的性能。
本论文以信号块或图像块作为信号或图像的表示基元,基于信号与图像的非局部相似性质对纹理合成以及去噪进行了系统深入的理论和应用研究。主要贡献及创新点包括：
(1)提出了一种基于离散小波变换的快速纹理合成方法
针对像素域基于纹理块拼接的合成算法合成效率不高的问题,提出了一种基于离散小波变换的快速纹理合成方法。合成过程只在低频子带内进行,然后利用同一尺度内以及不同尺度间系数之间的父子对应关系,合成相应高频子带内的系数。一方面,由于低频子带图像的尺寸减小,利用较小的图像块就可以表示较大范围的纹理特征。同时,由于参与相似性比较的像素点数目与合成的像素点数目都大为减少,从而大大降低了计算的复杂度。另一方面,小波变换的多分辨率分解特性可以更好地表示纹理图像的特征。在进行相似性比较时,可以利用不同频率子带内的系数,增强相似性比较的准确性,从而有利于生成视觉效果更好的纹理图像。实验结果表明,所提出的多分辨率合成算法对于一大类纹理图像都能够取得很好的合成结果,合成效率较原始的算法有了很大程度的提高。(2)对非局部均值算法的相似性测度进行了改进
在非局部均值算法中,邻域之间的相似性比较仅仅采用平移的邻域形式,不能充分地利用图像提供的自相似性质。针对此问题,将分形理论中的等距对称变换引入到非局部均值去噪算法中,对其相似性测度进行改进,提高了相似性比较的准确性。改进方法能够为图像中的像素找到更多的相似像素点,从而更充分地利用了图像的自相似性质,为非局部均值去噪提供了更好的前提。(3)提出了一种自适应的滤波参数选取方法
非局部均值算法中滤波参数选取的优劣对滤波性能有着至关重要的影响。原始的算法中对整幅图像采用同一个滤波参数,这必然会出现对图像中的某些像素点产生过度平滑,而对另外一些像素点滤波不充分的问题。并且,当噪声水平超过一定的值之后,很难找到一个全局的滤波参数,使其对图像的各个部分都能很好地去噪。我们注意到,邻域之间的欧氏距离与滤波参数的比值决定权值的大小。对于图像中不同的像素点,邻域之间的欧氏距离一般具有不同的分布。为了得到更好的滤波效果,对于不同的距离分布,选用不同的滤波参数更为合理。基于此想法,根据邻域之间欧氏距离的统计分布特点,提出一种基于图像灰度分布统计特性的滤波参数选取方法。该方法能够根据不同像素的特点自适应地选取滤波参数。对测试图像去噪的实验结果也验证了改进方法的有效性。(4)提出了一种两级的非局部均值去噪方法
非局部均值算法利用邻域内灰度值向量之间的欧氏距离衡量邻域之间的相似性。由于灰度值向量取自含有噪声的图像,因此,欧氏距离的计算势必会受到噪声的影响。特别地,当图像中含有较强的噪声时,直接利用含噪图像的灰度值计算欧氏距离已经不能很好地反映邻域之间的相似性。针对此问题,本论文提出-种两级非局部均值去噪方法。一级去噪时使用较小的滤波参数,在去除一部分噪声的同时,也使得二级去噪时的相似性比较更加准确。实验结果表明,与采用-次滤波相比,采用两级去噪能够更为有效地去除噪声。噪声强度越大,两级非局部均值方法对去噪性能的改善就越明显。
(5)提出一种基于自适应搜索区域的非局部均值去噪方法
非局部均值算法利用图像(子图像)中所有像素的加权平均来对含噪图像的真实灰度值进行估计。由于参与加权平均的某些像素点的灰度值很可能与当前像素点的灰度值之间存在着较大的差异,这些不相关的像素势必会对去噪性能产生负面的影响。局部自适应估计方法中的局部多项式逼近-置信区间交叉技术可以以-种逐点的方式为图像中的每一个像素点自适应地确定一个各向异性的邻域,邻域内的像素点与中心像素点具有相似的性质。因此,将该技术与非局部均值算法相结合,可以在加权平均的过程中去除不相关像素点的影响,从而提高非局部均值算法的去噪性能。
(6)在算法应用方面,提出一种基于非局部相似性与平移不变小波变换相结合的一维信号去噪方法,并将非局部均值算法应用于PET图像去噪
对于一维信号的去噪,首先利用块匹配的方法分组相似的信号块,将相似的信号块组成不同的信号块组。然后,对各个信号块组作平移不变的小波变换处理得到变换系数,再对这些系数作硬阈值收缩降噪。最后,经过小波逆变换得到空域信号。考虑到信号块之间的重叠,提出使用简单平均与加权平均两种方式进行组合来得到最终的去噪结果。实验结果表明,与基于小波变换以及平移不变小波变换的去噪方法相比,本文所提出的方法能够取得更高的信噪比,并且得到的去噪信号更接近于原始信号。此外,将非局部均值算法用于去除PET图像中的泊松噪声。对测试图像以及实际临床PET图像的去噪结果表明,非局部均值算法能够有效地去除PET图像中的噪声,对各部分功能结构具有非常好的保护能力,取得了比中值滤波和维纳滤波更好的结果,为PET图像的去噪提供了一种新的手段。
In signal and image processing field, the most crucial and also the most challenging issue is to find an effective way to represent signals or images. Traditionally, some function models or probability models are usually constructed based on certain assumptions for the signal or image as their representations. However, the complexity and variety of the signal and image make it a very difficult task to construct such a parametric model, which requires much prior knowledge about the signal. And what's more, the model only works well for some specific signals or images under the assumption constraints.
When people are still trying their best to find a more general parametric model to well represent signals, both the requirements for dealing with mass of data and the performance improvement of computers give birth to a new kind of signal and image analysis and processing methods-data driven methods, also known as example-based methods. Different with the traditional model-based methods, this new technology represents a signal based on the information provided by the data itself, and it is very suitable and effective for dealing with those data which are difficult to model due to their complexity.
Every pixel in an image is not alone; it builds up geometric structures together with its surrounding neighbors. A square window centered at a pixel, also called a patch, can well reflect its structure property. And all the patches corresponding to each pixel can constitute a set or a space, which can act as an overcomplete representation of an image. Meanwhile, self-similarity is an essential property of an image, i.e., the pixels at different locations resemble with each other. For example, the pixels along a long edge, or more specifically, the pixels in the texture images or images with periodic patterns all show strong long-range correlations. In example-based algorithms, the non-local similarity information provided by an image itself can be made use of to tackle some image processing problems. Currently, the algorithms based on non-local patch similarity have found their applications in many fields, such as texture synthesis, image and video denoising, image super-resolution etc., and have shown their superiority.
In this work, with signal blocks and image patches as the basic representations for a signal or an image, the algorithms and their applications based on non-local similarity information for texture synthesis and signal and image denoising are studied systematically. The main contributions of this thesis include:
(1) A fast texture synthesis algorithm based on DWT is proposed.
A fast texture synthesis algorithm based on DWT is proposed to improve the efficiency of the pixel-domain image quilting algorithm. The quilting of the coefficients is carried out only in the approximation sub-band, and then the coefficients in all detail sub-bands are synthesized simultaneously based on the parent-child relationship of the coefficients within the same scale and across different scales. On one hand, due to the reduced size of the low resolution image, larger texture pattern characteristics can be captured just by smaller sized patches; in addition, the number of pixels both for similarity comparison and to be synthesized become smaller, so the computational complexity is greatly reduced. On the other hand, the texture characteristics can be better represented in the wavelet domain, the coefficients in different sub-bands can give their contributions to the similarity comparison, which can help to generate visually more appealing textures. The synthesis results show that the proposed approach can synthesize a wide range of textures, and it is more efficient than the original one.
(2) A modified similarity metric for the non-local means algorithm is proposed.
In the original non-local means algorithm, only translational neighborhood patterns are used in similarity comparison, which do not fully exploit the symmetric characteristics that exist in many images. To address this problem, the isometry transformations in fractal theory are introduced to modify its similarity metric, so that the self-similarity property of images can be better made use of. In this way, the similarity comparisons become more accurate and more candidate pixels can be picked out for averaging a pixel to be restored, and the larger number of candidate pixels can provide a better precondition for non-local means denoising.
(3) An adaptive filtering parameter selection method is put forward.
The filtering parameter plays an important role in the non-local means algorithm, which takes a fixed value empirically for the whole image in the original scheme. Generally speaking, different pixels own different properties, the fixed global parameter will result in over-smoothing some pixels while not being able to filter others sufficiently. And what's more, when the noise level exceeds a certain value, it is no longer possible to choose a global parameter such that the noise is removed everywhere without destroying structures somewhere else in the image. It is noted that the ratio of the Euclidean distance between neighborhoods and the filtering parameter determines the weight. For different pixels in an image, the Euclidean distances between neighborhoods in the search region satisfy different distributions, so better denoising results should be obtained by choosing different filtering parameters for different pixels. Motivated by this idea, an adaptive filtering parameter selection method based on image intensity statistics is proposed, which can determine the filtering parameter adaptively according to individual pixel property. Experiment results verify the effectiveness of the proposed method.
(4) A two-stage non-local means filtering strategy is proposed.
The neighborhood similarity is measured by Euclidean distances between neighborhood gray value vectors in the non-local means algorithm. The calculation of the Euclidean distance will be affected by noise, especially when the noise level is too high, the Euclidean distances obtained on noisy images can no longer well reflect the neighborhood similarity. To solve this problem, a two-stage non-local means filtering strategy is proposed. With some noise removed with a smaller filtering parameter in the first stage, the similarity can be obtained more accurately and better adapted to the non-local means algorithm in the second filtering stage. Experiment results demonstrate that compared with the original algorithm, more noise can be removed by the proposed two-stage filtering approach, and it performs even better under higher noise level cases.
(5) An adaptive search based non-local means filtering scheme is proposed.
The non-local means algorithm uses the weighted average of all pixels in an image to recover a noise-free pixel. However, if the pixel values used for average do not lie in the same gray levels as the one to be restored, they will make negative contributions to the denoising performance. As a locally adaptive estimation method, the Local Polynomial Approximation-Intersection of Confidence Interval technique can provide anisotropic neighborhoods adapting to image features for pixels in an image in a point-wise manner, within which the image is homogeneous. We combine the non-local means algorithm with this locally adaptive anisotropic estimation method to develop a new denoising approach. It can exclude the pixels whose gray values are different from the one to be restored in the non-local averaging process, and this will alleviate the effect of non-similar pixels and thus enhance the denoising performance.
(6) As applications, a signal denoising method combining non-local signal similarities with translation invariant wavelet transform is developed; and also the non-local means algorithm is applied to suppress the poisson noise in PET images.
For 1-D signal denoising, signal blocks with similar structures are assembled together to build up groups with strong correlations; and then the translation invariant wavelet transform is applied on these groups to produce, in an enhanced sparsity manner, the transformed coefficients; these coefficients are then hard-thresholded and inverse transformed back into their denoised versions. Considering the overlapping between blocks, two aggregation methods, i.e. simple averaging and weighted averaging are proposed to fuse the different estimates together to get the final estimate. Experimental results illustrate that the proposed method can obtain superior denoising performance compared with the wavelet and translation invariant wavelet based methods. In addition, the non-local means algorithm is applied to remove the poisson noise in PET images. Experimental results for both the test image and real clinical PET images show that the non-local means can remove the noise in PET images efficiently with functional structures well preserved, and achieves better denoising results than median filtering and wiener filtering methods. Therefore, the non-local means algorithm can act as an alternative and potential powerful method for PET image denoising.
当人们还在努力寻求一种通用的参数模型表示方法的时候,海量数据的处理需求以及计算机计算性能的提高催生了一类新的信号及图像分析与处理方法—数据驱动(data driven)的方法,或者称作基于样例(example based)的方法。与传统的基于参数模型的方法不同,数据驱动的方法根据数据本身提供的信息对数据进行表示,适用于处理那些过于复杂而难以准确建模的信号。
图像中的每一个像素点都不是孤立存在的,而是与其邻域内的像素一起构成图像中的几何结构。以像素点为中心的窗口邻域,或者称为图像块,能够很好地体现像素点的结构特征。相应于每一个像素点的图像块的集合可以作为图像的一种过完备表示。同时,图像一般都具有自相似性质,即处于图像中不同位置处的像素点往往表现出很强的相关性,比如自然图像中的长边缘、纹理图像以及具有周期性结构的图像等,都表现出远距离的相关性。基于此,在数据驱动的算法中,可以利用图像自身提供的非局部相似信息来进行有效的图像处理。目前,基于非局部图像块相似性的方法在纹理合成、图像与视频去噪、图像超分辨率分析等诸多领域得到了广泛的应用,并表现出了非常优良的性能。
本论文以信号块或图像块作为信号或图像的表示基元,基于信号与图像的非局部相似性质对纹理合成以及去噪进行了系统深入的理论和应用研究。主要贡献及创新点包括：
(1)提出了一种基于离散小波变换的快速纹理合成方法
针对像素域基于纹理块拼接的合成算法合成效率不高的问题,提出了一种基于离散小波变换的快速纹理合成方法。合成过程只在低频子带内进行,然后利用同一尺度内以及不同尺度间系数之间的父子对应关系,合成相应高频子带内的系数。一方面,由于低频子带图像的尺寸减小,利用较小的图像块就可以表示较大范围的纹理特征。同时,由于参与相似性比较的像素点数目与合成的像素点数目都大为减少,从而大大降低了计算的复杂度。另一方面,小波变换的多分辨率分解特性可以更好地表示纹理图像的特征。在进行相似性比较时,可以利用不同频率子带内的系数,增强相似性比较的准确性,从而有利于生成视觉效果更好的纹理图像。实验结果表明,所提出的多分辨率合成算法对于一大类纹理图像都能够取得很好的合成结果,合成效率较原始的算法有了很大程度的提高。(2)对非局部均值算法的相似性测度进行了改进
在非局部均值算法中,邻域之间的相似性比较仅仅采用平移的邻域形式,不能充分地利用图像提供的自相似性质。针对此问题,将分形理论中的等距对称变换引入到非局部均值去噪算法中,对其相似性测度进行改进,提高了相似性比较的准确性。改进方法能够为图像中的像素找到更多的相似像素点,从而更充分地利用了图像的自相似性质,为非局部均值去噪提供了更好的前提。(3)提出了一种自适应的滤波参数选取方法
非局部均值算法中滤波参数选取的优劣对滤波性能有着至关重要的影响。原始的算法中对整幅图像采用同一个滤波参数,这必然会出现对图像中的某些像素点产生过度平滑,而对另外一些像素点滤波不充分的问题。并且,当噪声水平超过一定的值之后,很难找到一个全局的滤波参数,使其对图像的各个部分都能很好地去噪。我们注意到,邻域之间的欧氏距离与滤波参数的比值决定权值的大小。对于图像中不同的像素点,邻域之间的欧氏距离一般具有不同的分布。为了得到更好的滤波效果,对于不同的距离分布,选用不同的滤波参数更为合理。基于此想法,根据邻域之间欧氏距离的统计分布特点,提出一种基于图像灰度分布统计特性的滤波参数选取方法。该方法能够根据不同像素的特点自适应地选取滤波参数。对测试图像去噪的实验结果也验证了改进方法的有效性。(4)提出了一种两级的非局部均值去噪方法
非局部均值算法利用邻域内灰度值向量之间的欧氏距离衡量邻域之间的相似性。由于灰度值向量取自含有噪声的图像,因此,欧氏距离的计算势必会受到噪声的影响。特别地,当图像中含有较强的噪声时,直接利用含噪图像的灰度值计算欧氏距离已经不能很好地反映邻域之间的相似性。针对此问题,本论文提出-种两级非局部均值去噪方法。一级去噪时使用较小的滤波参数,在去除一部分噪声的同时,也使得二级去噪时的相似性比较更加准确。实验结果表明,与采用-次滤波相比,采用两级去噪能够更为有效地去除噪声。噪声强度越大,两级非局部均值方法对去噪性能的改善就越明显。
(5)提出一种基于自适应搜索区域的非局部均值去噪方法
非局部均值算法利用图像(子图像)中所有像素的加权平均来对含噪图像的真实灰度值进行估计。由于参与加权平均的某些像素点的灰度值很可能与当前像素点的灰度值之间存在着较大的差异,这些不相关的像素势必会对去噪性能产生负面的影响。局部自适应估计方法中的局部多项式逼近-置信区间交叉技术可以以-种逐点的方式为图像中的每一个像素点自适应地确定一个各向异性的邻域,邻域内的像素点与中心像素点具有相似的性质。因此,将该技术与非局部均值算法相结合,可以在加权平均的过程中去除不相关像素点的影响,从而提高非局部均值算法的去噪性能。
(6)在算法应用方面,提出一种基于非局部相似性与平移不变小波变换相结合的一维信号去噪方法,并将非局部均值算法应用于PET图像去噪
对于一维信号的去噪,首先利用块匹配的方法分组相似的信号块,将相似的信号块组成不同的信号块组。然后,对各个信号块组作平移不变的小波变换处理得到变换系数,再对这些系数作硬阈值收缩降噪。最后,经过小波逆变换得到空域信号。考虑到信号块之间的重叠,提出使用简单平均与加权平均两种方式进行组合来得到最终的去噪结果。实验结果表明,与基于小波变换以及平移不变小波变换的去噪方法相比,本文所提出的方法能够取得更高的信噪比,并且得到的去噪信号更接近于原始信号。此外,将非局部均值算法用于去除PET图像中的泊松噪声。对测试图像以及实际临床PET图像的去噪结果表明,非局部均值算法能够有效地去除PET图像中的噪声,对各部分功能结构具有非常好的保护能力,取得了比中值滤波和维纳滤波更好的结果,为PET图像的去噪提供了一种新的手段。
In signal and image processing field, the most crucial and also the most challenging issue is to find an effective way to represent signals or images. Traditionally, some function models or probability models are usually constructed based on certain assumptions for the signal or image as their representations. However, the complexity and variety of the signal and image make it a very difficult task to construct such a parametric model, which requires much prior knowledge about the signal. And what's more, the model only works well for some specific signals or images under the assumption constraints.
When people are still trying their best to find a more general parametric model to well represent signals, both the requirements for dealing with mass of data and the performance improvement of computers give birth to a new kind of signal and image analysis and processing methods-data driven methods, also known as example-based methods. Different with the traditional model-based methods, this new technology represents a signal based on the information provided by the data itself, and it is very suitable and effective for dealing with those data which are difficult to model due to their complexity.
Every pixel in an image is not alone; it builds up geometric structures together with its surrounding neighbors. A square window centered at a pixel, also called a patch, can well reflect its structure property. And all the patches corresponding to each pixel can constitute a set or a space, which can act as an overcomplete representation of an image. Meanwhile, self-similarity is an essential property of an image, i.e., the pixels at different locations resemble with each other. For example, the pixels along a long edge, or more specifically, the pixels in the texture images or images with periodic patterns all show strong long-range correlations. In example-based algorithms, the non-local similarity information provided by an image itself can be made use of to tackle some image processing problems. Currently, the algorithms based on non-local patch similarity have found their applications in many fields, such as texture synthesis, image and video denoising, image super-resolution etc., and have shown their superiority.
In this work, with signal blocks and image patches as the basic representations for a signal or an image, the algorithms and their applications based on non-local similarity information for texture synthesis and signal and image denoising are studied systematically. The main contributions of this thesis include:
(1) A fast texture synthesis algorithm based on DWT is proposed.
A fast texture synthesis algorithm based on DWT is proposed to improve the efficiency of the pixel-domain image quilting algorithm. The quilting of the coefficients is carried out only in the approximation sub-band, and then the coefficients in all detail sub-bands are synthesized simultaneously based on the parent-child relationship of the coefficients within the same scale and across different scales. On one hand, due to the reduced size of the low resolution image, larger texture pattern characteristics can be captured just by smaller sized patches; in addition, the number of pixels both for similarity comparison and to be synthesized become smaller, so the computational complexity is greatly reduced. On the other hand, the texture characteristics can be better represented in the wavelet domain, the coefficients in different sub-bands can give their contributions to the similarity comparison, which can help to generate visually more appealing textures. The synthesis results show that the proposed approach can synthesize a wide range of textures, and it is more efficient than the original one.
(2) A modified similarity metric for the non-local means algorithm is proposed.
In the original non-local means algorithm, only translational neighborhood patterns are used in similarity comparison, which do not fully exploit the symmetric characteristics that exist in many images. To address this problem, the isometry transformations in fractal theory are introduced to modify its similarity metric, so that the self-similarity property of images can be better made use of. In this way, the similarity comparisons become more accurate and more candidate pixels can be picked out for averaging a pixel to be restored, and the larger number of candidate pixels can provide a better precondition for non-local means denoising.
(3) An adaptive filtering parameter selection method is put forward.
The filtering parameter plays an important role in the non-local means algorithm, which takes a fixed value empirically for the whole image in the original scheme. Generally speaking, different pixels own different properties, the fixed global parameter will result in over-smoothing some pixels while not being able to filter others sufficiently. And what's more, when the noise level exceeds a certain value, it is no longer possible to choose a global parameter such that the noise is removed everywhere without destroying structures somewhere else in the image. It is noted that the ratio of the Euclidean distance between neighborhoods and the filtering parameter determines the weight. For different pixels in an image, the Euclidean distances between neighborhoods in the search region satisfy different distributions, so better denoising results should be obtained by choosing different filtering parameters for different pixels. Motivated by this idea, an adaptive filtering parameter selection method based on image intensity statistics is proposed, which can determine the filtering parameter adaptively according to individual pixel property. Experiment results verify the effectiveness of the proposed method.
(4) A two-stage non-local means filtering strategy is proposed.
The neighborhood similarity is measured by Euclidean distances between neighborhood gray value vectors in the non-local means algorithm. The calculation of the Euclidean distance will be affected by noise, especially when the noise level is too high, the Euclidean distances obtained on noisy images can no longer well reflect the neighborhood similarity. To solve this problem, a two-stage non-local means filtering strategy is proposed. With some noise removed with a smaller filtering parameter in the first stage, the similarity can be obtained more accurately and better adapted to the non-local means algorithm in the second filtering stage. Experiment results demonstrate that compared with the original algorithm, more noise can be removed by the proposed two-stage filtering approach, and it performs even better under higher noise level cases.
(5) An adaptive search based non-local means filtering scheme is proposed.
The non-local means algorithm uses the weighted average of all pixels in an image to recover a noise-free pixel. However, if the pixel values used for average do not lie in the same gray levels as the one to be restored, they will make negative contributions to the denoising performance. As a locally adaptive estimation method, the Local Polynomial Approximation-Intersection of Confidence Interval technique can provide anisotropic neighborhoods adapting to image features for pixels in an image in a point-wise manner, within which the image is homogeneous. We combine the non-local means algorithm with this locally adaptive anisotropic estimation method to develop a new denoising approach. It can exclude the pixels whose gray values are different from the one to be restored in the non-local averaging process, and this will alleviate the effect of non-similar pixels and thus enhance the denoising performance.
(6) As applications, a signal denoising method combining non-local signal similarities with translation invariant wavelet transform is developed; and also the non-local means algorithm is applied to suppress the poisson noise in PET images.
For 1-D signal denoising, signal blocks with similar structures are assembled together to build up groups with strong correlations; and then the translation invariant wavelet transform is applied on these groups to produce, in an enhanced sparsity manner, the transformed coefficients; these coefficients are then hard-thresholded and inverse transformed back into their denoised versions. Considering the overlapping between blocks, two aggregation methods, i.e. simple averaging and weighted averaging are proposed to fuse the different estimates together to get the final estimate. Experimental results illustrate that the proposed method can obtain superior denoising performance compared with the wavelet and translation invariant wavelet based methods. In addition, the non-local means algorithm is applied to remove the poisson noise in PET images. Experimental results for both the test image and real clinical PET images show that the non-local means can remove the noise in PET images efficiently with functional structures well preserved, and achieves better denoising results than median filtering and wiener filtering methods. Therefore, the non-local means algorithm can act as an alternative and potential powerful method for PET image denoising.
引文
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