在线客服

咨询热线

基于分组字典与变分模型的图像去噪算法

作者:未知

  摘 要:针对加性高斯噪声去除问题,在现有传统的K均值奇异值分解(K-SVD)字典学习算法的基础上,提出一种将字典学习与变分模型相融合的改进算法。首先,根据图像的几何和光度信息将图像进行聚类分组,再将图像组按照边缘和纹理类别进行分类,根据噪声水平和图像组类别训练一个自适应字典;其次,将通过所学字典得到的稀疏表示先验与图像本身的非局部相似先验进行融合来构建变分模型;最后,通过求解变分模型得到去噪后图像。实验结果表明,与同类去噪算法相比,当噪声比率较高时,所提算法可以解决前期算法准确性较差、纹理丢失较为严重、产生视觉伪影等问题,在视觉效果上要更为理想;同时该算法结构相似性指数有明显提高,峰值信噪比(PSNR)的值更是平均提高了10%以上。
  关键词:自适应字典学习;图像去噪;稀疏表示;变分模型;非局部相似
  中图分类号: TP391.41
  文献标志码:A
  Abstract: Aiming at problem of additive Gauss noise removal, an improved image restoration algorithm based on the existing K-means Singular Value Decomposition (K-SVD) method was proposed by integrating dictionary learning and variational model. Firstly, according to geometric and photometric information, image blocks were clustered into different groups, and these groups were classified into different types according to the texture and edge categories, then an adaptive dictionary was trained according to the types of these groups and the size of the atoms determined by the noise level. Secondly, a variational model was constructed by fusing the sparse representation priori obtained from the dictionary with the non-local similarity priori of the image itself. Finally, the final denoised image was obtained by solving the variational model. The experimental results show that compared with similar denoising algorithms, when the noise ratio is high, the proposed method has better visual effect, solving the problems of poor accuracy, serious texture loss and visual artifacts; the structural similarity index is also significantly improved, and the Peak Signal-to-Noise Ratio (PSNR) is increased by an average of more than 10%.
  Key words: adaptive dictionary learning; image denoising; sparse representation; variational model; nonlocal similarity
  0 引言
  在獲取图像时,由于外部环境、硬件设备缺陷等方面的影响,图像往往会含有不同程度的噪声,在图像的分割、配准、融合等应用中通常又需要清晰、高质量的图像,因此,图像去噪一直是图像处理领域中一个重要的课题。在噪声类型中,加性高斯噪声是最常见的噪声,可以以列向量的形式标识图像的退化模型为Y=X+V。其中,X是清晰图像,Y为受噪声污染的图像,V是均值为0、方差为σ的高斯噪声。去噪就是要设计一个算法从Y中删除噪声V近似得到原图像X。
  目前学术界已有许多有效的噪声去除算法,如基于变换域的方法[1-2]、空间自适应滤波算法[3] 等。在一些前沿算法中,图像的局部相似先验知识被广泛地应用到图像噪声去除领域中。Yin等[4]提出一种广义全变分(Total Variation,TV)模型,可以克服假边缘的产生,在去噪的同时又保持边缘细节,但模型中参数的取值往往造成实验结果过于敏感。Buades等[5]提出一种基于非局部平均的算法,该算法在非局部的邻域内搜索像素块的相似信息,但是当噪声强度较大时会影响相似性的判断。
  为了进一步提升去噪效果,基于字典的稀疏表示算法被应用到图像恢复中[6]。K均值奇异值分解(K-means Singular Value Decomposition,K-SVD)算法[7]是一个经典字典学习算法,它是通过学习给定的一组图像本身来自适应其内容,但该算法只训练一个固定原子尺寸的字典,在图像信息的精确描述方面存在不足。为了提高字典学习的有效性,一些研究者将图像的自相似模型与稀疏表示相结合。Horey等[8]提出一种基于双稀疏(Double Sparsity, DS) 字典的自适应图像压缩算法;Yang等[9]提出了一种稀疏表示的超分辨率算法,将高分辨率图像组成的图像库作为训练样本,因其包含了众多丰富细节的高分辨率图像,可以为字典学习提供较为充足的附加信息,但附加信息的准确性和可靠性得不到保证,所以存在较大的均方误差;Jiang等[10]提出一种加权编码算法,将图像的非局部相似性和稀疏表示结合起来构建一个变分模型,可以保留较多的有效信息,但其用于稀疏表示的字典没有根据图像含有的具体信息进行分类,不能准确地描述图像含有的信息。   为了更好地提升去噪效果,本文在现有字典算法[11-13]的基础上,提出一种将改进的字典学习算法与变分模型相融合的去噪模型。在该算法中,利用图像的光度和几何相似性构建一个特征检测器,利用该检测器搜索某一图像块的相似块;其次,根据特征检测器将图像分为不同的组,根据组所属的类别以及噪声水平,构建具有自适应原子尺寸的字典;最后,利用所学习的字典融合进变分模型进行图像去噪。本文算法充分利用了图像的稀疏表示与非局部相似先验知识,能够更好地保留图像的本真信息,對于图像的后续特征提取、图像匹配等有重要意义。
  4 结语
  针对加性高斯噪声污染图像的去噪问题,本文提出了一种基于改进的自适应原子尺寸字典学习的变分模型去噪算法。该算法充分利用了图像的稀疏表示先验与非局部相似先验,能够很大程度上保留图像的纹理细节等本真信息。实验结果表明,所提算法的去噪效果要优于同类去噪算法,PSNR和SSIM值都有不同程度的提升。对于噪声比率较高的图像进行去噪时,本文算法依然存在严重的细节丢失问题[18-19],因此,研究如何通过基于清晰图像字典对噪声图像进行恢复是今后工作的一个重要方向。
  参考文献:
  [1] TIAN J, CHEN L, MA L. A wavelet-domain non-parametric statistical approach for image denoising [J].IEICE Electronics Express, 2010, 7(18):1409-1415.
  [2] DABOV K, FOI A, KATKOVNIK V, et al. Image denoising by sparse 3-D transform-domain collaborative filtering [J]. IEEE Transactions on Image Processing, 2007,16(8): 2080-2095.
  [3] DAI T, LU W, WANG W, et al. Entropy-based bilateral filtering with a new range kernel [J]. Signal Processing, 2017, 137: 223-234.
  [4] YIN M, LIU W, SHUI J, et al. Quaternion wavelet analysis and application in image denoising [J].Mathematical Problems in Engineering, 2012, 2012: Article ID 493976.
  [5] BUADES A, COLL B, MOREL J-M. A non-local algorithm for image denoising [C]// Proceedings of the 2005 IEEE Computer Society Conference on Computer Vision and Pattern Recognition. Washington, DC: IEEE Computer Society, 2005: 60-65.
  [6] DONG W, ZHANG L, SHI G, et.al. Nonlocally centralized sparse representation for image restoration [J], IEEE Transactions on Image Processing, 2013, 22(4): 1620-1630.
  http://files.hostgator.co.in/hostgator179351/file/matlab2013-2014abstractscontact9448847874.pdf 未找到
  [7] AHARON M, ELAD M, BRUCKSTEIN A. K-SVD: an algorithm for designing overcomplete dictionaries for sparse representation [J]. IEEE Transactions on Signal Processing, 2006, 54(11): 4311-4322.
  [8] HOREY I, BRYT O, RUBINSTEIN R. Adaptive image compression using sparse dictionaries [C]// Proceedings of the 19th International Conference on Systems, Signals and Image Processing. Piscataway, NJ: IEEE, 2012: 592-595.
  [9] YANG J, WRIGHT J, HUANG T S, et al. Image super-resolution-via sparse representation [J]. IEEE Transactions on Image Processing, 2010, 19(11): 2861-2873.
  [10] JIANG J, ZHANG L, YANG J. Mixed noise removal by weighted encoding with sparse nonlocal regularization [J]. IEEE Transactions on Image Processing, 2014, 23(6): 2651-2662.
  [11] ELAD M, AHARON M. Image denoising via sparse and redundant representations over learned dictionaries [J]. IEEE Transactions on Image Processing, 2006,15(12): 3736-3745.   [12] LI S, CAO Q, CHEN Y, et al. Dictionary learning based sinogram inpainting for CT sparse reconstruction [J]. Optik — International Journal for Light and Electron Optics, 2014,125(12): 2862-2867.
  [13] JIA L, SONG S, YAO L, et al. Image denoising via sparse representation over grouped dictionaries with adaptive atom size [J]. IEEE Acces, 2017, 5: 22514-22529.
  [14] 张静妙,高双喜,王晓娜.基于低秩字典学习的高光谱遥感图像去噪[J].控制工程,2016,23(6):823-827. (ZHANG J M, GAO S X, WANG X N. Hyperspectral image denoising based on low rank dictionary learning [J]. Control Engineering, 2016, 23(6): 823-827.)
  [15] TOMASI C, MANDUCHI R. Bilateral filtering for gray and color images [C]// Proceedings of the 1998 International Conference on Computer Vision. Piscataway, NJ: IEEE, 1998: 839-846.
  [16] DAUBECHIES I, DEVORE R, FORNSIER F, et al. Iteratively re-weighted least squares minimization for sparse recovery [J]. Communications on Pure & Applied Mathematics, 2010, 63(1):1-38.
  [17] WANG Z, BOVIK A C, SHEIKH H R, et al. Image quality assessment: from error visibility to structural similarity [J]. IEEE Transactions on Image Processing, 2004,13(4): 600-612.
  [18] LI N, LAN J H. Image denoising using sparse representation and weighted nuclear norm minimization [J]. Acta Scientiarum Naturalium Universitatis Nankaiensis, 2016, 49(1): 99-104.李娜,蘭俊花.基于稀疏表示和加权核范数极小化的图像去噪(英文)[J].南开大学学报(自然科学版). 2016(01): 99-104.
  [19] 王智文,李绍滋.基于多元统计模型的分形小波自适应图像去噪[J]. 计算机学报,2014,37(6):1380-1389. (WANG Z W, LI S Z. Adaptive fractal-wavelet image denoising base on multivariate statistical mode[J].Chinese Journal of Computers, 2014, 37(6): 1380-1389.)
转载注明来源:https://www.xzbu.com/8/view-14941670.htm