一种基于过完备冗余字典的图像去噪方法
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摘要
针对基于字典学习的图像去噪方法中字典学习速度慢、反应时间长的不足,在稀疏表示字典学习的基础上,提出了一种改进的字典学习算法。字典学习过程分为稀疏编码和字典更新两个阶段,在字典更新阶段采用一种求近似解的方法替代K-SVD(K奇异值分解)算法中消耗时间最多的SVD分解,并舍弃K-SVD和近似K-SVD算法中字典更新阶段重复更新稀疏系数矩阵的过程。实验结果表明,与K-SVD和近似K-SVD字典学习算法相比,在不降低图像峰值信噪比和结构相似度的前提下,改进的字典学习算法减少了字典学习时间,提高了图像去噪的效率。
Aiming at the weakness of slow dictionary learning and long reaction time in the image denoising method based on dictionary learning, it proposes an improved dictionary learning algorithm based on sparse representation dictionary learning. The dictionary learning process is divided into two stages: sparse coding and dictionary updating. In the dictionary updating stage, it adopts an approximate solution instead of the K-SVD algorithm to approximate the SVD decomposition which consumes the most time with the K-SVD algorithm. It abandons the process of updating the sparse coefficient matrix in the dictionary updating stage in K-SVD and approximate K-SVD algorithm. The experimental results show: comparing with the classical dictionary learning algorithm, in the premise of not reducing the image peak signal-to-noise ratio and structure similarity, this improved algorithm significantly reduces the dictionary learning time, improves the efficiency of image denoising.
Aiming at the weakness of slow dictionary learning and long reaction time in the image denoising method based on dictionary learning, it proposes an improved dictionary learning algorithm based on sparse representation dictionary learning. The dictionary learning process is divided into two stages: sparse coding and dictionary updating. In the dictionary updating stage, it adopts an approximate solution instead of the K-SVD algorithm to approximate the SVD decomposition which consumes the most time with the K-SVD algorithm. It abandons the process of updating the sparse coefficient matrix in the dictionary updating stage in K-SVD and approximate K-SVD algorithm. The experimental results show: comparing with the classical dictionary learning algorithm, in the premise of not reducing the image peak signal-to-noise ratio and structure similarity, this improved algorithm significantly reduces the dictionary learning time, improves the efficiency of image denoising.
引文
[1] 练秋生, 石保顺, 陈书贞. 字典学习模型、算法及其应用研究进展[J]. 自动化学报,2015,41(2):240-260.
[2] 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.
[3] RUBINSTEIN R , ZIBULEVSKY M , ELAD M . Efficient implementation of the K-SVD algorithm using batch orthogonal matching pursuit[J]. CS Technion, 2008, 40(8):1-15.
[4] 赖剑煌, 蔡泽民. 一种基于超完备字典学习的图像去噪方法[J]. 电子学报, 2009, 37(2):347-350.
[5] 梁栋, 梁昭, 鲍文霞. 基于非局部正则化稀疏表示的图像去噪算法[J]. 系统工程与电子技术, 2013, 35(5):1104-1109.
[6] 任越美, 张艳宁, 李映. 压缩感知及其图像处理应用研究进展与展望[J]. 自动化学报, 2014, 40(8):1563-1575.
[7] ENGAN K,AASE S O,HUSOY J H. Method of optimal directions for frame design[C]//Proceedings of the 1999 IEEE International Conference on Acoustics,Speech, and Signal Processing.Phoenix:AZ,1999: 2443-2446.
[8] MAIRAL J , BACH F , PONCE J , et al. Online learning for matrix factorization and sparse coding[J]. Journal of Machine Learning Research, 2009, 11(1):19-60.
[2] 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.
[3] RUBINSTEIN R , ZIBULEVSKY M , ELAD M . Efficient implementation of the K-SVD algorithm using batch orthogonal matching pursuit[J]. CS Technion, 2008, 40(8):1-15.
[4] 赖剑煌, 蔡泽民. 一种基于超完备字典学习的图像去噪方法[J]. 电子学报, 2009, 37(2):347-350.
[5] 梁栋, 梁昭, 鲍文霞. 基于非局部正则化稀疏表示的图像去噪算法[J]. 系统工程与电子技术, 2013, 35(5):1104-1109.
[6] 任越美, 张艳宁, 李映. 压缩感知及其图像处理应用研究进展与展望[J]. 自动化学报, 2014, 40(8):1563-1575.
[7] ENGAN K,AASE S O,HUSOY J H. Method of optimal directions for frame design[C]//Proceedings of the 1999 IEEE International Conference on Acoustics,Speech, and Signal Processing.Phoenix:AZ,1999: 2443-2446.
[8] MAIRAL J , BACH F , PONCE J , et al. Online learning for matrix factorization and sparse coding[J]. Journal of Machine Learning Research, 2009, 11(1):19-60.