超复数稀疏表示及其应用的研究

【作者】 吕鹏；

【导师】 张建秋；

【作者基本信息】 复旦大学 ， 电路与系统， 2011， 硕士

【摘要】 本文首先将稀疏表示的方法扩展到超复数域,提出超复数域正交匹配跟踪算法(QOMP),然后给出了超复数域的稀疏字典学习方法(QK-SVD)。QK-SVD算法学习得到的稀疏字典能够在捕获重要结构信息的同时也能获取重要的超复数各成分空间关联信息,并且用一个超复数字典取代三个色彩通道的稀疏字典。QK-SVD算法在彩色图像去噪的应用结果表明：超复数将彩色图像的R、G、B三个分量统一处理的手段,保证了色彩空间的完整性；通过和标量信号处理中K-SVD图像去噪算法的对比,彩色图像去噪在QK-SVD自适应稀疏字典下有更稀疏的表示形式；QK-SVD算法在处理彩色图像去噪时取得了更好的处理效果。之后,针对在超复数稀疏表示的计算过程中,随着信号维度的上升,基于贪婪算法的计算复杂度大大增加的问题,本文提出了超复数平滑L0范数的稀疏表示求解算法(QSL0)。该算法在信号维度上升的同时仍能保持很好的计算复杂度。同时在稀疏成分分析这一问题上,QSL0能够很好的处理超复数矢量信号的各个维度,得到超复数域的稀疏成分分析结果。并且在处理有噪声情况下的超复数矢量时,QSL0可以保持很好的鲁棒性,分析近似出实际的稀疏信号源分量。最后,在研究了现有结构相似性测度(SSIM)算法中存在的问题及其原因后,本文通过结合边缘结构信息,提出了边缘加权的结构相似性测度评价方法。该方法能够更好的与主观评价结果保持一致性和正确性。通过引入边缘信息,改进SSIM原有的结构评价部分,解决了原有SSIM算法中对模糊失真评价过高和强高斯噪声失真评价过低的问题,取得了更好的评价效果。另外,本文还利用超复数自适应稀疏表示字典对彩色图像进行了质量评估。该评估方法利用超复数稀疏表示字典获取彩色图像的重要结构和纹理信息来对失真图像进行评估。仿真实验表明,该方法可以很好地评估高斯模糊图像。更多还原

【Abstract】 At first, we propose a hypercomplex adaptive sparse dictionary learning method (QK-SVD) after formulizing hypercomplex sparse representation problem. The QK-SVD algorithm can learn a hypercomplex adaptive sparse representation dictionary from training data by catching both the important structural atoms and component correlation atoms. We use QK-SVD in color image denoising problem. With the help of hypercomplex, we can process the three components of R, G, B channels at the same time, without losing the relationship between each other. This ensures the integrity of color space. In the experiments, we show that QK-SVD has better performance on color image denoising issue than using K-SVD separately on each color channel.Considering the quick growth of computation complexity when signal’s dimension rises, we propose a hypercomplex smooth Lo norm sparse representation (QSLo) algorithm. It is very suitable for hypercomplex sparse representation, due to its low computational complexity and little growth with higher signal’s dimension. The QSLo can be effectively used in hypercomplex sparse component analysis (SCA). It gives good approximation of each dimensionality of hypercomplex sparse source. Also, in this paper, we extend our discussion to a noise setting and give a more robust smooth Lo algorithm (NSLo).Finally, this paper introduces an edge-weighted structural similarity index (EWSSIM) in image quality assessment field. After analyzing issues in structural similarity index (SSIM), we show the reasons why SSIM gives poor evaluations on blurring images and high Guassian white noise distorted images. With the help of edge structural information, the proposed index outperforms SSIM in blurred and Gaussian white noise distorted images and also gives a better coherent evaluation for all kinds of distortions in LIVE database. This paper proposes a method to evaluate color image quality by using hypercomplex adaptive sparse dictionary. The adaptive dictionary extracts important structure and texture information to evaluate distorted images. This method shows better results on blurring images.更多还原