摘要
基于稀疏编码的复数图像降噪是目前的一个热门研究领域.该文研究一种基于分组稀疏编码的复数图像降噪算法,将复数值作为统一的整体进行分组和稀疏编码,通过限制同一分组中的图像块使用训练字典中相似的元素进行编码,从而抑制在稀疏编码过程中对噪声的编码.该文首先研究了图像块分组的算法,提出了一种图像块分组稀疏的编码算法并将其应用于复数图像的降噪问题.该文通过模拟真实的含噪干涉合成孔径雷达(InSAR)图像以及核磁共振图像(MRI)对该算法进行验证.从实验结果可以得出,相对于目前已有的算法,该文算法能够获得更低的降噪误差,特别是对于含有大片平滑区域的图像或者噪声水平较高的图像具有较大的降噪优势.
The denoising of the complex valued images based on the sparse representation is a hot topic recently, and abundant of algorithms are proposed to solve this problem in the last decades. Unfortunately, the problem is not solved perfectly and there is still space for improvement to achieve better denoising results. We take this challenge to move the denoising method of the complex valued images forward. This paper proposes a grouped sparse coding method based denoising algorithm of the complex valued images, which handles the complex values as a unity rather than processing the real part and the imaginary part separately. By doing this, the whole complex values are processed and the relationship between the real part and the imaginary part is considered. The complex valued images are separated into overlapped patches firstly and then these patches are divided into several clusters by the distance function which is defined in the complexed domain. By the constraint to the patches in each cluster that they are represented by the similar items in the trained dictionary with different coefficients, we can suppress the coding noise in the patches. This paper researches on the algorithm to cluster the patches firstly and proposes a grouped sparse coding method. The coding of the patches in a cluster is modeled by an object function to be minimized. The object function contains two terms. The first term is the fitting error part while the second term is to measure the sparsity of the codes. There is also a regularized parameter between the two terms. In order to constrain the codes in each cluster to be similar, the regularization term which induces the sparse codes to have same non-zero positions is proposed to the object function to be minimized. Then the coding algorithm is researched. What is more, the proposal is applied to the denoising of the complex valued images. The reason that the grouped sparse coding method can suppress the noise is that the information in the images can be coded by the grouped sparse coding
作者
郝红星
吴玲达
宋晓瑞
HAO Hong-Xing;WU Ling-Da;SONG Xiao-Rui(Science and Technology on Complex Electronic System Simulation Laboratory, Space Engineering University, Beijing 101416;Department of Graduate Management, Space Engineering University, Beijing 101416)
出处
《计算机学报》
EI
CSCD
北大核心
2019年第9期1991-2003,共13页
Chinese Journal of Computers
基金
国家自然科学基金(61801513)资助
supported by the basic research project of the national laboratory
关键词
复数域稀疏编码
图像降噪
分组稀疏
复数图像处理
冗余字典编码
sparse representation in the complex domain
image denoising
group sparsity
processing of complex valued images
coding based on redundant dictionary
