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Group-Sparse Representation With Dictionary Learning for Medical Image Denoising and Fusion

机译：字典学习的群体稀疏表示用于医学图像降噪和融合

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摘要

Recently, sparse representation has attracted a lot of interest in various areas. However, the standard sparse representation does not consider the intrinsic structure, i.e., the nonzero elements occur in clusters, called group sparsity. Furthermore, there is no dictionary learning method for group sparse representation considering the geometrical structure of space spanned by atoms. In this paper, we propose a novel dictionary learning method, called Dictionary Learning with Group Sparsity and Graph Regularization (DL-GSGR). First, the geometrical structure of atoms is modeled as the graph regularization. Then, combining group sparsity and graph regularization, the DL-GSGR is presented, which is solved by alternating the group sparse coding and dictionary updating. In this way, the group coherence of learned dictionary can be enforced small enough such that any signal can be group sparse coded effectively. Finally, group sparse representation with DL-GSGR is applied to 3-D medical image denoising and image fusion. Specifically, in 3-D medical image denoising, a 3-D processing mechanism (using the similarity among nearby slices) and temporal regularization (to perverse the correlations across nearby slices) are exploited. The experimental results on 3-D image denoising and image fusion demonstrate the superiority of our proposed denoising and fusion approaches.
机译：最近，稀疏表示法引起了各个领域的广泛兴趣。但是，标准的稀疏表示不考虑固有结构，即非零元素出现在簇中，称为组稀疏性。此外，考虑到原子跨越的空间的几何结构，没有用于字典稀疏表示的字典学习方法。在本文中，我们提出了一种新颖的字典学习方法，称为具有组稀疏性和图正则化的字典学习（DL-GSGR）。首先，将原子的几何结构建模为图正则化。然后，结合组稀疏性和图正则化，提出了DL-GSGR，通过交替进行组稀疏编码和字典更新来解决。这样，可以将学习字典的组相干性强制得足够小，从而可以对任何信号进行组稀疏编码。最后，将基于DL-GSGR的组稀疏表示应用于3-D医学图像去噪和图像融合。具体地，在3-D医学图像去噪中，利用了3-D处理机制（利用附近切片之间的相似性）和时间正则化（以使横跨附近切片的相关正交）。 3-D图像降噪和图像融合的实验结果证明了我们提出的降噪和融合方法的优越性。

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