Nonlocal Transform-Domain Filter for Volumetric Data Denoising and Reconstruction
Nonlocal Transform-Domain Filter for Volumetric Data Denoising and Reconstruction
复制标题
DOI：
10.1109/tip.2012.2210725
复制
发表时间：
2013-01-01
影响因子：
10.6
通讯作者：
Foi, Alessandro
中科院分区：
文献类型：
--
作者：
Maggioni, Matteo;Katkovnik, Vladimir;Foi, Alessandro
我们提出了 BM3D 滤波器对体积数据的扩展。所提出的算法 BM4D 实现了分组和协同过滤范例，其中相互相似的 d 维补丁在 (d + 1) 维数组中堆叠在一起，并在变换域中联合过滤。在 BM3D 中，基本数据块是像素块，而在 BM4D 中，我们使用体素立方体，它们堆叠成 4-D“组”。应用于该组的 4-D 变换同时利用每个立方体中的体素之间存在的局部相关性以及不同立方体的相应体素之间的非局部相关性。因此，该组的频谱高度稀疏，从而通过系数收缩非常有效地分离信号和噪声。经过逆变换后，我们获得每个分组立方体的估计，然后在其原始位置自适应聚合。我们评估了对被高斯和莱斯噪声破坏的体积数据进行去噪的算法，以及对来自噪声和不完整傅里叶域（k 空间）测量的非零相位体积模型数据的重建的算法。实验结果证明了 BM4D 的最先进的去噪性能，以及在体数据重建中用作正则化器时的有效性。
We present an extension of the BM3D filter to volumetric data. The proposed algorithm, BM4D, implements the grouping and collaborative filtering paradigm, where mutually similar d-dimensional patches are stacked together in a (d + 1)-imensional array and jointly filtered in transform domain. While in BM3D the basic data patches are blocks of pixels, in BM4D we utilize cubes of voxels, which are stacked into a 4-D "group." The 4-D transform applied on the group simultaneously exploits the local correlation present among voxels in each cube and the nonlocal correlation between the corresponding voxels of different cubes. Thus, the spectrum of the group is highly sparse, leading to very effective separation of signal and noise through coefficient shrinkage. After inverse transformation, we obtain estimates of each grouped cube, which are then adaptively aggregated at their original locations. We evaluate the algorithm on denoising of volumetric data corrupted by Gaussian and Rician noise, as well as on reconstruction of volumetric phantom data with non-zero phase from noisy and incomplete Fourier-domain (k-space) measurements. Experimental results demonstrate the state-of-the-art denoising performance of BM4D, and its effectiveness when exploited as a regularizer in volumetric data reconstruction.