发表机构
Bates College; Johannes Kepler Universitat（贝茨学院; 约翰内斯·开普勒大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
针对三维盲反卷积问题，提出基于CP分解核与TV正则化图像的交替最小化算法，有效处理运动模糊歧义，并在MRI、高光谱和视频数据上验证了有效性。
AI 中文摘要
我们考虑从卷积数据 $g = k*u$ 中重建核 $k$ 和图像 $u$ 的盲反卷积问题。我们特别关注三维情形，即体图像。该问题通过对核施加半参数CP分解、对图像施加变分TV惩罚来处理。我们还讨论了运动模糊歧义效应，即盲反卷积问题中核的非唯一性问题，该问题可能出现在某些运动物体视频中。盲反卷积算法采用交替最小化方法，对 $u$ 使用TV正则化，对核使用CP分解步骤。这些步骤通过非负投影、核归一化以及因果支持投影来实现。针对三维MRI图像、高光谱图像和灰度测试视频的若干数值示例验证了该方法的有效性。
英文摘要
We consider the problem of reconstructing a kernel $k$ and image $u$ in a blind deconvolution problem from convolutional data $g = k*u$. We particularly focus on the 3D case, i.e., on volumetric images. The problem is approached by imposing a semiparametric CP decomposition for the kernel and a variational TV penalty for the image. We also discuss a motion blur ambiguity effect, i.e., a nonuniqueness issue of the kernel in the blind deconvolution problem that may appear in certain videos of moving objects. The blind deconvolution algorithm uses an alternating minimization approach with TV regularization for $u$ and a CP decomposition step for the kernel. These are implemented with positivity projection, kernel normalization, and\textbackslash or causal support projection steps. Several numerical examples for 3D MRI images, hyperspectral images, and a grayscale test video show the effectiveness of the method.
Comments13 pages, 4 figures
