IEEE Trans Image Process. 2018 Mar;27(3):1448-1461. doi: 10.1109/TIP.2017.2771471. Epub 2017 Nov 9.
Recently, the annihilating filter-based low-rank Hankel matrix (ALOHA) approach was proposed as a powerful image inpainting method. Based on the observation that smoothness or textures within an image patch correspond to sparse spectral components in the frequency domain, ALOHA exploits the existence of annihilating filters and the associated rank-deficient Hankel matrices in an image domain to estimate any missing pixels. By extending this idea, we propose a novel impulse-noise removal algorithm that uses the sparse and low-rank decomposition of a Hankel structured matrix. This method, referred to as the robust ALOHA, is based on the observation that an image corrupted with the impulse noise has intact pixels; consequently, the impulse noise can be modeled as sparse components, whereas the underlying image can still be modeled using a low-rank Hankel structured matrix. To solve the sparse and low-rank matrix decomposition problem, we propose an alternating direction method of multiplier approach, with initial factorized matrices coming from a low-rank matrix-fitting algorithm. To adapt local image statistics that have distinct spectral distributions, the robust ALOHA is applied in a patch-by-patch manner. Experimental results from impulse noise for both single-channel and multichannel color images demonstrate that the robust ALOHA is superior to existing approaches, especially during the reconstruction of complex texture patterns.
最近，基于湮灭滤波器的低秩 Hankel 矩阵（ALOHA）方法被提出作为一种强大的图像修复方法。基于在图像补丁内的平滑度或纹理对应于频率域中稀疏的谱分量的观察，ALOHA 利用图像域中的湮灭滤波器和相关的秩亏 Hankel 矩阵的存在来估计任何缺失的像素。通过扩展这个想法，我们提出了一种新颖的脉冲噪声去除算法，该算法利用 Hankel 结构矩阵的稀疏和低秩分解。这种方法称为鲁棒 ALOHA，其基于以下观察结果：受到脉冲噪声污染的图像具有完整的像素；因此，脉冲噪声可以被建模为稀疏分量，而底层图像仍然可以使用低秩 Hankel 结构矩阵进行建模。为了解决稀疏和低秩矩阵分解问题，我们提出了一种基于交替方向乘子法的方法，初始分解矩阵来自于低秩矩阵拟合算法。为了适应具有不同谱分布的局部图像统计数据，鲁棒 ALOHA 以逐块的方式应用。来自单通道和多通道彩色图像的脉冲噪声的实验结果表明，鲁棒 ALOHA 优于现有方法，尤其是在复杂纹理模式的重建方面。
