Nonlocal Image Restoration With Bilateral Variance Estimation: A Low-Rank Approach

Simultaneous sparse coding (SSC) or nonlocal image representation has shown great potential in various low-level vision tasks, leading to several state-of-the-art image restoration techniques, including BM3D and LSSC. However, it still lacks a physically plausible explanation about why SSC is a better model than conventional sparse coding for the class of natural images. Meanwhile, the problem of sparsity optimization, especially when tangled with dictionary learning, is computationally difficult to solve. In this paper, we take a low-rank approach toward SSC and provide a conceptually simple interpretation from a bilateral variance estimation perspective, namely that singular-value decomposition of similar packed patches can be viewed as pooling both local and nonlocal information for estimating signal variances. Such perspective inspires us to develop a new class of image restoration algorithms called spatially adaptive iterative singular-value thresholding (SAIST). For noise data, SAIST generalizes the celebrated BayesShrink from local to nonlocal models; for incomplete data, SAIST extends previous deterministic annealing-based solution to sparsity optimization through incorporating the idea of dictionary learning. In addition to conceptual simplicity and computational efficiency, SAIST has achieved highly competent (often better) objective performance compared to several state-of-the-art methods in image denoising and completion experiments. Our subjective quality results compare favorably with those obtained by existing techniques, especially at high noise levels and with a large amount of missing data.

同时稀疏编码（SSC）或非局部图像表示在各种低级视觉任务中显示出巨大潜力，催生了多种先进的图像恢复技术，包括BM3D和LSSC。然而，对于自然图像类别，它仍然缺乏关于为什么SSC比传统稀疏编码是更好的模型的合理物理解释。同时，稀疏性优化问题，特别是当与字典学习交织在一起时，在计算上难以解决。在本文中，我们对SSC采用低秩方法，并从双边方差估计的角度提供了一个概念上简单的解释，即相似组合块的奇异值分解可被视为汇集局部和非局部信息以估计信号方差。这种视角启发我们开发了一类新的图像恢复算法，称为空间自适应迭代奇异值阈值法（SAIST）。对于噪声数据，SAIST将著名的贝叶斯收缩从局部模型推广到非局部模型；对于不完整数据，SAIST通过纳入字典学习的思想，将先前基于确定性退火的稀疏性优化解决方案进行了扩展。除了概念简单和计算高效外，在图像去噪和补全实验中，与几种先进的方法相比，SAIST取得了非常出色（通常更好）的客观性能。我们的主观质量结果与现有技术获得的结果相比具有优势，特别是在高噪声水平和大量数据缺失的情况下。