Abstract
Digital image inpainting is an interpolation problem, inferring the content in the missing (unknown) region to agree with the known region data such that the interpolated result fulfills some prior knowledge. Low-rank and nonlocal self-similarity are two important priors for image inpainting. Based on the nonlocal self-similarity assumption, an image is divided into overlapped square target patches (submatrices) and the similar patches of any target patch are reshaped as vectors and stacked into a patch matrix. Such a patch matrix usually enjoys a property of low rank or approximately low rank, and its missing entries are recoveried by low-rank matrix approximation (LRMA) algorithms. Traditionally, $n$ nearest neighbor similar patches are searched within a local window centered at a target patch. However, for an image with missing lines, the generated patch matrix is prone to having entirely-missing rows such that the downstream low-rank model fails to reconstruct it well. To address this problem, we propose a region-wise matching (RwM) algorithm by dividing the neighborhood of a target patch into multiple subregions and then search the most similar one within each subregion. A non-convex weighted low-rank decomposition (NC-WLRD) model for LRMA is also proposed to reconstruct all degraded patch matrices grouped by the proposed RwM algorithm. We solve the proposed NC-WLRD model by the alternating direction method of multipliers (ADMM) and analyze the convergence in detail. Numerous experiments on line inpainting (entire-row/column missing) demonstrate the superiority of our method over other competitive inpainting algorithms. Unlike other low-rank-based matrix completion methods and inpainting algorithms, the proposed model NC-WLRD is also effective for removing random-valued impulse noise and structural noise (stripes).
Abstract (translated)
数字图像填充是一种插值问题,通过推断缺失(未知)区域的内容与已知区域数据相等,使填充结果满足某些先前知识。低秩和非局部相似性是图像填充的重要前提。基于非局部相似性假设,图像被分解成重叠的正方形目标点(子矩阵),任意目标点的目标点相似点被重构为向量并堆叠成点矩阵。这样的点矩阵通常具有低秩或近似低秩的性质,其缺失项可以通过低秩矩阵逼近算法(LRMA)恢复。传统上,$n$个最邻近的相似点需要在目标点周围的 local 窗口中搜索。但对于有线条缺失的图像,生成的点矩阵容易出现完全缺失的行,导致后续低秩模型无法重构它。为了解决这个问题,我们提出了一种区域匹配(RwM)算法,通过将目标点周围的邻居区域划分为多个子区域,然后在每个子区域内搜索最相似的点。一种非凸加权低秩分解(NC-WLRD)模型也被提出用于 LRMA 算法恢复所有退化的点矩阵。通过交替方向乘法方法(ADMM)解决提出的 NC-WLRD 模型,并详细分析了收敛情况。许多实验在线条填充(全部行/列缺失)展示了我们方法的优势胜过其他竞争填充算法。与其他基于低秩的矩阵 completion 方法和填充算法不同,提出的 NC-WLRD 模型还有效去除随机值快速噪声和结构噪声(条纹)。
URL
https://arxiv.org/abs/2303.12421
