The paper presents a new algorithm for the image inpainting problem. The algorithm uses a recently designed versatile library of quasi-analytic complex-valued wavelet packets (qWPs) which originate from polynomial splines of arbitrary orders. Tensor products of 1D qWPs provide a diversity of 2D qWPs oriented in multiple directions. For example, a set of the fourth-level qWPs comprises 62 different directions. The properties of these qWPs such as refined frequency resolution, directionality of waveforms with unlimited number of orientations, (anti-)symmetry of waveforms and windowed oscillating structure of waveforms with a variety of frequencies, make them efficient in image processing applications, in particular, in dealing with the inpainting problem addressed in the paper. The obtained results for this problem are quite competitive with the best state-of-the-art algorithms. The inpainting is implemented by an iterative scheme, which expands the Split Bregman Iteration (SBI) procedure by supplying it with an adaptive variable soft thresholding based on the Bivariate Shrinkage algorithm. In the inpainting experiments, performance comparison between the qWP-based methods and the state-of-the-art algorithms is presented.

本文提出了一种新的图像修复问题算法。该算法使用最近设计的通用类准解析复值小波包 (qWP) 库，这些小波包源自任意阶的多项式样条。一维 qWP 的张量积提供了面向多个方向的多种二维 qWP。例如，一组第四级 qWP 包括 62 个不同的方向。这些 qWP 的特性，例如精细的频率分辨率、无限数量方向的波形的方向性、波形的（反）对称性和具有各种频率的波形的窗口振荡结构，使它们在图像处理应用中非常有效，尤其是，处理论文中提到的修复问题。这个问题的结果与最好的最先进算法相当。修复是通过迭代方案实现的，它扩展了Split Bregman Iteration (SBI) 过程通过基于双变量收缩算法为其提供自适应可变软阈值。在修复实验中，提出了基于 qWP 的方法和最先进算法之间的性能比较。