基于多项式样条方向小波包的图像修复
Image inpainting using directional wavelet packets originating from polynomial splines
摘要：
提出了一种新的图像修复算法。该算法是使用最近设计的通用库的准解析复值小波包（qWPs），起源于多项式样条的任意阶。1D qWP的张量积提供了在多个方向上取向的2D qWP的多样性。例如，一组第四级qWP包括62个不同的方向。所提出的qWP的属性，如精细的频率分辨率，波形的方向性与无限数量的方向，（反）对称的波形和窗口振荡结构的波形与各种频率，使他们有效的图像处理应用，特别是在处理修复问题的文件。这个问题所得到的结果是相当有竞争力的最好的国家的最先进的算法。修复是由一个迭代方案，这在本质上是分裂Bregman迭代（SBI）过程提供了一个自适应可变软阈值的基础上的双变量收缩算法。在修复实验中，基于qWP的方法和最先进的算法之间的性能比较。
英文摘要：
The paper presents a new algorithm for the image inpainting problem. The algorithm is using 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 the presented 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, in essence, is the Split Bregman Iteration (SBI) procedure supplied 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.
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