Pointwise Besov Space Smoothing of Images
Pointwise Besov Space Smoothing of Images
复制标题
图像的逐点贝索夫空间平滑
DOI：
10.1007/s10851-018-0821-1
复制
发表时间：
2019
影响因子：
2
通讯作者：
Lucier, Bradley J.
中科院分区：
文献类型：
--
作者：
Buzzard, Gregery T.;Chambolle, Antonin;Cohen, Jonathan D.;Levine, Stacey E.;Lucier, Bradley J.
我们提出了用Besov空间半范数测量函数平滑度的各种变分问题。等效Besov空间半模可以用平滑模或系数的序列模在适当的小波展开式中定义。基于小波的半规范在变分问题中已经被使用，但是现有的算法不能保留边缘，并且许多算法会产生块状伪影。在这里，我们设计了使用平滑模的besov空间半范数算法。我们选择这个特殊的空间是因为它与Rudin-Osher-Fatemi图像平滑中使用的有界变分函数空间以及与小波收缩算法相关的besov空间密切相关。它包含在中的所有函数，其中包括沿光滑曲线不连续的函数，以及“分形”粗糙区域；附录中给出了例子。此外，它更喜欢仿射区域而不是阶梯，这可能使它成为恢复分段仿射数据的理想正则化器。虽然我们的动机和计算示例来自图像处理，但我们并不声称我们的方法“击败”了当前最好的算法。这项工作的新颖之处在于一种新的算法，该算法结合了不依赖于小波的平移不变Besov正则器，从而改进了先前的结果。此外，该算法自然地暴露了一系列取决于图像数据、噪声水平和平滑参数的尺度。我们还分析了平滑、纹理和随机高斯噪声数据在、、和它们的对偶空间中的范数。数值结果证明了由该基于平滑的正则化器模得到的解的性质。
We formulate various variational problems in which the smoothness of functions is measured using Besov space semi-norms. Equivalent Besov space semi-norms can be defined in terms of moduli of smoothness or sequence norms of coefficients in appropriate wavelet expansions. Wavelet-based semi-norms have been used before in variational problems, but existing algorithms do not preserve edges, and many result in blocky artifacts. Here, we devise algorithms using moduli of smoothness for theBesov space semi-norm. We choose that particular space because it is closely related both to the space of functions of bounded variation,, that is used in Rudin–Osher–Fatemi image smoothing, and to theBesov space, which is associated with wavelet shrinkage algorithms. It contains all functions in, which include functions with discontinuities along smooth curves, as well as “fractal-like” rough regions; examples are given in an appendix. Furthermore, it prefers affine regions to staircases, potentially making it a desirable regularizer for recovering piecewise affine data. While our motivations and computational examples come from image processing, we make no claim that our methods “beat” the best current algorithms. The novelty in this work is a new algorithm that incorporates a translation-invariant Besov regularizer that does not depend on wavelets, thus improving on earlier results. Furthermore, the algorithm naturally exposes a range of scales that depends on the image data, noise level, and the smoothing parameter. We also analyze the norms of smooth, textured, and random Gaussian noise data in,,andand their dual spaces. Numerical results demonstrate properties of solutions obtained from this moduli of smoothness-based regularizer.
DOI：
--
发表时间：
1993
期刊：
影响因子：
--
作者：
Z. Ditzian;K. Ivanov
通讯作者：
K. Ivanov
DOI：
--
发表时间：
1979
期刊：
影响因子：
--
作者：
C. Ridders
通讯作者：
C. Ridders