Image super-resolution aims to reconstruct a high-resolution image from the known low-resolution version. During this process, it should keep the degree of image roughness non-decreasing, which reflects various texture features and appearance. However, this point is not well addressed in the current work. This work argues that reducing roughness during image super-resolution is the key reason causing various problems such as artificial texture and/or edge blur. In this work, keeping the image roughness non-decreasing during super-resolution is being well investigated for the first time to our best knowledge. Image super-resolution is cast as an optimization problem to keep image roughness non-decreasing. In order to tackle this problem, the image super-resolution is approached based on the theory of fractal, where adaptive fractal interpolation function is proposed. In this way, the rational fractal interpolation model is adaptive to every local region. Thus, the roughness of every image region can be best maintained while super-resolution is carried out through fractal interpolation. In this work, the image roughness is reflected by the fractal dimension, which is a key element affecting the construction of fractal interpolation model. That is, the image roughness is measurable using fractal dimension. Mathematically, the overall image super-resolution process can be converted into a fractal interpolation optimization problem where the local fractal dimension is maintained. Although adaptive super-resolution on image segments may best maintain image roughness using the proposed method, it still generates unnecessary block artifacts. To tackle this problem, this work proposes a fine-grained pixel-wise fractal function. Our extensive experimental results demonstrate that the proposed method achieves encouraging performance with the state-of-the-art super-resolution algorithms.

中文翻译：

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基于局部分形特征和图像粗糙度的加权自适应图像超分辨率方案

图像超分辨率旨在从已知的低分辨率版本重建高分辨率图像。在此过程中，应保持图像粗糙程度不降低，反映各种纹理特征和外观。然而，这一点在目前的工作中并没有得到很好的解决。这项工作认为，在图像超分辨率期间降低粗糙度是导致各种问题（例如人工纹理和/或边缘模糊）的关键原因。在这项工作中，我们第一次充分研究了在超分辨率期间保持图像粗糙度不降低的最佳知识。图像超分辨率被视为一个优化问题，以保持图像粗糙度不降低。为了解决这个问题，基于分形理论来处理图像超分辨率，其中提出了自适应分形插值函数。这样，有理分形插值模型对每个局部区域都是自适应的。因此，在通过分形插值进行超分辨率的同时，可以最好地保持每个图像区域的粗糙度。在这项工作中，图像粗糙度由分形维数来反映，这是影响分形插值模型构建的关键因素。即，图像粗糙度可使用分形维数来测量。从数学上讲，整个图像超分辨率过程可以转换为保持局部分形维数的分形插值优化问题。尽管使用所提出的方法对图像片段进行自适应超分辨率可以最好地保持图像粗糙度，但它仍然会产生不必要的块伪影。为了解决这个问题，这项工作提出了一个细粒度的逐像素分形函数。我们广泛的实验结果表明，所提出的方法通过最先进的超分辨率算法实现了令人鼓舞的性能。