Adaptive super-resolution image reconstruction based on fractal theory

Image super-resolution (SR) reconstruction has been a significant research field in image processing, although the current approaches to dealing with complicated image reconstruction still have some issues. In order to overcome these problems, traditional approaches apply fractal geometry to image super-resolution reconstruction, either in textured or non-textured regions, treating the image as a single fractal set. However, it won't be possible to classify the image specifically, such as edge, common texture, and complex texture, unless identifying the texture complexity of all regions in the image. For the texture region, this paper considers the fractal as a perturbation function of rational interpolation and constructs a new interpolation model with scale factor parameter. The parameter is related to the local fractal dimension (LFD). This paper defines a new function between scale factor and local fractal dimension so as to select the optimal value adaptively. Considering the image edge quality, this paper combines the non-texture regions and edge regions, applies an improved edge interpolation algorithm and sets a new pixel mapping method to meet the needs of different zoom factors. Based on the above, this paper proposes an adaptive super-resolution reconstruction algorithm. Particularly, region segmentation with different texture complexity is a foundational step of our algorithm, this paper proposes an image segmentation algorithm based on the research of local fractal dimension which combines the multi-scale analysis capability of wavelets with the multi-scale self-similarity feature of fractals. The experimental results show that our algorithm can obtain accurate texture details, smooth edges and low noise subjectively, and achieve the best evaluation objectively. This paper lays the theoretical foundation for fractal applications in super-resolution image reconstruction.