Abstract
Fractal coding techniques are an effective tool for describing image textures. Considering the shortcomings of the existing image super‐resolution (SR) method, the large‐scale factor reconstruction performance is poor and the texture details are incomplete. In this paper, we propose an SR method based on error compensation and fractal coding. First, quadtree coding is performed on the image, and the similarity between the range block and the domain block is established to determine the fractal code. Then, through this similarity relationship, the attractor is reconstructed by super‐resolution fractal decoding to obtain an interpolated image. Finally, the fractal error of the fractal code is estimated by the depth residual network, and the estimated version of the error image is added as an error compensation term to the interpolation image to obtain the final reconstructed image. The network structure is jointly trained by a deep network and a shallow network. Residual learning is introduced to greatly improve the convergence speed and reconstruction accuracy of the network. Experiments with other state‐of‐the‐art methods on the benchmark datasets Set5, Set14, B100, and Urban100 show that our algorithm achieves competitive performance quantitatively and qualitatively, with subtle edges and vivid textures. Large‐scale factor images can also be reconstructed better.
Highlights
Fractal is an effective tool for describing image textures and is widely used in image segmentation [23], classification [24], SR, and other fields. e fractal-based SR method utilizes the locality of the similarity and transitivity of a single image to search for similar image blocks
Yao et al [29] proposed an adaptive rational fractal interpolation model that reconstructs the relationship between the partial shape dimension and the vertical scale factor. ese methods have some improvement in the recovery of the edges, but the fractal dimension does not accurately represent the texture details
Fractal image coding can use the spatial information of the image and self-similar structural information to achieve super-resolution of the image. e basic idea is to estimate the fractal code of the original image from its degraded version and decode it at a higher resolution
Summary
Fractal is an effective tool for describing image textures and is widely used in image segmentation [23], classification [24], SR, and other fields. e fractal-based SR method utilizes the locality of the similarity and transitivity of a single image to search for similar image blocks. Yu et al [28] combined fractal technology with an instance-based approach to propose a super-resolution algorithm that preserves vivid texture details. E use of fractal codes to achieve image SR recovery inevitably introduces errors and leads to the loss of blockiness and partial detail. To improve this phenomenon, we input the encoded and decoded error image into the depth residual network for estimation and use this as a compensation term to correct the interpolation image to further improve the reconstruction accuracy. Since most of the error images are high-frequency details lost after fractal interpolation, to better learn the details in this part, we propose a method of the convolutional neural network for training. Our main contributions can be summarized as follows. (1) We propose a fractal coding method based on error compensation. (2) We propose a method to estimate the fractal error of fractal coding using the CNN method. (3) Compared with the state-of-the-art methods, our method does not lead to excessive smoothing and artifacts and exhibits superior performance as the scale factor increases
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