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This paper presents a novel single-image super-resolution (SR) procedure, which upscales a given low-resolution (LR) input image to a high-resolution image while preserving the textural and structural information. First, we construct a new type of bivariate rational fractal interpolation model and investigate its analytical properties. This model has different forms of expression with various values of the scaling factors and shape parameters; thus, it can be employed to better describe image features than current interpolation schemes. Furthermore, this model combines the advantages of rational interpolation and fractal interpolation, and its effectiveness is validated through theoretical analysis. Second, we develop a single-image SR algorithm based on the proposed model. The LR input image is divided into texture and non-texture regions, and then, the image is interpolated according to the characteristics of the local structure. Specifically, in the texture region, the scaling factor calculation is the critical step. We present a method to accurately calculate scaling factors based on local fractal analysis. Extensive experiments and comparisons with the other state-of-the-art methods show that our algorithm achieves competitive performance, with finer details and sharper edges.

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Generally, most existing super-resolution (SR) methods do not consider noise, which treats SR reconstruction and denoising as two separate problems and performs separately. However, noise is inevitably introduced in the imaging process. Based on analysis of the degraded model, in this paper, the problems of interpolation and denoising are modeled to estimate the noiseless and missing images under the same framework. By applying local fractal dimension (LFD) into image local feature analysis, a noisy singleimage SR method is proposed. For each noisy image, we first construct a rational fractal interpolation model containing scaling factors, which can effectively maintain the inherent properties of the data. Furthermore, the original image structure can be well preserved by applying the interpolation model. Considering the local characteristics of the image, scaling factors are calculated on the basis of the LFDs. Then, through further local feature analysis of the interpolated image, a denoising method based on LFD is proposed for recovering a noiseless image. Finally, a high-quality high-resolution image is obtained. Experimental results demonstrate that our method outperforms the state-of-the-art methods both quantitatively and qualitatively.INDEX TERMS Noisy image super-resolution, local fractal dimension, local fractal feature analysis, scaling factors.

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