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Single-image super-resolution based on local biquadratic spline with edge constraints and adaptive optimization in transform domain

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Abstract

This paper proposes a novel single-image super-resolution method based on local biquadratic spline with edge constraints and adaptive optimization in transform domain. The complex internal structure of the image makes the values of adjacent pixels often differ greatly. Using surface patches to interpolate image blocks can avoid large surface oscillation. Because the quadratic spline has better shape-preserving property, we construct the biquadratic spline surface on each image block to make the interpolation more flexible. The boundary conditions have great influence on the shape of local biquadratic spline surfaces and are the keys to constructing surfaces. Using edge information as a constraint to calculate them can reduce jagged and mosaic effects. To decrease the errors caused by surface fitting, we propose a new adaptive optimization model in transform domain. Compared with the traditional iterative back-projection, this model further improves the magnification accuracy by introducing SVD-based adaptive optimization. In the optimization, we convert similar block matrices to the transform domain by SVD. Then the contraction coefficients are calculated according to the non-local self-similarity, and the singular values are contracted. Experimental comparison with the other state-of-the-art methods shows that the proposed method has better performance in both visual effect and quantitative measurement.

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Acknowledgements

This work is supported partly by the NSFC Joint Fund with Zhejiang Integration of Informatization and Industrialization under Key Project under Grant No.U1609218; the Natural Science Foundation of Shandong Province under Grant Nos. (ZR2018BF009, ZR2017MF033).

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Authors and Affiliations

  1. School of Computer Science and Technology, Shandong University, **an, China

    Danya Zhou

  2. School of Software, Shandong University, **an, China

    Yepeng Liu, Xuemei Li & Caiming Zhang

  3. Shandong Co-Innovation Center of Future Intelligent Computing, Yantai, China

    Xuemei Li & Caiming Zhang

Authors
  1. Danya Zhou
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  2. Yepeng Liu
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  3. Xuemei Li
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  4. Caiming Zhang
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Correspondence to Xuemei Li.

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Zhou, D., Liu, Y., Li, X. et al. Single-image super-resolution based on local biquadratic spline with edge constraints and adaptive optimization in transform domain. Vis Comput 38, 119–134 (2022). https://doi.org/10.1007/s00371-020-02007-z

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