Single image super-resolution via non-local normalized graph Laplacian regularization: a self-similarity tribute.

*(English)*Zbl 07274911Summary: The process of producing a high-resolution image given a single low-resolution noisy measurement is called single-frame image super-resolution (SISR). Historically, many fractal-based schemes have been proposed in the literature to address the SISR problem. Many conventional interpolation schemes fail to preserve important edge information of natural images and cannot be used blindly for resolution enhancement. Generally, a-priori constraints are required in the process of high resolution image approximation. We model the SISR problem as an energy minimization procedure which balances data fidelity and a regularization term. The regularization term will implicitly incorporate natural image redundancy via a normalized graph Laplacian operator, as a self-similarity based prior. This operator applies a non-local kernel similarity measure due to the choice of a non-local operator for the weight assignment. The data fidelity term is modelled as a likelihood estimator that is scaled using a sharpening term composed from the normalized graph Laplacian operator. Finally, a conjugate gradient scheme is used to minimize the objective functional. Promising results on resolution enhancement for a variety of digital images will be presented.

##### MSC:

94A | Communication, information |

28B | Set functions, measures and integrals with values in abstract spaces |

68U | Computing methodologies and applications |

##### Keywords:

super-resolution; regularization; image restoration; image zooming; graph Laplacian; self-similarity; fractal-based restoration
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\textit{M. Ebrahimi} and \textit{S. Bohun}, Commun. Nonlinear Sci. Numer. Simul. 93, Article ID 105508, 13 p. (2021; Zbl 07274911)

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