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A total fractional-order variation model for image super-resolution and its SAV algorithm. (English) Zbl 1439.65100

Summary: Single-image super-resolution reconstruction aims to obtain a high-resolution image from a low-resolution image. Since the super-resolution problem is ill-posed, it is common to use a regularization technique. However, the choice of the fidelity and regularization terms is not obvious, and it plays a major role in the quality of the desired high resolution image. In this paper, a hybrid single-image super-resolution model integrated with total variation (TV) and fractional-order TV is proposed to provide an effective reconstruction of the HR image. We develop an efficient numerical scheme for this model using the scalar auxiliary variable approach with an adaptive time stepping strategy. Thorough experimental results suggest that the proposed model and numerical scheme can reconstruct high quality results both quantitatively and perceptually.

MSC:

65M06 Finite difference methods for initial value and initial-boundary value problems involving PDEs
65T50 Numerical methods for discrete and fast Fourier transforms
65D18 Numerical aspects of computer graphics, image analysis, and computational geometry
65K10 Numerical optimization and variational techniques
65J20 Numerical solutions of ill-posed problems in abstract spaces; regularization
26A33 Fractional derivatives and integrals
35R11 Fractional partial differential equations
35R09 Integro-partial differential equations

Software:

DnCNN
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Full Text: DOI

References:

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