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Title: Numerical analysis of an adjusted Cahn-Hilliard equation for binary image inpainting
Author: Poole, Gary A.
ISNI:       0000 0004 6062 3592
Awarding Body: University of Sussex
Current Institution: University of Sussex
Date of Award: 2017
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This thesis aims to analyse a finite element method applied to an adjusted Cahn-Hilliard equation that has been used for digital image inpainting applications. We consider both the standard model with a smooth double well potential and an alternative where an obstacle potential has been used. Existence and uniqueness results are derived for both formulations by adapting techniques existing in literature for other problems. For each formulation we then propose approximations, by discretising first in space and then in time, and we derive error bounds between the weak solution of the original formulation and the solution of the discrete approximations in terms of the discretisation parameters. We then propose and implement a practical numerical scheme for both models and investigate their use in applications, alongside some other models from literature. We investigate various real digital image examples and compare the resulting inpaintings for these competing models, considering their suitability for real-world applications.
Supervisor: Not available Sponsor: Not available
Qualification Name: Thesis (Ph.D.) Qualification Level: Doctoral
EThOS ID:  DOI: Not available
Keywords: TA0347.F5 Finite element method