Image restoration consists in recovering a high quality image estimate based only on
observations. This is considered an ill-posed inverse problem, which implies non-unique
unstable solutions. Regularization methods allow the introduction of constraints in such
problems and assure a stable and unique solution. One of these methods is Total Variation,
which has been broadly applied in signal processing tasks such as image denoising, image
deconvolution, and image inpainting for multiple noise scenarios. Total Variation features
a regularization parameter which defines the solution regularization impact, a crucial step
towards its high quality level. Therefore, an optimal selection of the regularization parameter
is required. Furthermore, while the classic Total Variation applies its constraint to the
entire image, there are multiple scenarios in which this approach is not the most adequate.
Defining different regularization levels to different image elements benefits such cases. In
this work, an optimal regularization parameter selection framework for Total Variation image
restoration is proposed. It covers two noise scenarios: Impulse noise and Impulse over
Gaussian Additive noise. A broad study of the state of the art, which covers noise estimation
algorithms, risk estimation methods, and Total Variation numerical solutions, is
included. In order to approach the optimal parameter estimation problem, several adaptations
are proposed in order to create a local-fashioned regularization which requires no
a-priori information about the noise level. Quality and performance results, which include
the work covered in two recently published articles, show the effectivity of the proposed
regularization parameter selection and a great improvement over the global regularization
framework, which attains a high quality reconstruction comparable with the state of the art
algorithms. / Tesis
| Identifer | oai:union.ndltd.org:PUCP/oai:tesis.pucp.edu.pe:123456789/4461 |
| Date | 27 March 2013 |
| Creators | Rojas Gómez, Renán Alfredo |
| Contributors | Rodríguez Valderrama, Paúl Antonio |
| Publisher | Pontificia Universidad Católica del Perú |
| Source Sets | Pontificia Universidad Católica del Perú |
| Language | Spanish |
| Detected Language | English |
| Type | info:eu-repo/semantics/masterThesis |
| Format | application/pdf |
| Source | Pontificia Universidad Católica del Perú, Repositorio de Tesis - PUCP |
| Rights | info:eu-repo/semantics/openAccess, Atribución-NoComercial-SinDerivadas 2.5 Perú, http://creativecommons.org/licenses/by-nc-nd/2.5/pe/ |
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