dc.contributor.author | Lefkimmiatis, S | |
dc.contributor.author | Roussos, A | |
dc.contributor.author | Maragos, P | |
dc.contributor.author | Unser, M | |
dc.date.accessioned | 2018-03-05T14:41:34Z | |
dc.date.issued | 2015-05-07 | |
dc.description.abstract | We introduce a novel generic energy functional that we employ to solve inverse imaging problems
within a variational framework. The proposed regularization family, termed as structure tensor
total variation (STV), penalizes the eigenvalues of the structure tensor and is suitable for both
grayscale and vector-valued images. It generalizes several existing variational penalties, including
the total variation seminorm and vectorial extensions of it. Meanwhile, thanks to the structure
tensor’s ability to capture first-order information around a local neighborhood, the STV functionals
can provide more robust measures of image variation. Further, we prove that the STV regularizers
are convex while they also satisfy several invariance properties w.r.t. image transformations. These
properties qualify them as ideal candidates for imaging applications. In addition, for the discrete
version of the STV functionals we derive an equivalent definition that is based on the patch-based
Jacobian operator, a novel linear operator which extends the Jacobian matrix. This alternative
definition allow us to derive a dual problem formulation. The duality of the problem paves the
way for employing robust tools from convex optimization and enables us to design an efficient
and parallelizable optimization algorithm. Finally, we present extensive experiments on various
inverse imaging problems, where we compare our regularizers with other competing regularization
approaches. Our results are shown to be systematically superior, both quantitatively and visually. | en_GB |
dc.identifier.citation | Vol. 8 (2), pp. 1090 - 1122 | en_GB |
dc.identifier.doi | https://doi.org/10.1137/14098154X | |
dc.identifier.uri | http://hdl.handle.net/10871/31833 | |
dc.language.iso | en | en_GB |
dc.publisher | Society for Industrial and Applied Mathematics | en_GB |
dc.rights | Copyright © by SIAM. Unauthorized reproduction of this article is prohibited. | en_GB |
dc.subject | structure tensor | en_GB |
dc.subject | patch-based Jacobian | en_GB |
dc.subject | image reconstruction | en_GB |
dc.subject | convex optimization | en_GB |
dc.subject | total variation | en_GB |
dc.subject | inverse problems | en_GB |
dc.title | Structure tensor total variation | en_GB |
dc.type | Article | en_GB |
dc.date.available | 2018-03-05T14:41:34Z | |
exeter.article-number | 2 | en_GB |
dc.description | This is the final version of the article. Available from Society for Industrial and Applied Mathematics via the DOI in this record. | en_GB |
dc.identifier.eissn | 1936-4954 | |
dc.identifier.journal | SIAM Journal on Imaging Sciences | en_GB |