[IPOL announce] new article: On the Implementation of Collaborative TV Regularization: Application to Cartoon+Texture Decomposition
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Wed Apr 20 10:33:26 CEST 2016
A new article is available in IPOL: http://www.ipol.im/pub/art/2016/141/
Joan Duran, Michael Moeller, Catalina Sbert, and Daniel Cremers,
On the Implementation of Collaborative TV Regularization: Application to
Cartoon+Texture Decomposition,
Image Processing On Line, 6 (2016), pp. 27–74.
http://dx.doi.org/10.5201/ipol.2016.141
Abstract
This paper deals with the analysis, implementation, and comparison of
several vector-valued total variation (TV) methods that extend the
Rudin-Osher-Fatemi variational model to color images. By considering the
discrete gradient of a multichannel image as a 3D structure matrix with
dimensions corresponding to the spatial extend, the differences to other
pixels and the color channels, we introduce in [J. Duran, M. Moeller, C.
Sbert, and D. Cremers, 'Collaborative Total Variation: A General
Framework for Vectorial TV Models', SIAM Journal on Imaging Sciences,
9(1), pp.116-151, 2016] collaborative sparsity enforcing norms for
penalizing the resulting tensor. We call this class of regularizations
collaborative total variation (CTV). We first analyze the denoising
properties of each collaborative norm for suppressing color artifacts
while preserving image features and aligning edges. We then describe the
primal-dual hybrid gradient method for solving the minimization problem
in detail. The resulting CTV–L2 variational model can successfully be
applied to many image processing tasks. On the one hand, an extensive
performance comparison of several collaborative norms for color image
denoising is provided. On the other hand, we analyze the ability of
different CTV methods for decomposing a multichannel image into a
cartoon and a textural part. Finally, we also include a short discussion
on alternative minimization methods and compare their computational
efficiency.
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