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Volume 8, Issue 3
An $ℓ_q$ - Seminorm Variational Model for Impulse Noise Reduction

Yoon Mo Jung, Taeuk Jeong & Sangwoon Yun

DOI: 10.4208/eajam.101117.130418

East Asian J. Appl. Math., 8 (2018), pp. 586-597.

Published online: 2018-08

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  • Abstract

A variational $ℓ_q$-seminorm model to reduce the impulse noise is proposed. For $0<q<1$, it captures sparsity better than the $ℓ_1$-norm model. Numerical experiments show that for small $q$ this model is more efficient than TV$ℓ_1$ model if the noise level is low. If the noise level grows, the best possible parameter $q$ in the model approaches 1.

  • Keywords

Impulse noise, sparsity, ℓq-seminorm, total variation, iterative reweighted algorithm.

  • AMS Subject Headings

94A08, 90C26

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{EAJAM-8-586, author = {Yoon Mo Jung, Taeuk Jeong and Sangwoon Yun}, title = {An $ℓ_q$ - Seminorm Variational Model for Impulse Noise Reduction}, journal = {East Asian Journal on Applied Mathematics}, year = {2018}, volume = {8}, number = {3}, pages = {586--597}, abstract = {

A variational $ℓ_q$-seminorm model to reduce the impulse noise is proposed. For $0<q<1$, it captures sparsity better than the $ℓ_1$-norm model. Numerical experiments show that for small $q$ this model is more efficient than TV$ℓ_1$ model if the noise level is low. If the noise level grows, the best possible parameter $q$ in the model approaches 1.

}, issn = {2079-7370}, doi = {https://doi.org/10.4208/eajam.101117.130418}, url = {http://global-sci.org/intro/article_detail/eajam/12627.html} }
TY - JOUR T1 - An $ℓ_q$ - Seminorm Variational Model for Impulse Noise Reduction AU - Yoon Mo Jung, Taeuk Jeong & Sangwoon Yun JO - East Asian Journal on Applied Mathematics VL - 3 SP - 586 EP - 597 PY - 2018 DA - 2018/08 SN - 8 DO - http://doi.org/10.4208/eajam.101117.130418 UR - https://global-sci.org/intro/article_detail/eajam/12627.html KW - Impulse noise, sparsity, ℓq-seminorm, total variation, iterative reweighted algorithm. AB -

A variational $ℓ_q$-seminorm model to reduce the impulse noise is proposed. For $0<q<1$, it captures sparsity better than the $ℓ_1$-norm model. Numerical experiments show that for small $q$ this model is more efficient than TV$ℓ_1$ model if the noise level is low. If the noise level grows, the best possible parameter $q$ in the model approaches 1.

Yoon Mo Jung, Taeuk Jeong and Sangwoon Yun. (2018). An $ℓ_q$ - Seminorm Variational Model for Impulse Noise Reduction. East Asian Journal on Applied Mathematics. 8 (3). 586-597. doi:10.4208/eajam.101117.130418
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