TY - GEN
T1 - Fast Newton-type methods for total variation regularization
AU - Barbero, Álvaro
AU - Sra, Suvrit
PY - 2011
Y1 - 2011
N2 - Numerous applications in statistics, signal processing, and machine learning regularize using Total Variation (TV) penalties. We study anisotropic (ℓ1-based) TV and also a related ℓ2-norm variant. We consider for both variants associated (1D) proximity operators, which lead to challenging optimization problems. We solve these problems by developing Newton-type methods that outperform the state-of-the-art algorithms. More importantly, our 1D-TV algorithms serve as building blocks for solving the harder task of computing 2- (and higher-dimensional TV proximity. We illustrate the computational benefits of our methods by applying them to several applications: (i) image denoising; (ii) image deconvolution (by plugging in our TV solvers into publicly available software); and (iii) four variants of fused-lasso. The results show large speedups - and to support our claims, we provide software accompanying this paper.
AB - Numerous applications in statistics, signal processing, and machine learning regularize using Total Variation (TV) penalties. We study anisotropic (ℓ1-based) TV and also a related ℓ2-norm variant. We consider for both variants associated (1D) proximity operators, which lead to challenging optimization problems. We solve these problems by developing Newton-type methods that outperform the state-of-the-art algorithms. More importantly, our 1D-TV algorithms serve as building blocks for solving the harder task of computing 2- (and higher-dimensional TV proximity. We illustrate the computational benefits of our methods by applying them to several applications: (i) image denoising; (ii) image deconvolution (by plugging in our TV solvers into publicly available software); and (iii) four variants of fused-lasso. The results show large speedups - and to support our claims, we provide software accompanying this paper.
UR - http://www.scopus.com/inward/record.url?scp=80053439604&partnerID=8YFLogxK
M3 - Conference contribution
AN - SCOPUS:80053439604
SN - 9781450306195
T3 - Proceedings of the 28th International Conference on Machine Learning, ICML 2011
SP - 313
EP - 320
BT - Proceedings of the 28th International Conference on Machine Learning, ICML 2011
T2 - 28th International Conference on Machine Learning, ICML 2011
Y2 - 28 June 2011 through 2 July 2011
ER -