TY - GEN
T1 - A fast algorithm for a mean curvature based image denoising model using augmented lagrangian method
AU - Zhu, Wei
AU - Tai, Xue Cheng
AU - Chan, Tony
N1 - Funding Information:
The authors thank the anonymous referees for their valuable comments and suggestions. The work was supported by NSF contract DMS-1016504.
PY - 2014
Y1 - 2014
N2 - Recently, many variational models using high order derivatives have been proposed to accomplish advanced tasks in image processing. Even though these models are effective in fulfilling those tasks, it is very challenging to minimize the associated high order functionals. In [33], we focused on a recently proposed mean curvature based image denoising model and developed an efficient algorithm to minimize it using augmented Lagrangian method, where minimizers of the original high order functional can be obtained by solving several low order functionals. Specifically, these low order functionals either have closed form solutions or can be solved using FFT. Since FFT yields exact solutions to the associated equations, in this work, we consider to use only approximations to replace these exact solutions in order to reduce the computational cost. We thus employ the Gauss-Seidel method to solve those equations and observe that the new strategy produces almost the same results as the previous one but needs less computational time, and the reduction of the computational time becomes salient for images of large sizes.
AB - Recently, many variational models using high order derivatives have been proposed to accomplish advanced tasks in image processing. Even though these models are effective in fulfilling those tasks, it is very challenging to minimize the associated high order functionals. In [33], we focused on a recently proposed mean curvature based image denoising model and developed an efficient algorithm to minimize it using augmented Lagrangian method, where minimizers of the original high order functional can be obtained by solving several low order functionals. Specifically, these low order functionals either have closed form solutions or can be solved using FFT. Since FFT yields exact solutions to the associated equations, in this work, we consider to use only approximations to replace these exact solutions in order to reduce the computational cost. We thus employ the Gauss-Seidel method to solve those equations and observe that the new strategy produces almost the same results as the previous one but needs less computational time, and the reduction of the computational time becomes salient for images of large sizes.
UR - http://www.scopus.com/inward/record.url?scp=84958523170&partnerID=8YFLogxK
U2 - 10.1007/978-3-642-54774-4_5
DO - 10.1007/978-3-642-54774-4_5
M3 - Conference contribution
AN - SCOPUS:84958523170
SN - 9783642547737
T3 - Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
SP - 104
EP - 118
BT - Efficient Algorithms for Global Optimization Methods in Computer Vision - International Dagstuhl Seminar, Revised Selected Papers
PB - Springer Verlag
T2 - 2011 International Dagstuhl Seminar 11471 on Efficient Algorithms for Global Optimization Methods in Computer Vision
Y2 - 20 November 2011 through 25 November 2011
ER -