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

PY - 2014/1/1

Y1 - 2014/1/1

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 -