Continuation method for total variation denoising problems

Tony F. Chan; H. M. Zhou; Raymond Hon-fu Chan

doi:10.1117/12.211408

7 June 1995 Continuation method for total variation denoising problems

Tony F. Chan, H. M. Zhou, Raymond Hon-fu Chan

Proceedings Volume 2563, Advanced Signal Processing Algorithms; (1995) https://doi.org/10.1117/12.211408
Event: SPIE's 1995 International Symposium on Optical Science, Engineering, and Instrumentation, 1995, San Diego, CA, United States

Abstract

The denoising problem can be solved by posing it as a constrained minimization problem. The objective function is the TV norm of the denoised image whereas the constraint is the requirement that the denoised image does not deviate too much from the observed image. The Euler-Lagrangian equation corresponding to the minimization problem is a nonlinear equation. The Newton method for such equation is known to have a very small domain of convergence. In this paper, we propose to couple the Newton method with the continuation method. Using the Newton-Kantorovich theorem, we give a bound on the domain of convergence. Numerical results are given to illustrate the convergence.

Citation Download Citation

Tony F. Chan, H. M. Zhou, and Raymond Hon-fu Chan "Continuation method for total variation denoising problems", Proc. SPIE 2563, Advanced Signal Processing Algorithms, (7 June 1995); https://doi.org/10.1117/12.211408

ACCESS THE FULL ARTICLE

INSTITUTIONAL
Select your institution to access the SPIE Digital Library.

SELECT YOUR INSTITUTION

PERSONAL
Sign in with your SPIE account to access your personal subscriptions or to use specific features such as save to my library, sign up for alerts, save searches, etc.

PERSONAL SIGN IN

No SPIE Account? Create one

PURCHASE THIS CONTENT

SUBSCRIBE TO DIGITAL LIBRARY

50 downloads per 1-year subscription

Members: $195

Non-members: $335 ADD TO CART

25 downloads per 1 - year subscription

Members: $145

Non-members: $250 ADD TO CART

PURCHASE SINGLE ARTICLE

Includes PDF, HTML & Video, when available