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.
| Original language | English (US) |
|---|---|
| Pages (from-to) | 314-325 |
| Number of pages | 12 |
| Journal | Proceedings of SPIE - The International Society for Optical Engineering |
| Volume | 2563 |
| DOIs | |
| State | Published - 1995 |
| Externally published | Yes |
| Event | Advanced Signal Processing Algorithms - San Diego, United States Duration: Jul 9 1995 → … |
Keywords
- Denoising
- Fixed-point method
- Newton method
- Total-variation
ASJC Scopus subject areas
- Electronic, Optical and Magnetic Materials
- Condensed Matter Physics
- Computer Science Applications
- Applied Mathematics
- Electrical and Electronic Engineering