Estimation of the optimal variational parameter via SNR analysis

Authors:
Guy Gilboa;Nir A. Sochen;Yehoshua Y. Zeevi
Affiliations:
Department of Mathematics, UCLA, Los Angeles, CA;Department of Applied of Mathematics, Tel-Aviv Univ., Tel-Aviv, Israel;Department of Electrical Engineering, Technion, Haifa, Israel
Venue:
Scale-Space'05 Proceedings of the 5th international conference on Scale Space and PDE Methods in Computer Vision
Year:
2005

Citing 7
Cited 4

A posteriori parameter choice for general regularization methods for solving linear ill-posed problems

Applied Numerical Mathematics
Scale-Space and Edge Detection Using Anisotropic Diffusion

IEEE Transactions on Pattern Analysis and Machine Intelligence
Nonlinear total variation based noise removal algorithms

Proceedings of the eleventh annual international conference of the Center for Nonlinear Studies on Experimental mathematics : computational issues in nonlinear science: computational issues in nonlinear science
Iterative methods for total variation denoising

SIAM Journal on Scientific Computing - Special issue on iterative methods in numerical linear algebra; selected papers from the Colorado conference
Oscillating Patterns in Image Processing and Nonlinear Evolution Equations: The Fifteenth Dean Jacqueline B. Lewis Memorial Lectures

Oscillating Patterns in Image Processing and Nonlinear Evolution Equations: The Fifteenth Dean Jacqueline B. Lewis Memorial Lectures
Coherence-Enhancing Diffusion Filtering

International Journal of Computer Vision
Selection of Optimal Stopping Time for Nonlinear Diffusion Filtering

International Journal of Computer Vision

Structure-Texture Image Decomposition--Modeling, Algorithms, and Parameter Selection

International Journal of Computer Vision
Constrained and SNR-Based Solutions for TV-Hilbert Space Image Denoising

Journal of Mathematical Imaging and Vision
Structure-Texture decomposition by a TV-Gabor model

VLSM'05 Proceedings of the Third international conference on Variational, Geometric, and Level Set Methods in Computer Vision
Retinal vessel segmentation using multiwavelet kernels and multiscale hierarchical decomposition

Pattern Recognition

Quantified Score

Hi-index	0.00

Visualization

Abstract

We examine the problem of finding the optimal weight of the fidelity term in variational denoising. Our aim is to maximize the signal to noise ratio (SNR) of the restored image. A theoretical analysis is carried out and several bounds are established on the performance of the optimal strategy and a widely used method, wherein the variance of the residual part equals the variance of the noise. A necessary condition is set to achieve maximal SNR. We provide a practical method for estimating this condition and show that the results are sufficiently accurate for a large class of images, including piecewise smooth and textured images.