A Study of Methods of Choosing the Smoothing Parameter in Image Restoration by Regularization
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
Regularization, Scale-Space, and Edge Detection Filters
Journal of Mathematical Imaging and Vision
Oscillating Patterns in Image Processing and Nonlinear Evolution Equations: The Fifteenth Dean Jacqueline B. Lewis Memorial Lectures
Selection of Optimal Stopping Time for Nonlinear Diffusion Filtering
International Journal of Computer Vision
On Generalized Entropies and Scale-Space
SCALE-SPACE '97 Proceedings of the First International Conference on Scale-Space Theory in Computer Vision
An Algorithm for Total Variation Minimization and Applications
Journal of Mathematical Imaging and Vision
A Non-Local Algorithm for Image Denoising
CVPR '05 Proceedings of the 2005 IEEE Computer Society Conference on Computer Vision and Pattern Recognition (CVPR'05) - Volume 2 - Volume 02
IJCAI'83 Proceedings of the Eighth international joint conference on Artificial intelligence - Volume 2
Information measures in scale-spaces
IEEE Transactions on Information Theory
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We analyze the rate in which image details are suppressed as a function of the regularization parameter, using first order Tikhonov regularization, Linear Gaussian Scale Space and Total Variation image decomposition. The squared L 2-norm of the regularized solution and the residual are studied as a function of the regularization parameter. For first order Tikhonov regularization it is shown that the norm of the regularized solution is a convex function, while the norm of the residual is not a concave function. The same result holds for Gaussian Scale Space when the parameter is the variance of the Gaussian, but may fail when the parameter is the standard deviation. Essentially this imply that the norm of regularized solution can not be used for global scale selection because it does not contain enough information. An empirical study based on synthetic images as well as a database of natural images confirms that the squared residual norms contain important scale information.