Tikhonov regularization versus scale space: A new result

It is well-known that scale space theory and Tikhonov regularization are close-knit. In previous studies qualitative analogies and formal relations had already been found, but none of these established both an exact as well as operational connection. We establish such a connection for the case of a Gaussian scale space representation and a first order Tikhonov scheme. The free parameter of the latter turns out to be related to a particular attenuation of scales in a procedure whereby one "collapses" the scale space image along the scale axis via the Laplace transform. The result provides a physical interpretation of first order Tikhonov regularization and its associated control parameter.

• Type: Conference
• Year: 2004
• Where: ICIP
• Authors: Luc Florack, Remco Duits, Joris Bierkens
• Keywords: Associated Control Parameter, Gaussian Scale Space, ICIP 2004, Image Processing, Order Tikhonov Regularization, Scale Space Image, Scale Space Theory