Continuous-Domain Solutions of Linear Inverse Problems With Tikhonov Versus Generalized TV Regularization

Continuous-Domain Solutions of Linear Inverse Problems with Tikhonov vs. Generalized TV Regularization

We consider linear inverse problems that are formulated in the continuous domain. The object of recovery is a function that is assumed to minimize a convex objective functional. The solutions are constrained by imposing a continuousdomain regularization. We derive the parametric form of the solution (representer theorems) for Tikhonov (quadratic) and generalized total-variation (gTV) regulariza...

Splines Are Universal Solutions of Linear Inverse Problems with Generalized TV Regularization

Splines come in a variety of flavors that can be characterized in terms of some differential operator L. The simplest piecewise-constant model corresponds to the derivative operator. Likewise, one can extend the traditional notion of total variation by considering more general operators than the derivative. This results in the definition of a generalized total variation semi-norm and of its cor...

A Method for Choosing the Regularization Parameter in Generalized Tikhonov Regularized Linear Inverse Problems

This paper presents a systematic and computable method for choosing the regularization parameter appearing in Tikhonov-type regularization based on non-quadratic regularizers. First, we extend the notion of the L-curve, originally defined for quadratically regularized problems, to the case of non-quadratic functions. We then associate the optimal value of the regularization parameter for these ...

Regularization of linear inverse problems with total generalized variation

The regularization properties of the total generalized variation (TGV) functional for the solution of linear inverse problems by means of Tikhonov regularization are studied. Considering the associated minimization problem for general symmetric tensor fields, the wellposedness is established in the space of symmetric tensor fields of bounded deformation, a generalization of the space of functio...

A Generalized Tikhonov Regularization Fornonlinear Inverse Ill - Posed Problemsmichael