  The Tikhonov-Phillips method is widely used for regularizing ill-posed
inverse problems mainly due to the simplicity of its formulation as an
optimization problem. The use of different penalizers in the functionals
associated to the corresponding optimization problems has originated a variety
other methods which can be considered as "variants" of the traditional
Tikhonov-Phillips method of order zero. Such is the case for instance of the
Tikhonov-Phillips method of order one, the total variation regularization
method, etc. In this article we find sufficient conditions on the penalizers in
generalized Tikhonov-Phillips functionals which guarantee existence and
uniqueness and stability of the minimizers. The particular cases in which the
penalizers are given by the bounded variation norm, by powers of seminorms and
by linear combinations of powers of seminorms associated to closed operators,
are studied. Several examples are presented and a few results on image
restoration are shown.
