On a Variational Problem with a Nonstandard Growth Functional and Its Applications to Image Processing

Abstract We propose a new variational model in Sobolev–Orlicz spaces with non-standard growth conditions of the objective functional and discuss its applications to image processing. The characteristic feature proposed is that variable exponent, which associated growth, unknown priori it depends on particular function belongs domain functional. So, we deal constrained minimization problem lives spaces. In view this, consistency model, give scheme for regularization, derive corresponding optimality system, an iterative algorithm practical implementations.