Variational approach to simultaneous fusion and denoising of color images with different spatial resolution

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

Keywords

inverse problem, image fusion, denoising, constrained minimization problems, approximationmethods, Sobolev-Orlicz space

2010 Mathematics Subject Classification

90C90, 94A08

Full Text (PDF format)

Received 23 February 2023

Received revised 11 July 2023

Accepted 12 October 2023

Published 12 July 2024