Abstract
In this paper we propose a new statement of the spatial increasing resolution problem of MODIS-like multi-spectral images via their fusion with Lansat-like imagery at higher resolution. We give a precise definition of the solution to the indicated problem, postulate assumptions that we impose at the initial data, establish existence and uniqueness result, and derive the corresponding necessary optimality conditions. For illustration, we supply the proposed approach by results of numerical simulations with real-life satellite images.
Highlights
Following in some aspects the paper [5], we propose a new variational approach to the spatial increasing resolution of multi spectral MODIS-like images via their fusion with Lansat-like imagery at higher resolution
Our approach is based on the variational model in Sobolev-Orlicz space with a non-standard growth condition of the objective functional and on the assumption that, to a large extent, the image topology in the each spectral channel is contained in the topographic map of its spectral energy
The following embedding results for BV -function plays a crucial role for qualitative analysis of variational problems that we study in this paper
Summary
Following in some aspects the paper [5], we propose a new variational approach to the spatial increasing resolution of multi spectral MODIS-like images via their fusion with Lansat-like imagery at higher resolution. Our approach is based on the variational model in Sobolev-Orlicz space with a non-standard growth condition of the objective functional and on the assumption that, to a large extent, the image topology in the each spectral channel is contained in the topographic map of its spectral energy. We discuss the well foundedness of the above approach, the consistency of the corresponding variational problem, and show that this problem admits a unique solution. We derive some optimality conditions and supply our approach by results of numerical simulations with the real satellite images
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