Spectral or spatial quality for fused satellite imagery? A trade-off solution using the wavelet a trous algorithm

Several different methods for the fusion of multispectral and panchromatic images based on the wavelet transform have been proposed. The majority provide satisfactory results, but there is one, the a trous algorithm, that presents several advantages over the other fusion methods. Its computation is very simple; it only involves elementary algebraic operations, such as products, differences and convolutions. It yields a better spatial and spectral quality than the other methods. Standard fusion methods do not allow control of the spatial and spectral quality of the fused image; high spectral quality implies low spatial quality and vice versa. This paper proposes a new version of a fusion method based on the wavelet transform, computed through the a trous algorithm, that permits customization of the trade-off between the spectral and spatial quality of the fused image through the evaluation of two quality indices: a spectral index (the ERGAS index) and a spatial one. For the latter, a new spatial index based on ERGAS concepts and translated to the spatial domain has been defined. In addition, several different schemes for the computation of the fusion method investigated have been evaluated to optimize the degradation level of the source image required to perform the fusion process. The performance of the proposed fusion method has been compared with the fusion methods based on wavelet Mallat and filtering in the Fourier domain.