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

Abstract

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 à 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 à 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.

Image Fusion for Remote Sensing Applications

“…It also requires more space to store the results of each level of transformation and, although it is shift-invariant, it does not resolve the problem of feature orientation (González-Audícana et al, 2005 ;Garzelli & Nencini, 2005). Most methods based on wavelet transform exploits the context dependency by thresholding the local correlation coefficient between the images to be merged, to avoid injection of spatial details that are not likely to occur in the high spatial image (Choi et al, 2005;Li et al, 2005;Lillo-Saavedra & Gonzalo, 2006;Song et al, 2007;Ventura et al, 2002;Yang et al, 2007). These techniques seem to reduce the color distortion problem and to keep the statistical parameters invariable.…”

Toward reduction of artifacts in fused images

“…As mentioned above, the fusion methodology proposed in this paper is based on the discrete wavelet transform (DWT) fusion methodology, calculated by the á trous algorithm (WAT) (LilloSaavedra and Gonzalo, 2006). Eq.…”

“…)', and C PANk corresponds to the panchromatic wavelet coefficients. This fusion strategy does not consider spectral differences between bands and cannot control the inherent tradeoff between spatial-spectral quality in the fused image (Choi, 2006;Garzelli et al, 2004;Lillo-Saavedra and Gonzalo, 2006).…”

“…It will be applied to the Discrete Wavelet Transform fusion methodology, implemented through the á trous algorithm (WAT) (Lillo-Saavedra and Gonzalo, 2006). This paradigm will be called fractal dimension maps fusion (FDMF), where the fractal dimension maps (FDMs) are estimated by the box-counting algorithm (Conci and Nunes, 2001;Parrinello and Vaughan, 2002;Sun, 2006), using a windowing process (see Appendix A).…”

Scale-Aware Pansharpening Algorithm for Agricultural Fragmented Landscapes

“…Many PS algorithms are available today [7][8][9][10][11][12]; most of them follow two approaches [8,9]: component substitution (CS) and multi-resolution analysis (MRA). The former includes widely-used PS algorithms, such as: intensity-hue-saturation (IHS) [13], principal component analysis (PCA) [14], Grand-Schmidt (GS) [15] and Brovey transform (BT) [16].…”