Advantages of Laplacian pyramids over "a trous" wavelet transforms for pansharpening of multispectral images

The advantages provided by the generalized Laplacian pyramid (GLP) over the widespread "`a trous" wavelet (ATW) transform for multispectral (MS) pansharpening based on multiresolution analysis (MRA) are investigated. The most notable difference depends on the way GLP and ATW deal with aliasing possibly occurring in the MS data, which is originated by insufficient sampling step size, or equivalently by a too high amplitude value of the modulation transfer function (MTF) at Nyquist frequency and may generate annoying jagged patterns that survive in the sharpened image. In this paper, it is proven that GLP is capable of compensating the aliasing of MS, unlike ATW, and analogously to component substitution (CS) fusion methods, thanks to the decimation and interpolation stages present in its flowchart. Experimental results will be presented in terms of quality/distortion global score indexes (SAM, ERGAS and Q4) for increasing amounts of aliasing, measured by the amplitude at Nyquist frequency of the Gaussian-like lowpass filter simulating the average MTF of the individual spectral channels of the instrument. GLP and ATW-based methods, both using the same MTF filters and the same global injection gain, will be compared to show the advantages of GLP over ATW in the presence of aliasing of the MS bands.