Spatial methods for multispectral pansharpening: multiresolution analysis demystified

The majority of multispectral (MS) pansharpening methods may be labeled as spectral or spatial, depending on whether the geometric details that shall be injected into the interpolated MS bands are extracted from the panchromatic (P) image by means of a spectral transformation of MS pixels or a spatial transformation of the P image, achieved by means of linear shift-invariant digital filters. Spectral methods are known as component substitution; spatial methods are based on multiresolution analysis (MRA). In this paper, the authors show that, under the most general conditions, MRA-based pansharpening is characterized by a unique separable low-pass filter, which can be parametrically optimized based on the modulation transfer function (MTF) of the MS instrument, possibly followed by decimation and interpolation stages. This happens for the discrete wavelet transform (DWT) and its undecimated version (UDWT), for the 'à-trous' wavelet (ATW) transform and its decimated version, i.e., the generalized Laplacian pyramid (GLP), and for nonseparable wavelet transforms, such as the nonsubsampled contourlet transform (NSCT). Hybrid methods, in which MRA fusion is performed on the intensity component derived from a spectral transformation, are equivalent to MRA fusion with a specific detail injection model. ATW and GLP are preferable to DWT, UDWT, and NSCT, because of computational benefits and of a looser choice of the low-pass filter, unconstrained from the requirement of generating a perfect reconstruction filter bank. Ultimately, GLP outperforms ATW, because its decimation and interpolation stages allow the aliasing impairments intrinsically present in the original MS bands to be removed from the pansharpened product.