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transform (DWT) (Garguet-Duport et al ., 1996; Yocky, 1996),
uniform rational filter banks (Aiazzi et al ., 2000), curvelet trans-
form (Nencini et al ., 2007) and Laplacian pyramids (LP) (Wilson,
Rogers and Kabrisky, 1997; Alparone et al ., 1998). The rationale
of high-pass detail injection as a problem of spatial frequency
spectrum substitution from one signal to another, was formally
developed in a multiresolution framework as an application of
filter banks theory (Argenti and Alparone, 2000). The DWT has
been extensively employed for remote sensing data fusion (Zhou,
Civco, and Silander, 1998; Ranchin and Wald, 2000; Scheunders
andDe Backer, 2001). According to the basicDWT fusion scheme
(Li, Manjunath and Mitra, 1995), pairs of subbands of corre-
sponding frequency content are merged together. Afterwards,
the fused image is synthesized by taking the inverse transform.
Fusion schemes based on the '' `atrous '' wavelet algorithm and
Laplacian pyramids were successively proposed (N unez et al .,
1999; Chibani and Houacine, 2000; Garzelli et al ., 2000). The
'' `atrous '' wavelet and the LP are oversampled, unlike the DWT,
which is critically subsampled. The missing out of the decimation
step allows an image to be decomposed into nearly disjointed
band-pass channels in the spatial frequency domain, without
losing the spatial connectivity (translation invariance property)
of its high-pass details, e.g., edges and textures. This property is
fundamental because, for critically subsampled schemes, spatial
distortions, typically ringing or aliasing effects, may be present
in the fused products and originate shifts or blur of contours
and textures. As a simple outcome of multirate signal processing
theory (Vaidyanathan, 1992), the LP can be easily generalized
(GLP) to deal with scales whose ratios are whatsoever integer or
even fractional numbers (Aiazzi et al ., 1997, 1999).
whose scale ratio is equal to four by investigating a Kalman-based
fusion method which performs a prediction of fusion param-
eters across scales (Garzelli and Nencini, 2007). It should also
be advisable to compute an HRIBSM by considering additional
information on the MS-imaging system. The goal is to make
the fused bands the most similar to what the narrow-band MS
sensor would capture if it had the same spatial resolution as
the broadband Pan. Notable examples of injection models are
additive combination of '' a-trous '' wavelet frames, as in the
additive wavelet to the luminance component (AWL) technique
(N unez et al ., 1999), the injection of wavelet details after apply-
ing intensity-hue-saturation (IHS) transformation or principal
component analysis (Gonzalez-Audıcana et al ., 2004), the spec-
tral distortionminimization (SDM) with respect to the resampled
MS data (Alparone et al ., 2003), or the spatially adaptive injec-
tion, as in the context-based-decision (CBD) algorithm (Aiazzi
et al ., 2002) and in the RWM method (Ranchin, et al ., 2003).
More efficient schemes can be obtained by taking into account
the modulation transfer functions (MTFs) of the MS scanner
and of the Pan sensor in order to design the MRA reduction
filters or the decimation filters generating the MS and Pan data
at degraded scales. In this way, it is possible to avoid a poor
enhancement that sometimes occurs when MTFs are assumed
to be ideal filters (Aiazzi et al ., 2006). Theoretical considera-
tions on injection models and experimental comparisons among
MRA-based Pan-sharpening methods can be found in (Garzelli
and Nencini, 2005). A further question concerns the adoption of
global or local (context adaptive - CA) injection models. Com-
putational cost is lower for global models but results are superior
in general for local ones (Aiazzi et al ., 2009) even if some caution
should be adopted for local models since due to their nature
they can bring local improvements but also cause possible local
distortions or impairments. Since urban areas are characterized
by the presence of important spatial details, investigations on
injection models for such areas should be considered a relevant
topic for future research.
10.1.3 Injectionmodel of details
The definition of an efficient, physically consistent, and compu-
tationally practical Pan-sharpening method lies on three main
issues. The first regards how to extract the spatial-detail infor-
mation from the Pan image (using MRA or CS frameworks
for example). The second concerns how the spatial details are
injected into the resampledMS data and involves two aspects: (a)
the estimation of a mathematical relationship to transform the
spatial details extracted from the Pan image into those suitable
for the MS representations, this step being defined within the
Amelioration de la Resolution Spatiale par Injection de Structures
(ARSIS) concept as interband structure model (IBSM) (Ranchin
and Wald, 2000; Ranchin et al ., 2003); (b) the adaptation of this
mathematical relationship to the high resolution representation
in order to transform the high-resolution details of Pan by defin-
ing a high-resolution IBSM (HRIBSM). The third issue is related
to the quality assessment of the spatially enhanced MS images
and to possibly drive the fusion process.
Regardless of how the spatial details are extracted from the
Pan image, data fusion methods require the definition of a
model that establishes how the missing high-pass information
is injected into the resampled MS bands (Ranchin and Wald,
2000). In other words, the model, referred to as IBSM, deals
with the radiometric transformation (gain and offset) of spatial
structures (edges and textures) when passing from the Pan to
MS images. The model is generally calculated at the coarser res-
olution and extrapolated to the finest resolution. This condition
has been proved to be satisfactory for the MS and Pan data
10.1.4 Quality assessment
The evaluation of fusion results underlies on both qualitative
and quantitative assessment. Qualitative assessment is usually
demanded to visual analysis of skilled experts and depends on
the application targets. Quantitative results of data fusion are
provided thanks to the availability of reference originals obtained
either by simulating the target sensor bymeans of high-resolution
data from an airborne platform (Laporterie-Dejean et al ., 2005),
or by degrading all available data to a coarser resolution and
carrying out fusion from such data. In practical cases, the first
strategy is not feasible. Concerning the second strategy, how-
ever, the underlying assumption is that fusion performances are
invariant to scale changes (Wald, Ranchin and Mangolini, 1997;
Wald, 1999). Hence, algorithms optimized to yield the best results
at coarser scales, i.e., on spatially degraded data, should still be
optimal when the data are considered at the finest scales. This
assumption may be reasonable in general, but may not hold for
very high-resolution data, especially in a highly detailed urban
environment, unless the spatial degradation is performedby using
low-pass filters whose frequency responses match the shape of the
MTFs of the sensors (Aiazzi et al ., 2006). Generally, the original
MS images are used as reference data for pan-sharpened images
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