Image Processing Reference
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distortion in the result [61, 202]. The PCA-based methods introduce less color dis-
tortion, but affect spectral responses of the multispectral data [61]. This spectral
distortion is caused due to the mismatch of overlap between the spectral responses
of the multispectral image, and the bandwidth of the pan image [61].
We have already discussed the utility of the multi-resolution based methodologies
for fusion. This has also been used for pan-sharpening. The pan image is decomposed
into a set of low-resolution images yielding a pyramidal structure. The low-resolution
multispectral bands replace the pan image at an appropriate level of resolution from
the pyramid. The reverse wavelet transform is then employed on each of the mul-
tispectral bands to produce the corresponding output. A non-orthogonal undeci-
mated multi-resolution decomposition known as the “à trous” wavelet transform is
most commonly employed by several pan-sharpening techniques [1, 4, 39, 149].
Aiazzi et al. have proposed a context driven thresholding of correlation coefficients
between the images to be fused in the wavelet domain in order to avoid injection
of undesired spatial details [1]. Zhang and Hong have integrated the IHS- and the
wavelet-based techniques to reduce the color distortion [202]. In their technique,
the multispectral bands are first projected onto the IHS color space prior to their
wavelet decomposition. After the component substitution, the inverse wavelet trans-
form followed by the inverse IHS transform generates the resultant sharpened image.
In [66], the IHS transform of the multispectral image has been resampled to the size
of the pan image. These images and the pan image are then decomposed using the
Daubechies wavelet where the detail coefficients of the pan image are injected into
the corresponding intensity component.
Contourlets have been known for better directional representation than wavelets,
and capturing the geometrical structure of the objects [50]. Shah et al. have proposed
the use of contourlets along with an adaptive PCA which preserves the spectral
information [162]. Since the curvelets are more suitable for edge representation,
they are also well suited for pan-sharpening. In [39, 40], curvelets have been used to
extract the spatial details from the pan image.
Alparone et al. have proposed to extract the texture details from the pan image
which are used to modulate the intensity of the multispectral image bands [4]. This
technique is different from several others as it does not employ direct combination
of image components. Joshi et al. compute a set of autoregressive (AR) parameters
by modeling the spatial correlation of multispectral bands which are assumed to
be the same for the pan image due to spectral correlation among them [83]. These
parameters are then used in the process of regularization employed to combine the
spectral characteristics of themultispectral image and the pan image. The generalized
intensity component has been modeled as the weighted linear combination of the
multispectral bands in [2]. These weights have been computed as the regression
coefficients between the multispectral bands and the spatially degraded version of
the pan image. The pan-sharpening has been carried out using the Gram-Schmidt
spectral sharpening technique. Garzelli et al. have proposed a procedure to obtain a
pan-sharpened image which minimizes the squared error between the multispectral
data and the fused image [62]. Their technique provides the optimal results in the
sense of themean squared error (MSE). Moeller et al. have developed awavelet-based
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