milou <[email protected]> wrote:
>
> hello,
> on Bayesian fusion, the general formulation is:
> y = Z + E, here are the input images the multispectral and the panchromatic
> one for example, and Z is the fusion image (the output image) is this
> equation means the medele of Bayesian data fusion?
>
Hi,
Here goes a description of the method implemented in OTB which uses this paper:
@ARTICLE{fasbender-radoux,
author={Fasbender, D. and Radoux, J. and Bogaert, P.},
journal={Geoscience and Remote Sensing, IEEE Transactions on}, title={Bayesian
Data Fusion for Adaptable Image Pansharpening},
year={2008},
month=jun ,
volume={46},
number={6},
pages={1847 -1857},
keywords={Bayesian data fusion;IKONOS images;SAR;adaptable image
pansharpening;hyperspectral image fusion;multispectral image;optical Earth
observation satellites;panchromatic sensor;spatial resolution multispectral
sensors;wavelet-based methods;geophysical techniques;image fusion;remote
sensing;},
doi={10.1109/TGRS.2008.917131},
ISSN={0196-2892},}
------------------------
The Bayesian Data Fusion (BDF) method developed by Fasbender et
al. \cite{fasbender-radoux} estimates the statistical link between the
HR and the LR images in order to find the most probable value for a HR
pixel given the LR one.
A simple sensor model for the observed pixels,
$$ Y = g(Z) + E, $$
is used, where $g(.)$ are the sensor function and $E$ is random noise.
This statistical link is represented by the conditional probability of
the high resolution multi-spectral value (the fused pixel), $z$, when
the high resolution panchromatic pixel, $y_P$, and the low resolution
multi-spectral pixel, $y_S$, are known:
$$ f(z \vert y_S , y_P) \propto f_Z(z) \times f_{E_S} \times f_{E_P}. $$
The authors introduce the additional possibility of giving different
confidence levels to the panchromatic and the multi-spectral images by
slightly modifying the formulation to:
$$ f(z \vert y_S , y_P) \propto f_Z(z) \times f_{E_S}^{2(1-w)} \times
f_{E_P}^{2w}, $$
where $w \in ]0,1[$ is a weight parameter. A low value for $w$ gives
more weight to the multi-spectral data.
------------------------
I have copied this verbatim from a report I wrote a while ago. I think
that Julien Radoux is on this mailing list. He may correct or complete
the information.
Jordi
> thank you.
>
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