Spectrally consistent pansharpening

Several widely used methods have been proposed for fusing high resolution panchromatic data and lower resolution multi-channel data. However, many of these methods fail to maintain spectral consistency of the fused high resolution image, which is of high importance to many of the applications based on satellite data. Additionally, most conventional methods are loosely connected to the image forming physics of the satellite image, giving these methods an ad hoc feel. In this chapter, a method for image fusion of satellite images is given. The method is based on the properties of imaging physics in a statistically meaningful way. Based on our analysis, it is seen that spectral consistency is a direct consequence of imaging physics and hence guaranteed by our method. This is achieved while exploiting the high resolution single-channel data in what can be seen as a statistical optimal way, yielding a framework to which additional constraints can be added in a straight forward manner. In this chapter we exploit this framework and add some simple optimization terms for smoothing the fused image. Specifically, the method is based on the observation that any given channel of the satellites imaging device can be seen as an inner-product between the radiated light arriving at the sensor and the spectral response function of that channel. This gives a simple inner product space encompassing the relationship between the different channels as well as imposing spectral consistency. Normal distributed statistics - inducing the same norm as the above mentioned inner product - are used for regularization. This yields a framework to which additional constraints are added in a straight forward manner. Here we add a simple term to the discussed framework for smoothing the image, although more elaborate terms might be preferable. Computationally, we achieve a solution for the derived objective function via stochastic optimization, i.e., using the Metropolis algorithm in conjunction with simulated annealing. Apart from contributing with a novel analysis giving more insight into the image fusion problem, the method proposed in this chapter has been applied to images from the IKONOS satellite. These experimental results validate the proposed method.