Recently, many researchers have attempted to solve the problem of multi-resolution image fusion by using model based approaches, with emphasis on improving the fused image quality and reducing color distortion [273, 121]. They model the low resolution (LR) MS image as a blurred and noisy version of its ideal high resolution (HR) fused image. Solving the problem of fusion by the model based approach is desirable since the aliasing present due to undersampling of the MS image can be taken care of while modelling. Fusion using the interpolation of MS images and edge-preserving filters as given in Chapter 3 do not consider the effect of aliasing which is due to undersampling of MS images. The aliasing in the acquired image causes distortion and, hence, there exists degradation in the LR MS image. In this chapter, we propose a model based approach in which a learning based method is used to obtain the required degradation matrix that accounts for aliasing. Using the proposed model, the final solution is obtained by considering the model as an inverse problem. The proposed approach uses sub-sampled as well as non sub-sampled contourlet transform based learning and a Markov random field (MRF) prior for regularizing the solution.

Previous Works

As stated earlier, many researchers have used the model based approach for fusion with the emphasis on improving fusion quality and reducing color distortion [6, 149, 105, 273, 143, 116, 283, 76, 121]. Aanaes et al. [6] have proposed a spectrally consistent method for pixel-level fusion based on the model of the imaging sensor. The fused image is obtained by optimizing an energy function consisting of a data term and a prior term by using pixel neighborhood regularization. Image fusion based on a restoration framework is suggested by Li and Leung [149] who modelled the LR MS image as a blurred and noisy version of its ideal. They also modelled the Pan image as a linear combination of true MS images. The final fused image was obtained by using a constrained least squares (CLS) framework. The same model with maximum a posteriori (MAP) framework was used by Hardie et al. and Zhang et al. [105, 273]. Hardie et al. [105] used the model based approach to enhance the hyper-spectral images using the Pan image.