In this chapter, we introduce a concept called self-similarity and use the same for obtaining the initial fused image. We also use a new prior called Gabor prior for regularizing the solution. In Chapter 4, degradation matrix entries were estimated by modelling the relationship between the Pan-derived initial estimate of the fused MS image and the LR MS image. This may lead to inaccurate estimate of the final fused image since we make use of the Pan data suffering from low spectral resolution in getting the initial estimate. However, if we derive the initial fused image using the available LR MS image, which has high spectral resolution, mapping between LR and HR would be better and the derived degradation matrix entries are more accurate. This makes the estimated degradation matrix better represent the aliasing since we now have an initial estimate that has both high spatial and spectral resolutions. To do this, we need to obtain the initial estimate using only the available LR MS image since the true fused image is not available. We perform this by using the property of natural images that the probability of the availability of redundant information in the image and its downsampled versions is high [89]. We exploit this self-similarity in the LR observation and the sparse representation theory in order to obtain the initial estimate of the fused image. Finally, we solve the Pan-sharpening or multi-resolution image fusion problem by using a model based approach in which we regularize the solution by proposing a new prior called the Gabor prior.

Related Work

Before we discuss our proposed approach, we review few works carried out by researchers on image fusion that use compressive sensing (CS) theory since our work also uses sparse representation involved in CS. Li and Yang [143] applied CS to obtain the fusion of remotely sensed images in which a dictionary was constructed from sample images having high spatial resolution. They obtained the fused image as a linear combination of HR patches available in the dictionary. The performance of their method depends on the availability of high resolution MS images that have spectral components similar to that of the test image.