Image Fusion using Gaussian Mixture Models

In recent years, a number of works have demonstrated that processing images using patch-based features provides more robust results than their pixel based counterparts. A contributing factor to their success is that image patches can be expressed sparsely in appropriately defined dictionaries, and these dictionaries can be tuned to a variety of applications. Yu, Sapiro and Mallat [24] demonstrated that estimating image patches from multivariate Gaussians is equivalent to finding sparse representations in a structured overcomplete PCA-based dictionary. Furthermore, their model reduces to a straightforward piecewise linear estimator (PLE). In this work we show how a similar PLE can be formulated to fuse images with various linear degradations and different levels of additive noise. Furthermore, the solution can be interpreted as a sparse patch-based representation in an appropriately defined PCA dictionary. The model can also be adapted to better preserve edges and increase PSNR by adapting the level of smoothing to each local patch.