Multiresolution fusion using contourlet transform based edge learning

In this paper, we propose a new approach for multi-resolution fusion of remotely sensed images based on the contourlet transform based learning of high frequency edges. We obtain a high spatial resolution (HR) and high spectral resolution multi-spectral (MS) image using the available high spectral but low spatial resolution MS image and the Panchromatic (Pan) image. Since we need to predict the missing high resolution pixels in each of the MS images the problem is posed in a restoration framework and is solved using maximum a posteriori (MAP) approach. Towards this end, we first obtain an initial approximation to the HR fused image by learning the edges from the Pan image using the contourlet transform. A low resolution model is used for the MS image formation and the texture of the fused image is modeled as a homogeneous Markov random field (MRF) prior. We then optimize the cost function which is formed using the data fitting term and the prior term and obtain the fused image, in which the edges correspond to those in the initial HR approximation. The procedure is repeated for each of the MS images. The advantage of the proposed method lies in the use of simple gradient based optimization for regularization purposes while preserving the discontinuities. This in turn reduces the computational complexity since it avoids the use of computationally taxing optimization methods for discontinuity preservation. Also, the proposed method has minimum spectral distortion as we are not using the actual Pan digital numbers, instead learn the texture using contourlet coefficients. We demonstrate the effectiveness of our approach by conducting experiments on real satellite data captured by Quickbird satellite.