Multiresolution fusion in remotely sensed images: Use of Gibbs prior and PSO optimization

Abstract

In this paper, we propose a model based approach for multi-resolution fusion of remotely sensed images. We obtain a high spatial resolution (HR) and high spectral resolution multi-spectral (MS) image using a high spatial resolution Panchromatic (Pan) image and a low spatial resolution (LR) MS image. This problem is ill-posed since we need to predict the missing high resolution pixels in each of the MS images and requires proper regularization in order to get better solution. Each of the low spatial resolution MS images is modeled as aliased and noisy versions of the corresponding fused HR image. The decimation matrix entries are estimated using the Pan data and the MS image. The prior for regularization is obtained by modeling the texture of the HR MS image as a Markov random field (MRF) that can be expressed as a joint probability density function (PDF) using the Gibbs distribution (GD). In our work we make inference about this joint PDF by using the available high spatial resolution Pan image. As proposed in a set of filters is chosen from a filter bank to obtain the estimates of the marginal distributions of the GD as the histograms of the filtered outputs. Our final cost function consists of a data fitting term and a prior term which is then minimized to obtain the high spatial and spectral resolution MS image. The process is repeated for each of the MS images. The optimization is done using Particle swarm optimization (PSO) which can be implemented in parallel mode in order to reduce the time complexity. The main advantages of our approach are: 1) It requires no registration between Pan and MS images; 2) The spectral distortion is minimum as we are not using the actual Pan digital numbers; 3) The method can be applied to the fusion of Pan and MS images captured at different times and using different sensors. The drawback of the proposed method is its time complexity as one cannot use fast optimization approaches for minimization. However, we have attempted to reduce the computational complexity by using PSO. We demonstrate the effectiveness of our approach by conducting experiments on real satellite data captured by Quickbird satellite.