A fast approach for edge preserving super-resolution

In this paper we propose a fast approach for edge preserving super-resolution (SR) based on learning of contourlet coefficients. Given a low resolution test image, we first obtain an initial HR estimate i.e., a close approximation to SR image by learning the contourlet coefficients from a training database consisting of low resolution (LR) and high resolution (HR) images. The final SR image is obtained by using a regularization framework in which both the SR and the LR images are modeled as separate homogeneous Markov Random Fields (MRFs). The LR image formation process is modeled as a decimated and noisy version of the SR image and the final cost function is minimized by using a gradient descent method. Novelty of our approach lies in preserving the edges in the final SR image while using a non edge preserving MRF prior. This is definitely advantageous since it avoids the use of discontinuity preserving prior and hence the computationally taxing optimization methods. The edges in the final SR correspond to those learned from the initial HR estimate. The use of MRF on the low resolution image imposes an additional constraint on the final solution and hence we expect a better solution. In addition, we use the initial HR image for estimating the decimation matrix entries as well as for learning the corresponding MRF parameter. We show the effectiveness of the proposed approach by conducting the experiments on images captured using a real camera.