Multiframe Super-Resolution Reconstruction Using Sparse Directional Regularization

Abstract

We present a variational approach to obtain high-resolution images from multiframe low-resolution video stills. The objective functional for the variational approach consists of a data fidelity term and a regularizer. The fidelity term is formed by adaptively mimicking <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">l</i> <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">1</sub> and <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">l</i> <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sub> norms. The regularization uses the <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">l</i> <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">1</sub> norm of the framelet coefficients of a high-resolution image with a geometric tight framelet system constructed in this paper. The tight framelet system has abilities to detect multi-orientation and multi-order variations of an image. A two-phase iterative method for super-resolution reconstruction is proposed to construct a high-resolution image. The first phase is to get an approximation of the solution (i.e., the ideal image) using the steepest descent method. The second phase is to enhance the sparsity of the approximate solution by using the soft thresholding operator with variable thresholding parameters. Numerical results based on both synthetic data and real videos show that our algorithm is efficient in terms of removing visual artifacts and preserving edges in restored images.