We propose a simple preconditioning method for accelerating the solution of edge-preserving image super-resolution (SR) problems in which a linear shift-invariant point spread function is employed. Our technique involves reordering the high-resolution (HR) pixels in a similar manner to what is done in preconditioning methods for quadratic SR formulations. However, due to the edge preserving requirements, the Hessian matrix of the cost function varies during the minimization process. We develop an efficient update scheme for the preconditioner in order to cope with this situation. Unlike some other acceleration strategies that round the displacement values between the low-resolution (LR) images on the HR grid, the proposed method does not sacrifice the optimality of the observation model. In addition, we describe a technique for preconditioning SR problems involving rational magnification factors. The use of such factors is motivated in part by the fact that, under certain circumstances, optimal SR zooms are nonintegers. We show that, by reordering the pixels of the LR images, the structure of the problem to solve is modified in such a way that preconditioners based on circulant operators can be used.

Image restoration is an ill-posed problem that must be regularized in order to reduce noise amplification in the restored image. Although quadratic penalty terms allow for fast restoration algorithms based on the fast Fourier transform (FFT), they often lead to images whose discontinuities are not well preserved. On the other hand, edge-preserving penalty terms can produce better results at the expense of computational efficiency. A restoration technique exploiting the Woodbury matrix identity was recently presented. However, its performance decreases when the number of discontinuities becomes significant. To overcome this problem, we propose a simple preconditioner to be employed in conjunction with the preconditioned nonlinear conjugate gradient method. Experiments are employed to demonstrate the effectiveness of our approach.

Super-resolution (SR) is a technique that generates a high-resolution (HR) image from a set of low-resolution (LR) ones. Previous preconditioning methods for SR did not consider the case of rational magnification factors. In this paper, a method for preconditioning SR problems involving such factors is presented. We show that by reordering the pixels of the observed LR images, the structure of the linear problem to solve is modified in such a way that preconditioners based on circulant operators can be used. Simulations with magnification factors of practical interest demonstrate the effectiveness of our approach.

Temporal superresolution produces a video sequence of high temporal resolution (HTR), i.e. frame rate, from a set of video sequences of low temporal resolution (LTR). A method for preconditioning large systems of linear equations arising in temporal video superresolution problems is presented. We show that circulant block preconditioners can accelerate the convergence of iterative techniques such as the conjugate gradient method when solving such problems. Simulations demonstrate the effectiveness of our approach.