Multi-Image Super Resolution with k-sparse Compressive Sensing and a Traditional Initial Guess
DescriptionMulti-Image Super Resolution (MISR) is the problem of recovering a high-resolution (HR) image from multiple overlapping low-resolution (LR) images. Much recent progress in MISR has investigated the use of compressive sensing (CS) as a method for reconstructing the HR image as an undersampled sparse linear system. However, older techniques for MISR have used iterative optimization from a traditional initial guess of simply averaging the overlapping images based on their fractional pixel contributions. We show that this initial guess is analogous to crudely “inverting” a non-orthogonal matrix via its transpose. As such, we integrate the traditional initial guess with CS as an initial solution to the underdetermined linear system, and empirically evaluate the ability for the traditional initial guess to improve the convergence speed of Matching Pursuit (MP) to super-resolve the HR image. We compare the convergence speed in both the native pixel basis and a wavelet basis spaces with and without the traditional initial guess. We demonstrate that CS using MP initialized with the traditional initial guess converges faster to its optimal solution than when comparably initialized from the zero vector. Furthermore, we find that faster convergence can be achieved when CS is performed in the basis space of the native pixels as opposed to wavelets so long as the initial guess is incorporated. As such, we conclude that the traditional initial guess improves the convergence speed of CS-based MISR using MP.