Wavelet-Based Super-Resolution Reconstruction: Theory and Algorithm

We present a theoretical analysis and a new algorithm for the problem of super-resolution imaging: the reconstruction of HR (high-resolution) images from a sequence of LR (low-resolution) images. Super-resolution imaging entails solutions to two problems. One is the alignment of image frames. The other is the reconstruction of a HR image from multiple aligned LR images. Our analysis of the latter problem reveals insights into the theoretical limits of super-resolution reconstruction. We find that at best we can reconstruct a HR image blurred by a specific low-pass filter. Based on the analysis we present a new wavelet-based iterative reconstruction algorithm which is very robust to noise. Furthermore, it has a computationally efficient built-in denoising scheme with a nearly optimal risk bound. Roughly speaking, our method could be described as a better-conditioned iterative back-projection scheme with a fast and optimal regularization criteria in each iteration step. Experiments with both simulated and real data demonstrate that our approach has significantly better performance than existing super-resolution methods. It has the ability to remove even large amounts of mixed noise without creating smoothing artifacts.