Super-Resolution of Wavelet-Encoded Images

Abstract

Multiview super-resolution image reconstruction (SRIR) is often cast as a resampling problem by merging non-redundant data from multiple low-resolution (LR) images on a finer high-resolution (HR) grid, while inverting the effect of the camera point spread function (PSF). One main problem with multiview methods is that resampling from nonuniform samples (provided by LR images) and the inversion of the PSF are highly nonlinear and ill-posed problems. Non-linearity and ill-posedness are typically overcome by linearization and regularization, often through an iterative optimization process, which essentially trade off the very same information (i.e. high frequency) that we want to recover. We propose a novel point of view for multiview SRIR: Unlike existing multiview methods that reconstruct the entire spectrum of the HR image from the multiple given LR images, we derive explicit expressions that show how the high-frequency spectra of the unknown HR image are related to the spectra of the LR images. Therefore, by taking any of the LR images as the reference to represent the low-frequency spectra of the HR image, one can reconstruct the super-resolution image by focusing only on the reconstruction of the high-frequency spectra. This is very much like single-image methods, which extrapolate the spectrum of one image, except that we rely on information provided by all other views, rather than by prior constraints as in single-image methods (which may not be an accurate source of information). This is made possible by deriving explicit closed-form expressions that define how the local high frequency information that we aim to recover for the reference high resolution image is related to the local low frequency information in the sequence of views. The locality of these expressions due to modeling using wavelets reduces the problem to an exact and linear set of equations that are well-posed and solved algebraically without requiring regularization or interpolation. Results and comparisons with recently published state-of-the-art methods show the superiority of the proposed solution.