A Linear Well-Posed Solution To Recover High-Frequency Information For Super Resolution Image Reconstruction

Multiview super resolution image reconstruction (SRIR) is often cast as a resampling problem by merging non-redundant data from multiple images on a finer 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 multiple 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 different point of view for multiview SRIR that is very much like single-image methods which extrapolate the spectrum of one image selected as reference from among all views. However, for this, the proposed method relies on information provided by all other views, rather than 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

Super Resolution of Wavelet-Encoded Images and Videos

In this dissertation, we address the multiframe super resolution reconstruction problem for wavelet-encoded images and videos. The goal of multiframe super resolution is to obtain one or more high resolution images by fusing a sequence of degraded or aliased low resolution images of the same scene. Since the low resolution images may be unaligned, a registration step is required before super resolution reconstruction. Therefore, we first explore in-band (i.e. in the wavelet-domain) image registration; then, investigate super resolution. Our motivation for analyzing the image registration and super resolution problems in the wavelet domain is the growing trend in wavelet-encoded imaging, and wavelet-encoding for image/video compression. Due to drawbacks of widely used discrete cosine transform in image and video compression, a considerable amount of literature is devoted to wavelet-based methods. However, since wavelets are shift-variant, existing methods cannot utilize wavelet subbands efficiently. In order to overcome this drawback, we establish and explore the direct relationship between the subbands under a translational shift, for image registration and super resolution. We then employ our devised in-band methodology, in a motion compensated video compression framework, to demonstrate the effective usage of wavelet subbands. Super resolution can also be used as a post-processing step in video compression in order to decrease the size of the video files to be compressed, with downsampling added as a pre-processing step. Therefore, we present a video compression scheme that utilizes super resolution to reconstruct the high frequency information lost during downsampling. In addition, super resolution is a crucial post-processing step for satellite imagery, due to the fact that it is hard to update imaging devices after a satellite is launched. Thus, we also demonstrate the usage of our devised methods in enhancing resolution of pansharpened multispectral images