Least-squares optimal interpolation for direct image super-resolution : a thesis presented in partial fulfilment of the requirements for the degree of Doctor of Philosophy in Engineering at Massey University, Palmerston North, New Zealand
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Date
2009
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Massey University
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Abstract
Image super-resolution aims to produce a higher resolution representation of a scene
from an ensemble of low-resolution images that may be warped, aliased, blurred and
degraded by noise. There are a variety of methods for performing super-resolution
described in the literature, and in general they consist of three major steps: image
registration, fusion and deblurring. This thesis proposes a novel method of performing
the first two of these steps.
The ultimate aim of image super-resolution is to produce a higher-quality image
that is visually clearer, sharper and contains more detail than the individual input
images. Machine algorithms can not assess images qualitatively and typically use a
quantitative error criterion, often least-squares. This thesis aims to optimise leastsquares
directly using a fast method, in particular one that can be implemented using
linear filters; hence, a closed-form solution is required.
The concepts of optimal interpolation and resampling are derived and demonstrated
in practice. Optimal filters optimised on one image are shown to perform nearoptimally
on other images, suggesting that common image features, such as stepedges,
can be used to optimise a near-optimal filter without requiring the knowledge
of the ground-truth output. This leads to the construction of a pulse model, which is
used to derive filters for resampling non-uniformly sampled images that result from
the fusion of registered input images. An experimental comparison shows that a 10th
order pulse model-based filter outperforms a number of methods common in the
literature.
The use of optimal interpolation for image registration linearises an otherwise nonlinear
problem, resulting in a direct solution. Experimental analysis is used to show
that optimal interpolation-based registration outperforms a number of existing
methods, both iterative and direct, at a range of noise levels and for both heavily
aliased images and images with a limited degree of aliasing. The proposed method
offers flexibility in terms of the size of the region of support, offering a good trade-off
in terms of computational complexity and accuracy of registration. Together, optimal
interpolation-based registration and fusion are shown to perform fast, direct and
effective super-resolution.
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Keywords
Image resolution, Optimal filters, Optimal interpolation, Image registration