Aliasing is Good for You: Joint Registration and Reconstruction for Super-Resolution

Abstract

In many applications, the sampling frequency is limited by the physical characteristics of the components: the pixel pitch, the rate of the A/D converter, etc. A low-pass filter is then often applied before the sampling operation to avoid aliasing. However, when multiple copies are available, it is possible to use the information that is inherently present in the aliasing to reconstruct a higher resolution signal. If the different copies have unknown relative offsets, this is a non-linear problem in the offsets and the signal coefficients. They are not easily separable in the set of equations describing the super-resolution problem. Thus, we perform joint registration and reconstruction from multiple unregistered sets of samples. We give a mathematical formulation for the problem when there are M sets of N samples of a signal that is described by L expansion coefficients. We prove that the solution of the registration and reconstruction problem is generically unique if M N >= L + M - 1. We describe two subspace-based methods to compute this solution. Their complexity is analyzed, and some heuristic methods are proposed. Finally, some numerical simulation results on one and two-dimensional signals are given to show the performance of these methods.

Reference

Vandewalle, Patrick and Sbaiz, Luciano and Vandewalle, Joos and Vetterli, Martin (2006) Aliasing is Good for You: Joint Registration and Reconstruction for Super-Resolution. Technical Report, Ecole Polytechnique Fédérale de Lausanne, Switzerland. [BibTeX]

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Acknowledgements

The work presented in this paper was supported by the National Competence Center in Research on Mobile Information and Communication Systems (NCCR-MICS), a center supported by the Swiss National Science Foundation under grant number 5005-67322. The work of Joos Vandewalle was supported by the Research Council KULeuven: GOA-Ambiorics and Center of Excellence on Optimization in Engineering; the Belgian Federal Science Policy Office : IUAP V-22.

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Tested Configurations

Matlab 7.0.1 on Linux

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