TRACKING SOLUTIONS OF TIME VARYING LINEAR INVERSE PROBLEMS

Martin Kleinsteuber, Simon Hawe

2012

Abstract

The reconstruction of a signal from only a few measurements, deconvolving, or denoising are only a few interesting signal processing applications that can be formulated as linear inverse problems. Commonly, one overcomes the ill-posedness of such problems by finding solutions which best match some prior assumptions. These are often sparsity assumptions as in the theory of Compressive Sensing. In this paper, we propose a method to track solutions of linear inverse problems. We assume that the corresponding solutions vary smoothly over time. A discretized Newton flow allows to incorporate the time varying information for tracking and predicting the subsequent solution. This prediction requires to solve a linear system of equation, which is in general computationally cheaper than solving a new inverse problem. It may also serve as an additional prior that takes the smooth variation of the solutions into account, or, as an initial guess for the preceding reconstruction. We exemplify our approach with the reconstruction of a compressively sampled synthetic video sequence.

Paper Citation

in Harvard Style

Kleinsteuber M. and Hawe S. (2012). TRACKING SOLUTIONS OF TIME VARYING LINEAR INVERSE PROBLEMS . In Proceedings of the 1st International Conference on Pattern Recognition Applications and Methods - Volume 1: ICPRAM, ISBN 978-989-8425-98-0, pages 253-257. DOI: 10.5220/0003864102530257

in Bibtex Style

@conference{icpram12,
author={Martin Kleinsteuber and Simon Hawe},
title={TRACKING SOLUTIONS OF TIME VARYING LINEAR INVERSE PROBLEMS},
booktitle={Proceedings of the 1st International Conference on Pattern Recognition Applications and Methods - Volume 1: ICPRAM,},
year={2012},
pages={253-257},
publisher={SciTePress},
organization={INSTICC},
doi={10.5220/0003864102530257},
isbn={978-989-8425-98-0},
}

in EndNote Style

TY - CONF
JO - Proceedings of the 1st International Conference on Pattern Recognition Applications and Methods - Volume 1: ICPRAM,
TI - TRACKING SOLUTIONS OF TIME VARYING LINEAR INVERSE PROBLEMS
SN - 978-989-8425-98-0
AU - Kleinsteuber M.
AU - Hawe S.
PY - 2012
SP - 253
EP - 257
DO - 10.5220/0003864102530257