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A Discretized Newton Flow for Time-Varying Linear Inverse Problems

  • Martin KleinsteuberEmail author
  • Simon Hawe
Conference paper
Part of the Springer Proceedings in Mathematics & Statistics book series (PROMS, volume 30)

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 that match some prior assumptions on the signal best. These are often sparsity assumptions as in the theory of Compressive Sensing. In this paper, we propose a method to track the solutions of linear inverse problems, and consider the two conceptually different approaches based on the synthesis and the analysis signal model. 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 equations, 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.

Keywords

Sparse Representation Compressive Sensing Measurement Matrix Blind Signal Synthesis Model 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Notes

Acknowledgements

This work has partially been supported by the Cluster of Excellence CoTeSys – Cognition for Technical Systems, funded by the German Research Foundation (DFG).

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Copyright information

© Springer Science+Business Media New York 2013

Authors and Affiliations

  1. 1.Department of Electrical Engineering and Information TechnologyTechnische Universität MünchenMünchenGermany

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