Efficient and Robust Compressed Sensing using High-Quality Expander Graphs
Sina Jafarpour, Weiyu Xu, Babak Hassibi, Robert Calderbank

TL;DR
This paper improves compressed sensing algorithms using high-quality expander graphs, reducing recovery iterations to O(k) and enabling efficient, robust signal reconstruction with fewer measurements and faster algorithms.
Contribution
It introduces a method leveraging expander graphs with high expansion coefficients to significantly reduce recovery iterations and improve efficiency in compressed sensing.
Findings
Recovery can be achieved in at most 2k iterations.
Number of iterations can be made arbitrarily close to k.
The method is robust and extends to approximate sparse signals.
Abstract
Expander graphs have been recently proposed to construct efficient compressed sensing algorithms. In particular, it has been shown that any -dimensional vector that is -sparse (with ) can be fully recovered using measurements and only simple recovery iterations. In this paper we improve upon this result by considering expander graphs with expansion coefficient beyond 3/4 and show that, with the same number of measurements, only recovery iterations are required, which is a significant improvement when is large. In fact, full recovery can be accomplished by at most very simple iterations. The number of iterations can be made arbitrarily close to , and the recovery algorithm can be implemented very efficiently using a simple binary search tree. We also show that by tolerating a small penalty on the number of measurements,…
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Taxonomy
TopicsSparse and Compressive Sensing Techniques · Microwave Imaging and Scattering Analysis · Distributed Sensor Networks and Detection Algorithms
