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Bayesian online compressed sensing.

Paulo V Rossi1, Yoshiyuki Kabashima2, Jun-Ichi Inoue3

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Summary
This summary is machine-generated.

This study introduces an online sparse signal recovery algorithm using mean field approximation. The algorithm achieves optimal performance similar to offline methods with Gaussian noise but may differ in noiseless scenarios due to computational constraints.

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Area of Science:

  • Signal processing
  • Machine learning
  • Information theory

Background:

  • Sparse signal recovery is crucial in various fields.
  • Existing methods often require offline processing.
  • Online algorithms offer real-time processing capabilities.

Purpose of the Study:

  • To develop and analyze an online algorithm for sparse signal recovery.
  • To evaluate its performance against optimal offline methods.
  • To understand the impact of computational cost on recovery performance.

Main Methods:

  • Utilized mean field approximation of the Bayes recursion formula.
  • Developed a computationally efficient online signal recovery algorithm.
  • Analyzed algorithm performance in both noisy and noiseless conditions.

Main Results:

  • The online algorithm achieves performance asymptotically close to the optimal offline method with Gaussian noise.
  • Differences in computational costs can lead to performance gaps in noiseless scenarios.
  • The algorithm's computational cost is linear with signal length per update.

Conclusions:

  • The proposed online algorithm provides an efficient approach to sparse signal recovery.
  • Performance is robust in the presence of Gaussian noise.
  • Computational cost is a critical factor influencing performance, especially in noiseless settings.