Phase Diagram and Approximate Message Passing for Blind Calibration and Dictionary Learning

Abstract

We consider dictionary learning and blind calibration for signals and matrices created from a random ensemble. We study the mean-squared error in the limit of large signal dimension using the replica method and unveil the appearance of phase transitions delimiting impossible, possible-but-hard and possible inference regions. We also introduce an approximate message passing algorithm that asymptotically matches the theoretical performance, and show through numerical tests that it performs very well, for the calibration problem, for tractable system sizes.

5 pages

References in corpus (4)

• Probabilistic Reconstruction in Compressed Sensing: Algorithms, Phase Diagrams, and Threshold Achieving Matrices
• Local stability and robustness of sparse dictionary learning in the presence of noise
• Compressed Sensing under Matrix Uncertainty: Optimum Thresholds and Robust Approximate Message Passing
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