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Analysis of fast structured dictionary learning.

Saiprasad Ravishankar¹, Anna Ma², Deanna Needell³

¹Department of Computational Mathematics, Science and Engineering, Department of Biomedical Engineering, Michigan State University, East Lansing, MI 48824, USA.

Information and Inference : a Journal of the IMA

|December 21, 2020

Summary

This summary is machine-generated.

This study analyzes alternating minimization for learning structured unitary sparsifying operators. The research demonstrates local linear convergence to the data

Keywords:

alternating minimization convergence guarantees dictionary learning fast algorithms generative models sparse representations transform learning

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Area of Science:

Signal Processing
Image Processing
Machine Learning

Background:

Sparsity-based models are crucial in signal and image processing.
Data-driven dictionary and sparsifying transform learning offer superior feature extraction compared to analytical models.
Alternating optimization algorithms are widely used for learning these data-driven models.

Purpose of the Study:

To provide a convergence analysis for alternating minimization applied to structured unitary sparsifying operator learning.
To establish conditions for local linear convergence of the algorithm.
To validate the findings through analysis and numerical simulations.

Main Methods:

Focus on alternating minimization for structured unitary sparsifying operator learning.
Conduct theoretical convergence analysis under mild assumptions.
Perform numerical simulations using standard probabilistic data models.

Main Results:

The algorithm generally converges to critical points.
Under mild assumptions, local linear convergence to the underlying sparsifying model is established.
Numerical simulations confirm that the assumptions hold for typical data models.
The algorithm demonstrates robustness to initialization.

Conclusions:

The developed convergence analysis provides theoretical guarantees for the alternating minimization algorithm in sparsifying operator learning.
The findings suggest the practical applicability and reliability of the algorithm for learning effective data-driven models.
The robustness to initialization is a key practical advantage for real-world applications.