Algorithms for dictionary learning aim to learn a dictionary under which training data have sparse representations. This paper addresses the dictionary update sub-problem, the goal of which is to update the dictionary and the corresponding sparse coefficients given a fixed sparsity pattern. It is a non-convex bilinear inverse problem, and hence challenging to solve. Inspired by a recent work by Ling and Strohmer, we re-formulate the dictionary update problem as a linear least squares problem, which is convex and easy to solve. Necessary bounds on the number of training samples required for a unique solution are derived when exact sparsity pattern is known. Further, for dictionary update with unknown sparsity patterns, an efficient iterative algorithm based on total least squares is developed. Embedding the new dictionary update procedure into an overall dictionary learning algorithm achieves better numerical performance compared to state of the art algorithms.
|Title of host publication
|2019 IEEE International Conference on Acoustics, Speech, and Signal Processing, ICASSP 2019 - Proceedings
|Institute of Electrical and Electronics Engineers Inc.
|Number of pages
|Published - 1 May 2019
|44th IEEE International Conference on Acoustics, Speech, and Signal Processing, ICASSP 2019 - Brighton, United Kingdom
Duration: 12 May 2019 → 17 May 2019
|44th IEEE International Conference on Acoustics, Speech, and Signal Processing, ICASSP 2019
|12/05/2019 → 17/05/2019
- Bilinear inverse problem
- dictionary learning
- dictionary update
- linear least squares
- total least squares