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Fast learning of fast transforms, with guarantees (ICASSP 2022 video)

Citation Author(s):
Quoc-Tung Le, Léon Zheng, Elisa Riccietti, Rémi Gribonval
Submitted by:
Leon Zheng
Last updated:
5 May 2022 - 9:17am
Document Type:
Presentation Slides
Document Year:
2022
Event:
Presenters:
Léon Zheng
Paper Code:
MLSP-9.3
 

Approximating a matrix by a product of few sparse factors whose supports possess the butterfly structure, which is common to many fast transforms, is key to learn fast transforms and speed up algorithms for inverse problems. We introduce a hierarchical approach that recursively factorizes the considered matrix into two factors. Using recent advances on the well-posedness and tractability of the two-factor fixed-support sparse matrix factorization problem, the proposed algorithm is endowed with exact recovery guarantees. Experiments show that speed and accuracy of the factorization can be jointly improved by several orders of magnitude, compared to gradient-based optimization methods.

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