On Multi-Layer Basis Pursuit, Efficient Algorithms and Convolutional Neural Networks

Parsimonious representations are ubiquitous in modeling and processing information. Motivated by the recent Multi-Layer Convolutional Sparse Coding (ML-CSC) model, we herein generalize the traditional Basis Pursuit problem to a multi-layer setting, introducing similar sparse enforcing penalties at d...

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Bibliographic Details
Published in:IEEE transactions on pattern analysis and machine intelligence 2020-08, Vol.42 (8), p.1968-1980
Main Authors: Sulam, Jeremias, Aberdam, Aviad, Beck, Amir, Elad, Michael
Format: Article
Language:English
Subjects:
Algorithms
Analytical models
Artificial neural networks
Convolution
Convolutional codes
Dictionaries
First order algorithms
Fixed points (mathematics)
Iterative algorithms
Iterative methods
iterative shrinkage algorithms
Mathematical model
Mathematical models
Multi-layer convolutional sparse coding
Multilayers
network unfolding
Neural networks
Parameters
recurrent neural networks
Representations
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Summary:Parsimonious representations are ubiquitous in modeling and processing information. Motivated by the recent Multi-Layer Convolutional Sparse Coding (ML-CSC) model, we herein generalize the traditional Basis Pursuit problem to a multi-layer setting, introducing similar sparse enforcing penalties at different representation layers in a symbiotic relation between synthesis and analysis sparse priors. We explore different iterative methods to solve this new problem in practice, and we propose a new Multi-Layer Iterative Soft Thresholding Algorithm (ML-ISTA), as well as a fast version (ML-FISTA). We show that these nested first order algorithms converge, in the sense that the function value of near-fixed points can get arbitrarily close to the solution of the original problem. We further show how these algorithms effectively implement particular recurrent convolutional neural networks (CNNs) that generalize feed-forward ones without introducing any parameters. We present and analyze different architectures resulting from unfolding the iterations of the proposed pursuit algorithms, including a new Learned ML-ISTA, providing a principled way to construct deep recurrent CNNs. Unlike other similar constructions, these architectures unfold a global pursuit holistically for the entire network. We demonstrate the emerging constructions in a supervised learning setting, consistently improving the performance of classical CNNs while maintaining the number of parameters constant.
ISSN:0162-8828
1939-3539
2160-9292
DOI:10.1109/TPAMI.2019.2904255