Projecting on to the Multi-Layer Convolutional Sparse Coding Model

The recently proposed Multi-Layer Convolutional Sparse Coding (ML-CSC) model, consisting of a cascade of convolutional sparse layers, provides a new interpretation of Convolutional Neural Networks (CNNs). Under this framework, the forward pass in a CNN is equivalent to an algorithm that estimates ne...

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Bibliographic Details
Published in:2018 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP) pp. 6757 - 6761
Main Authors: Sulam, Jeremias, Papyant, Vardan, Romano, Yaniv, Elad, Michael
Format: Conference Proceeding
Language:English
Published: IEEE 01.04.2018
Subjects:
Atomic measurements
Coherence
Convolution
Convolutional codes
Convolutional Neural Networks
Convolutional Sparse Coding
Dictionaries
Encoding
Multilayer Pursuit
Stability analysis
Stability Guarantees
ISSN:2379-190X
Online Access:Get full text
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Summary:The recently proposed Multi-Layer Convolutional Sparse Coding (ML-CSC) model, consisting of a cascade of convolutional sparse layers, provides a new interpretation of Convolutional Neural Networks (CNNs). Under this framework, the forward pass in a CNN is equivalent to an algorithm that estimates nested sparse representation vectors from a given input signal. Despite having served as a pivotal connection between CNNs and sparse modeling, it is still unclear how to develop pursuit algorithms that serve this model exactly. In this work, we propose a new pursuit formulation by adopting a projection approach. We provide new and improved bounds on the stability of the resulting convolutional sparse representations, and we propose a multi-layer projection algorithm to retrieve them. We demonstrate this algorithm numerically, showing that it is superior to the Layered Basis Pursuit alternative in retrieving the representations of signals belonging to the ML-CSC model.
ISSN:2379-190X
DOI:10.1109/ICASSP.2018.8462552