TY - JOUR
T1 - Multiscale adaptive representation of signals
T2 - I. The basic framework
AU - Tai, Cheng
AU - E, Weinan
N1 - Funding Information:
This work is supported in part by the 973 program of the Ministry of Science and Technology of China, the Major Program of NNSFC under grant 91130005 and an ONR grant N00014-13-1-0338.
Publisher Copyright:
©2016 Cheng Tai and Weinan E.
PY - 2016/8/1
Y1 - 2016/8/1
N2 - We introduce a framework for designing multi-scale, adaptive, shift-invariant frames and bi-frames for representing signals. The new framework, called AdaFrame, improves over dictionary learning-based techniques in terms of computational efficiency at inference time. It improves classical multi-scale basis such as wavelet frames in terms of coding efficiency. It provides an attractive alternative to dictionary learning-based techniques for low level signal processing tasks, such as compression and denoising, as well as high level tasks, such as feature extraction for object recognition. Connections with deep convolutional networks are also discussed. In particular, the proposed framework reveals a drawback in the commonly used approach for visualizing the activations of the intermediate layers in convolutional networks, and suggests a natural alternative.
AB - We introduce a framework for designing multi-scale, adaptive, shift-invariant frames and bi-frames for representing signals. The new framework, called AdaFrame, improves over dictionary learning-based techniques in terms of computational efficiency at inference time. It improves classical multi-scale basis such as wavelet frames in terms of coding efficiency. It provides an attractive alternative to dictionary learning-based techniques for low level signal processing tasks, such as compression and denoising, as well as high level tasks, such as feature extraction for object recognition. Connections with deep convolutional networks are also discussed. In particular, the proposed framework reveals a drawback in the commonly used approach for visualizing the activations of the intermediate layers in convolutional networks, and suggests a natural alternative.
KW - AdaFrame
KW - Dictionary learning
KW - Wavelet frames/Bi-frames
UR - http://www.scopus.com/inward/record.url?scp=84989177808&partnerID=8YFLogxK
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M3 - Article
AN - SCOPUS:84989177808
SN - 1532-4435
VL - 17
SP - 1
EP - 38
JO - Journal of Machine Learning Research
JF - Journal of Machine Learning Research
ER -