AdaFrame swMATH ID: 25550 Software Authors: Tai, Cheng; E, Weinan Description: Multiscale adaptive representation of signals. I: The basic framework. 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. Homepage: http://jmlr.org/papers/volume17/15-072/15-072.pdf Keywords: AdaFrame; dictionary learning; wavelet frames/bi-frames Related Software: Adam; ASTRA; AlexNet; PDE-Net; MgNet; V-Net; torchdiffeq; U-Net; SegNet; AdaGrad; ImageNet; KSVD-Box; MNIST Cited in: 4 Publications Standard Articles 1 Publication describing the Software, including 1 Publication in zbMATH Year Multiscale adaptive representation of signals. I: The basic framework. Zbl 1391.94406Tai, Cheng; E, Weinan 2016 all top 5 Cited by 9 Authors 3 Dong, Bin 1 E, Weinan 1 Shen, Ziju 1 Tai, Cheng 1 Wang, Yufei 1 Wu, Dufan 1 Yang, Xu 1 Zhan, Ruohan 1 Zhang, Haimiao Cited in 4 Serials 1 Journal of Machine Learning Research (JMLR) 1 Inverse Problems and Imaging 1 SIAM Journal on Imaging Sciences 1 Journal of the Operations Research Society of China Cited in 5 Fields 4 Computer science (68-XX) 3 Biology and other natural sciences (92-XX) 2 Numerical analysis (65-XX) 1 Operations research, mathematical programming (90-XX) 1 Information and communication theory, circuits (94-XX) Citations by Year