Multiscale Adaptive Representation of Signals: I. The Basic Framework
This work addresses signal processing tasks for applications in compression and object recognition, but appears incremental as it builds on existing multi-scale and dictionary learning methods.
The authors introduced AdaFrame, a framework for designing multi-scale, adaptive, shift-invariant frames and bi-frames to represent signals, improving computational efficiency over dictionary learning and coding efficiency over wavelet frames for tasks like compression, denoising, and feature extraction.
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.