A new image decomposition and reconstruction approach -- adaptive fourier decomposition

© Springer International Publishing Switzerland 2015. Fourier has been a powerful mathematical tool for representing a signal into an expression consist of sin and cos. Recently a new developed signal decomposition theory is proposed by Pro. Tao Qian named Adaptive Fourier Decomposition, which has the advantage in time frequency over Fourier decomposition and without the need for a fixed window size problem such as short-time frequency transform. Studies show that AFD can fast decompose signals into positive-frequency functions with good analytical properties. In this paper we apply AFD into image decomposition and reconstruction area first time in the literature, which shows a promising result and gives the fundamental prospect for image compression

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