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

Abstract

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.