可自適應性模型分解運用在信號分析和多尺度影像分解

Abstract

自適應模式分解方法為任意複雜信號分析提供了有效的方法，它們既不需要建構任何先驗基礎來匹配信號特徵結構，也不需要施加額外的任何約束，可以自適應突出顯示信號的局部特徵。因此，這些方法可以從非穩態且非線性的信號中自適應地表示為幾個基礎的單分量和殘餘的疊加，再利用每個單分量分解出正確的瞬時頻率和瞬時幅值。因此基於自適應信號分解方法為全數據驅動的處理方式越來越受到圖像處理的關注。圖像被認為是二維非穩態和非線性的多尺度複雜信號，對於準確的自適應圖像分析和紋理識別是有困難度的。因此，許多研究人員已經開始研究如何將一維自適應分解信號方法擴展為分解多尺度圖像的自適應方法，並將其應用於紋理提取和圖像濾波。本文主旨在比較經驗模式分解（EMD）和變分模式分解（VMD）以及局部均值分解（LMD）三種自適應模式分解方法的信號處理能力和二維多尺度影像分析的差異。其中，我們提出了基於局部均值分解的二維局部均值分解（2D LMD）方法，詳細討論一維擴展到二維的演算法會遇到的問題和解決辦法，最後在實驗結果中顯示二維局部均值分解的可行性和有效性。

Adaptive mode decomposition methods provide effective methods for arbitrary complex signal analysis. They neither need to construct any a priori basis to match the signal characteristic structure, nor impose any constraints. They adaptive highlight local features of a signal. Thus, they can be adaptively represented from any signal as a superposition of several mono-components and a residue. Each mono-component decomposition correctly estimates its instantaneous frequency and instantaneous amplitude. However, adaptive signal decomposition methods based on full data-driven methods are increasingly receiving attention from image processing. Images are considered as two-dimensional unsteady and nonlinear and multi-scale complex signals, and accurate adaptive analysis of image and texture recognition is always difficult. Therefore, many researchers have begun to study how to extend the one-dimensional adaptive decomposition signal method into an adaptive method to decompose multi-scale images and apply them to texture extraction and image filtering. This paper aims to compare signal processing capabilities and the 2D multi-scale image analysis capabilities through the empirical mode decomposition (EMD) and the variational mode decomposition (VMD) and the local mean decomposition (LMD). Among them, we propose the two-dimensional local mean decomposition (2D LMD) based on the LMD, and discuss the problem of extending the algorithm to the two-dimensional algorithm in detail. The feasibility and effectiveness of 2D LMD are shown in the experimental results.