一、简介
1974年，法国工程师J.Morlet首先提出小波变换的概念，1986年著名数学家Y.Meyer偶然构造出一个真正的小波基，并与S.Mallat合作建立了构造小波基的多尺度分析之后，小波分析才开始蓬勃发展起来。小波分析的应用领域十分广泛，在数学方面，它已用于数值分析、构造快速数值方法、曲线曲面构造、微分方程求解、控制论等。在信号分析方面的滤波、去噪声、压缩、传递等。在图像处理方面的图像压缩、分类、识别与诊断，去噪声等。本章将着重阐述小波在图像中的应用分析。
1 小波变换原理
小波分析是一个比较难的分支，用户采用小波变换，可以实现图像压缩，振动信号的分解与重构等，因此在实际工程上应用较广泛。小波分析与Fourier变换相比，小波变换是空间域和频率域的局部变换，因而能有效地从信号中提取信息。小波变换通过伸缩和平移等基本运算，实现对信号的多尺度分解与重构，从而很大程度上解决了Fourier变换带来的很多难题。
小波分析作一个新的数学分支，它是泛函分析、Fourier分析、数值分析的完美结晶；小波分析也是一种“时间—尺度”分析和多分辨分析的新技术，它在信号分析、语音合成、图像压缩与识别、大气与海洋波分析等方面的研究，都有广泛的应用。
（1）小波分析用于信号与图像压缩。小波压缩的特点是压缩比高，压缩速度快，压缩后能保持信号与图像的特征不变，且在传递中能够抗干扰。基于小波分析的压缩方法很多，具体有小波压缩，小波包压缩，小波变换向量压缩等。
（2）小波也可以用于信号的滤波去噪、信号的时频分析、信噪分离与提取弱信号、求分形指数、信号的识别与诊断以及多尺度边缘检测等。
（3）小波分析在工程技术等方面的应用概括的包括计算机视觉、曲线设计、湍流、远程宇宙的研究与生物医学方面。
2 多尺度分析
3 图像的分解和量化
4 图像压缩编码
5 图像编码评价
二、源代码
function varargout = MainForm(varargin)% MAINFORM MATLAB code for MainForm.fig%MAINFORM, by itself, creates a new MAINFORM or raises the existing%singleton*.%%H = MAINFORM returns the handle to a new MAINFORM or the handle to%the existing singleton*.%%MAINFORM('CALLBACK',hObject,eventData,handles,...) calls the local%function named CALLBACK in MAINFORM.M with the given input arguments.%%MAINFORM('Property','Value',...) creates a new MAINFORM or raises the%existing singleton*. Starting from the left, property value pairs are%applied to the GUI before MainForm_OpeningFcn gets called. An%unrecognized property name or invalid value makes property application%stop. All inputs are passed to MainForm_OpeningFcn via varargin.%%*See GUI Options on GUIDE's Tools menu. Choose "GUI allows only one%instance to run (singleton)".%% See also: GUIDE, GUIDATA, GUIHANDLES% Edit the above text to modify the response to help MainForm% Last Modified by GUIDE v2.5 01-May- 22:52:25% Begin initialization code - DO NOT EDITgui_Singleton = 1;gui_State = struct('gui_Name', mfilename, ...'gui_Singleton', gui_Singleton, ...'gui_OpeningFcn', @MainForm_OpeningFcn, ...'gui_OutputFcn', @MainForm_OutputFcn, ...'gui_LayoutFcn', [] , ...'gui_Callback', []);if nargin && ischar(varargin{1})gui_State.gui_Callback = str2func(varargin{1});endif nargout[varargout{1:nargout}] = gui_mainfcn(gui_State, varargin{:});elsegui_mainfcn(gui_State, varargin{:});end% End initialization code - DO NOT EDIT% --- Executes just before MainForm is made visible.function MainForm_OpeningFcn(hObject, eventdata, handles, varargin)% This function has no output args, see OutputFcn.% hObject handle to figure% eventdata reserved - to be defined in a future version of MATLAB% handles structure with handles and user data (see GUIDATA)% varargin command line arguments to MainForm (see VARARGIN)% Choose default command line output for MainFormhandles.output = hObject;clc; axes(handles.axes1); cla reset; box on; set(gca, 'XTickLabel', '', 'YTickLabel', '');axes(handles.axes2); cla reset; box on; set(gca, 'XTickLabel', '', 'YTickLabel', '');axes(handles.axes3); cla reset; box on; set(gca, 'XTickLabel', '', 'YTickLabel', '');% Update handles structureguidata(hObject, handles);% UIWAIT makes MainForm wait for user response (see UIRESUME)% uiwait(handles.figure1);% --- Outputs from this function are returned to the command line.function varargout = MainForm_OutputFcn(hObject, eventdata, handles) % varargout cell array for returning output args (see VARARGOUT);% hObject handle to figure% eventdata reserved - to be defined in a future version of MATLAB% handles structure with handles and user data (see GUIDATA)% Get default command line output from handles structurevarargout{1} = handles.output;% --- Executes on button press in pushbutton1.function pushbutton1_Callback(hObject, eventdata, handles)% hObject handle to pushbutton1 (see GCBO)% eventdata reserved - to be defined in a future version of MATLAB% handles structure with handles and user data (see GUIDATA)clc; axes(handles.axes1); cla reset; box on; set(gca, 'XTickLabel', '', 'YTickLabel', '');axes(handles.axes2); cla reset; box on; set(gca, 'XTickLabel', '', 'YTickLabel', '');axes(handles.axes3); cla reset; box on; set(gca, 'XTickLabel', '', 'YTickLabel', '');handles.file1 = [];handles.file2 = [];handles.result = [];[filename, pathname] = uigetfile({'*.jpg;*.bmp;*.tif;*.png;*.gif', 'All Image Files';...'*.*', 'All Files' }, '选择图像1', ...fullfile(pwd, 'images\\实验图像1\\a.tif'));if isequal(filename, 0)return;endhandles.file1 = fullfile(pathname, filename);Img1=imread(fullfile(pathname, filename));% I=rgb2gray(Img);% Img1 = imresize(I,[240,320]);axes(handles.axes1); imshow(Img1, []);handles.Img1 =Img1 ;guidata(hObject, handles);% --- Executes on button press in pushbutton2.function pushbutton2_Callback(hObject, eventdata, handles)% hObject handle to pushbutton2 (see GCBO)% eventdata reserved - to be defined in a future version of MATLAB% handles structure with handles and user data (see GUIDATA)[filename, pathname] = uigetfile({'*.jpg;*.bmp;*.tif;*.png;*.gif', 'All Image Files';...'*.*', 'All Files' }, '选择图像2', ...fullfile(pwd, 'images\\实验图像1\\b.tif'));if isequal(filename, 0)return;endhandles.file2 = fullfile(pathname, filename);Img2 =imread(fullfile(pathname, filename));axes(handles.axes2);imshow(Img2, []);handles.Img2 =Img2 ;guidata(hObject, handles);% --- Executes on button press in pushbutton3.function pushbutton3_Callback(hObject, eventdata, handles)% hObject handle to pushbutton3 (see GCBO)% eventdata reserved - to be defined in a future version of MATLAB% handles structure with handles and user data (see GUIDATA)%% 小波变换算法imA = handles.Img1;imB = handles.Img2;M1 = double(imA) / 256;M2 = double(imB) / 256;zt = 2;wtype = 'haar';[c0, s0] = Wave_Decompose(M1, zt, wtype);[c1, s1] = Wave_Decompose(M2, zt, wtype);Coef_Fusion = Fuse_Process(c0, c1, s0, s1);Y = Wave_Reconstruct(Coef_Fusion, s0, wtype);handles.result = im2uint8(mat2gray(Y));guidata(hObject, handles);msgbox('小波融合处理完毕！', '提示信息', 'modal');% if isempty(handles.result)%msgbox('请进行填充处理！', '提示信息', 'modal');%return;% endaxes(handles.axes3); imshow(handles.result, []);title('小波变换融合处理结果')% --- Executes on button press in pushbutton4.function pushbutton4_Callback(hObject, eventdata, handles)% hObject handle to pushbutton4 (see GCBO)% eventdata reserved - to be defined in a future version of MATLAB% handles structure with handles and user data (see GUIDATA)%% 拉普拉斯金字塔算法addpath('./拉普拉斯金字塔算法图像融合')imA = handles.Img1;imB = handles.Img2;% im1 = double(imA) / 256;% im2= double(imB) / 256;im1 = double(imA);im2 = double(imB);%%%拉普拉斯滤波器w = [1 4 6 4 1; 4 16 24 16 4; 6 24 36 24 6; 4 16 24 16 4; 1 4 6 4 1]/256;G = cell(1,5);H = cell(1,5);I = cell(1,5);G{1} = im1;%第一层为原图像H{1} = im2;function Y = Wave_Reconstruct(Coef_Fusion, s, wtype)if nargin < 3endY = waverec2(Coef_Fusion, s, wtype);KK = size(c1);Coef_Fusion = zeros(1, KK(2));Coef_Fusion(1:s1(1,1)*s1(1,2)) = (c0(1:s1(1,1)*s1(1,2))+c1(1:s1(1,1)*s1(1,2)))/2; MM1 = c0(s1(1,1)*s1(1,2)+1:KK(2));MM2 = c1(s1(1,1)*s1(1,2)+1:KK(2));mm = (abs(MM1)) > (abs(MM2));Y = (mm.*MM1) + ((~mm).*MM2);
三、运行结果
四、matlab版本及参考文献
1 matlab版本
a
2 参考文献
[1] 蔡利梅.MATLAB图像处理——理论、算法与实例分析[M].清华大学出版社，.
[2]杨丹,赵海滨,龙哲.MATLAB图像处理实例详解[M].清华大学出版社，.
[3]周品.MATLAB图像处理与图形用户界面设计[M].清华大学出版社，.
[4]刘成龙.精通MATLAB图像处理[M].清华大学出版社，.
