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 22-Dec-2013 09:58:50

% Begin initialization code - DO NOT EDIT
gui_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});
end

if nargout
    [varargout{1:nargout}] = gui_mainfcn(gui_State, varargin{:});
else
    gui_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 MainForm
handles.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 structure
guidata(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 structure
varargout{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;*.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;
end
handles.file1 = fullfile(pathname, filename);
guidata(hObject, handles);
Img1 = imread(fullfile(pathname, filename));
axes(handles.axes1); 
imshow(Img1, []);


% --- 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;*.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;
end
handles.file2 = fullfile(pathname, filename);
guidata(hObject, handles);
Img2 = imread(fullfile(pathname, filename));
axes(handles.axes2);
imshow(Img2, []);

% --- 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)
if isempty(handles.file1)
    msgbox('请载入图像1！', '提示信息', 'modal');
    return;
end
if isempty(handles.file2)
    msgbox('请载入图像2！', '提示信息', 'modal');
    return;
end
[imA, map1] = imread(handles.file1);
[imB, map2] = imread(handles.file2);
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);
 
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');

% --- 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)
if isempty(handles.result)
    msgbox('请进行填充处理！', '提示信息', 'modal');
    return;
end
function [c, s] = Wave_Decompose(M, zt, wtype)

if nargin < 3
    wtype = 'haar';
end
if nargin < 2
    zt = 2;
end

三、运行结果

四、备注

版本：2014a
完整代码或代写加1564658423