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合做创建了构造小波基的多尺度分析以后,小波分析才开始蓬勃发展起来。小波分析的应用领域十分普遍,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,能够实现图像压缩,振动信号的分解与重构等,所以在实际工程上应用较普遍。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,于是能有效地从信号中提取信息。小波变换经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变换带来的不少难题。
小波分析做一个新的数学分支,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,都有普遍的应用。
(1)小波分析用于信号与图像压缩。小波压缩的特色是压缩比高,压缩速度快,压缩后能保持信号与图像的特征不变,且在传递中可以抗干扰。基于小波分析的压缩方法不少,具体有小波压缩,小波包压缩,小波变换向量压缩等。
(2)小波也能够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归纳的包括计算机视觉、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markdown
function varargout = mainGUI(varargin) % MAINGUI MATLAB code for mainGUI.fig % MAINGUI, by itself, creates a new MAINGUI or raises the existing % singleton*. % % H = MAINGUI returns the handle to a new MAINGUI or the handle to % the existing singleton*. % % MAINGUI('CALLBACK',hObject,eventData,handles,...) calls the local % function named CALLBACK in MAINGUI.M with the given input arguments. % % MAINGUI('Property','Value',...) creates a new MAINGUI or raises the % existing singleton*. Starting from the left, property value pairs are % applied to the GUI before mainGUI_OpeningFcn gets called. An % unrecognized property name or invalid value makes property application % stop. All inputs are passed to mainGUI_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 mainGUI % Last Modified by GUIDE v2.5 26-Mar-2021 12:46:25 % Begin initialization code - DO NOT EDIT gui_Singleton = 1; gui_State = struct('gui_Name', mfilename, ... 'gui_Singleton', gui_Singleton, ... 'gui_OpeningFcn', @mainGUI_OpeningFcn, ... 'gui_OutputFcn', @mainGUI_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 mainGUI is made visible. function mainGUI_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 mainGUI (see VARARGIN) % Choose default command line output for mainGUI handles.output = hObject; % Update handles structure guidata(hObject, handles); % UIWAIT makes mainGUI wait for user response (see UIRESUME) % uiwait(handles.figure1); % --- Outputs from this function are returned to the command line. function varargout = mainGUI_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; function edit1_Callback(hObject, eventdata, handles) % hObject handle to edit1 (see GCBO) % eventdata reserved - to be defined in a future version of MATLAB % handles structure with handles and user data (see GUIDATA) % Hints: get(hObject,'String') returns contents of edit1 as text % str2double(get(hObject,'String')) returns contents of edit1 as a double % --- Executes during object creation, after setting all properties. function edit1_CreateFcn(hObject, eventdata, handles) % hObject handle to edit1 (see GCBO) % eventdata reserved - to be defined in a future version of MATLAB % handles empty - handles not created until after all CreateFcns called % Hint: edit controls usually have a white background on Windows. % See ISPC and COMPUTER. if ispc && isequal(get(hObject,'BackgroundColor'), get(0,'defaultUicontrolBackgroundColor')) set(hObject,'BackgroundColor','white'); end % --- 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) global x [filename,pathname]=uigetfile({'*.xlsx';'*.csv';'*.txt';'*.'},'载入文件'); set( handles.edit1,'String',strcat(pathname,filename)); data=xlsread(strcat(pathname,filename)); x=data'; axes(handles.axes1) plot(x); axis tight grid on title('原始癫痫脑电信号') xlabel('采样点'); ylabel('幅值/mV'); msgbox('数据导入已完成!') % --- Executes on selection change in popupmenu1. function popupmenu1_Callback(hObject, eventdata, handles) % hObject handle to popupmenu1 (see GCBO) % eventdata reserved - to be defined in a future version of MATLAB % handles structure with handles and user data (see GUIDATA) % Hints: contents = cellstr(get(hObject,'String')) returns popupmenu1 contents as cell array % contents{get(hObject,'Value')} returns selected item from popupmenu1 % --- Executes during object creation, after setting all properties. function popupmenu1_CreateFcn(hObject, eventdata, handles) % hObject handle to popupmenu1 (see GCBO) % eventdata reserved - to be defined in a future version of MATLAB % handles empty - handles not created until after all CreateFcns called % Hint: popupmenu controls usually have a white background on Windows. % See ISPC and COMPUTER. if ispc && isequal(get(hObject,'BackgroundColor'), get(0,'defaultUicontrolBackgroundColor')) set(hObject,'BackgroundColor','white'); end function varargout = jiemian(varargin) % JIEMIAN MATLAB code for jiemian.fig % JIEMIAN, by itself, creates a new JIEMIAN or raises the existing % singleton*. % % H = JIEMIAN returns the handle to a new JIEMIAN or the handle to % the existing singleton*. % % JIEMIAN('CALLBACK',hObject,eventData,handles,...) calls the local % function named CALLBACK in JIEMIAN.M with the given input arguments. % % JIEMIAN('Property','Value',...) creates a new JIEMIAN or raises the % existing singleton*. Starting from the left, property value pairs are % applied to the GUI before jiemian_OpeningFcn gets called. An % unrecognized property name or invalid value makes property application % stop. All inputs are passed to jiemian_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 jiemian % Last Modified by GUIDE v2.5 29-Jul-2020 18:27:56 % Begin initialization code - DO NOT EDIT gui_Singleton = 1; gui_State = struct('gui_Name', mfilename, ... 'gui_Singleton', gui_Singleton, ... 'gui_OpeningFcn', @jiemian_OpeningFcn, ... 'gui_OutputFcn', @jiemian_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 jiemian is made visible. function jiemian_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 jiemian (see VARARGIN) % Choose default command line output for jiemian handles.output = hObject; % Update handles structure guidata(hObject, handles); % UIWAIT makes jiemian wait for user response (see UIRESUME) % uiwait(handles.figure1); % --- Outputs from this function are returned to the command line. function varargout = jiemian_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; function edit1_Callback(hObject, eventdata, handles) % hObject handle to edit1 (see GCBO) % eventdata reserved - to be defined in a future version of MATLAB % handles structure with handles and user data (see GUIDATA) % Hints: get(hObject,'String') returns contents of edit1 as text % str2double(get(hObject,'String')) returns contents of edit1 as a double % --- Executes during object creation, after setting all properties. function edit1_CreateFcn(hObject, eventdata, handles) % hObject handle to edit1 (see GCBO) % eventdata reserved - to be defined in a future version of MATLAB % handles empty - handles not created until after all CreateFcns called % Hint: edit controls usually have a white background on Windows. % See ISPC and COMPUTER. if ispc && isequal(get(hObject,'BackgroundColor'), get(0,'defaultUicontrolBackgroundColor')) set(hObject,'BackgroundColor','white'); end ha=axes('units','normalized','pos',[0 0 1 1]); uistack(ha,'down'); ii=imread('105.jpg'); image(ii); colormap gray set(ha,'handlevisibility','off','visible','on'); if ispc && isequal(get(hObject,'BackgroundColor'), get(0,'defaultUicontrolBackgroundColor')) set(hObject,'BackgroundColor','white'); end function edit2_Callback(hObject, eventdata, handles) % hObject handle to edit2 (see GCBO) % eventdata reserved - to be defined in a future version of MATLAB % handles structure with handles and user data (see GUIDATA) % Hints: get(hObject,'String') returns contents of edit2 as text % str2double(get(hObject,'String')) returns contents of edit2 as a double % --- Executes during object creation, after setting all properties. function edit2_CreateFcn(hObject, eventdata, handles) % hObject handle to edit2 (see GCBO) % eventdata reserved - to be defined in a future version of MATLAB % handles empty - handles not created until after all CreateFcns called % Hint: edit controls usually have a white background on Windows. % See ISPC and COMPUTER. if ispc && isequal(get(hObject,'BackgroundColor'), get(0,'defaultUicontrolBackgroundColor')) set(hObject,'BackgroundColor','white'); end % --- 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) userChar = get( handles.edit1, 'string' ); passChar = get( handles.edit2,'string' ); accountNumber = '20171008189'; % 默认帐号 keyWord = 'dfgdbfd697'; % 默认密码 n = find( strcmp(accountNumber, {userChar}),1 ); % 判断输入的用户名和默认值是否一致。若是一致,则 n 非空 if ~isempty( n ) && strcmp( keyWord,{passChar} ) h = msgbox( '欢迎进入脑电信号处理系统!' ); uiwait( h ); delete( gcf ); % 关闭当前的用户登陆界面 bishe%调用数据GUI else errordlg( '帐号或密码错误,请从新输入!' ); end % --- 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) close % --- Executes during object creation, after setting all properties. function text3_CreateFcn(hObject, eventdata, handles) % hObject handle to text3 (see GCBO) % eventdata reserved - to be defined in a future version of MATLAB % handles empty - handles not created until after all CreateFcns called
版本:2014aapp