一、简介
沃尔什-哈达玛变换（Walsh-Hadmard Transform,WHT），是一种典型的非正弦函数变换，采用正交直角函数作为基函数，具有与傅里叶函数类似的性质，图像数据越是均匀分布，经过沃尔什-哈达玛变换后的数据越是集中于矩阵的边角上，因此沃尔什变换具有能量集中的性质，可以用于压缩图像信息。
Matlab中的Hadamard函数：
格式：H=hadamard( n ) ，返回一个 n * n的hadamard矩阵。
二、源代码
function varargout = hadamard_encoding(varargin)% HADAMARD_ENCODING M-file for hadamard_encoding.fig%HADAMARD_ENCODING, by itself, creates a new HADAMARD_ENCODING or raises the existing%singleton*.%%H = HADAMARD_ENCODING returns the handle to a new HADAMARD_ENCODING or the handle to%the existing singleton*.%%HADAMARD_ENCODING('CALLBACK',hObject,eventData,handles,...) calls the local%function named CALLBACK in HADAMARD_ENCODING.M with the given input arguments.%%HADAMARD_ENCODING('Property','Value',...) creates a new HADAMARD_ENCODING or raises the%existing singleton*. Starting from the left, property value pairs are%applied to the GUI before hadamard_encoding_OpeningFunction gets called. An%unrecognized property name or invalid value makes property application%stop. All inputs are passed to hadamard_encoding_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 hadamard_encoding% Last Modified by GUIDE v2.5 18-Jun- 20:25:20% Begin initialization code - DO NOT EDITgui_Singleton = 1;gui_State = struct('gui_Name', mfilename, ...'gui_Singleton', gui_Singleton, ...'gui_OpeningFcn', @hadamard_encoding_OpeningFcn, ...'gui_OutputFcn', @hadamard_encoding_OutputFcn, ...'gui_LayoutFcn', [] , ...'gui_Callback', []);if nargin & isstr(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 hadamard_encoding is made visible.function hadamard_encoding_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 hadamard_encoding (see VARARGIN)cr = 0.5; I = imread('lena.bmp');axes(handles.axes1);imshow(I);I = double(I)/255;t = hadamard(8);fftcoe = blkproc(I,[8 8],'P1*x*P2',t,t);coevar = im2col(fftcoe,[8 8],'distinct');coe = coevar;[y,ind] = sort(coevar);[m,n] = size(coevar);snum = 64-64*cr;for i = 1:ncoe(ind(1:snum),i) = 0;endB2 = col2im(coe,[8 8],[512 512],'distinct');I2 = blkproc(B2,[8,8],'P1*x*P2',t,t);I2 = I2./(8*8);axes(handles.axes2);imshow(I2);e = double(I) - double(I2);[m,n]=size(e);erms = sqrt(sum(e(:).^2)/(m*n));set(handles.erms_edit,'string',erms);set(handles.cr_edit,'string',0.5);% Choose default command line output for hadamard_encodinghandles.output = hObject;% Update handles structureguidata(hObject, handles);% UIWAIT makes hadamard_encoding wait for user response (see UIRESUME)% uiwait(handles.figure1);% --- Outputs from this function are returned to the command line.function varargout = hadamard_encoding_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 during object creation, after setting all properties.function image_pop_menu_CreateFcn(hObject, eventdata, handles)% hObject handle to image_pop_menu (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 ispcset(hObject,'BackgroundColor','white');elseset(hObject,'BackgroundColor',get(0,'defaultUicontrolBackgroundColor'));end% --- Executes on selection change in image_pop_menu.function image_pop_menu_Callback(hObject, eventdata, handles)% hObject handle to image_pop_menu (see GCBO)% eventdata reserved - to be defined in a future version of MATLAB% handles structure with handles and user data (see GUIDATA)val = get(hObject,'value');str = get(hObject,'string');cr = str2num(get(handles.cr_edit,'string'));switch str{val}case 'Lena'I = imread('lena.bmp');case 'Cameraman'I = imread('cameraman.tif');case 'Peppers'I = imread('peppers.bmp');case 'Fingerprint'I = imread('fingerprint.jpg');case 'Licenceplate'I = imread('licenceplate.jpg');case 'Cloudy'I = imread('cloudy.tif');endaxes(handles.axes1);imshow(I);I = double(I)/255;t = hadamard(8);fftcoe = blkproc(I,[8 8],'P1*x*P2',t,t);coevar = im2col(fftcoe,[8 8],'distinct');coe = coevar;[y,ind] = sort(coevar);[m,n] = size(coevar);snum = 64-64*cr;for i = 1:ncoe(ind(1:snum),i) = 0;endB2 = col2im(coe,[8 8],size(I),'distinct');I2 = blkproc(B2,[8,8],'P1*x*P2',t,t);I2 = I2./(8*8);axes(handles.axes2);imshow(I2);e = double(I) - double(I2);[m,n]=size(e);erms = sqrt(sum(e(:).^2)/(m*n));set(handles.erms_edit,'string',erms);set(handles.cr_edit,'string',0.5);% Hints: contents = get(hObject,'String') returns image_pop_menu contents as cell array% contents{get(hObject,'Value')} returns selected item from image_pop_menu% --- Executes during object creation, after setting all properties.function cr_edit_CreateFcn(hObject, eventdata, handles)% hObject handle to cr_edit (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 ispcset(hObject,'BackgroundColor','white');elseset(hObject,'BackgroundColor',get(0,'defaultUicontrolBackgroundColor'));endfunction cr_edit_Callback(hObject, eventdata, handles)% hObject handle to cr_edit (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 cr_edit as text% str2double(get(hObject,'String')) returns contents of cr_edit as a double% --- Executes on button press in apply_button.function apply_button_Callback(hObject, eventdata, handles)% hObject handle to apply_button (see GCBO)% eventdata reserved - to be defined in a future version of MATLAB% handles structure with handles and user data (see GUIDATA)cr = str2num(get(handles.cr_edit,'string'));I = getimage(handles.axes1);I = double(I)/255;t = hadamard(8);fftcoe = blkproc(I,[8 8],'P1*x*P2',t,t);coevar = im2col(fftcoe,[8 8],'distinct');coe = coevar;[y,ind] = sort(coevar);[m,n] = size(coevar);snum = 64-floor(64*cr);for i = 1:ncoe(ind(1:snum),i) = 0;end
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，.
