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-2009 20:25:20

% Begin initialization code - DO NOT EDIT
gui_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});
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 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:n
    coe(ind(1:snum),i) = 0;
end
B2 = 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_encoding
handles.output = hObject;

% Update handles structure
guidata(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 structure
varargout{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 ispc
    set(hObject,'BackgroundColor','white');
else
    set(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');
end
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:n
    coe(ind(1:snum),i) = 0;
end
B2 = 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 ispc
    set(hObject,'BackgroundColor','white');
else
    set(hObject,'BackgroundColor',get(0,'defaultUicontrolBackgroundColor'));
end



function 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:n
    coe(ind(1:snum),i) = 0;
end

三、运行结果

四、备注

完整代码或者代写添加QQ 1564658423