一、简介
自适应滤波器由参数可调的数字滤波器和自适应算法两部分组成。 自适应滤波与维纳滤波、卡尔曼滤波最大的区别在于，自适应滤波在输出与滤波系统之间存在有反馈通道，根据某一时刻滤波器的输出与期望信号的误差调整滤波器的系数，从而实现滤波器系数的动态调整，实现最优滤波。
1 信号模型
自适应滤波的目的仍然是从观测信号中提取真实准确的期望信号，因此涉及到的信号有：
1）期望信号 d(n)
2）输入信号 x(n)=d(n)+v(n)
3）输出信号 y(n)
2 算法原理
一个M阶滤波器，系数为w(m)，则输出为：y(n)=Σw(m)x(n-m) m=0…M，写成矩阵形式：y(j)=WT(j)*X(j)，n时刻的输出误差为： e(j)=d(j)-y(j)= d(j)- WT(j)X(j)，
定义目标函数为 E[e(j)2]，则有：J(j)=E[e(j)2]= E[(d(j)- WT(j)X(j))^2]。
当上述误差达到最小时，即实现最优滤波，这种目标函数确定的为最小方差自适应滤波。对于目标函数J(j)，需要求得使其取到最小值对应的W，这里使用梯度下降法进行最优化：W(j+1)=W(j)+1/2μ(-▽J(j))
▽J(j)=-2E[X(j)( d(j)- WT(j)*X(j))]= -2E[X(j)e(j)]
W(j+1)=W(j)+μE[X(j)e(j)]
其中-2X(j)e(j)称为瞬时梯度，因为瞬时梯度是真实梯度的无偏估计，这里可以使用瞬时梯度代替真实梯度。W(j+1)=W(j)+μX(j)e(j)
由此，可以得到自适应滤波最佳系数的迭代公式。
二、源代码
function varargout = adpmedian_filter(varargin)
% ADPMEDIAN_FILTER M-file for adpmedian_filter.fig
% ADPMEDIAN_FILTER, by itself, creates a new ADPMEDIAN_FILTER or raises the existing
% singleton*.
%
% H = ADPMEDIAN_FILTER returns the handle to a new ADPMEDIAN_FILTER or the handle to
% the existing singleton*.
%
% ADPMEDIAN_FILTER('CALLBACK',hObject,eventData,handles,...) calls the local
% function named CALLBACK in ADPMEDIAN_FILTER.M with the given input arguments.
%
% ADPMEDIAN_FILTER('Property','Value',...) creates a new ADPMEDIAN_FILTER or raises the
% existing singleton*. Starting from the left, property value pairs are
% applied to the GUI before adpmedian_filter_OpeningFunction gets called. An
% unrecognized property name or invalid value makes property application
% stop. All inputs are passed to adpmedian_filter_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 adpmedian_filter
% Last Modified by GUIDE v2.5 06-Jul-2009 20:13:38
% Begin initialization code - DO NOT EDIT
gui_Singleton = 1;
gui_State = struct('gui_Name', mfilename, ...
'gui_Singleton', gui_Singleton, ...
'gui_OpeningFcn', @adpmedian_filter_OpeningFcn, ...
'gui_OutputFcn', @adpmedian_filter_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 adpmedian_filter is made visible.
function adpmedian_filter_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 adpmedian_filter (see VARARGIN)
img = imread('lena.bmp');
axes(handles.axes1);
imshow(img);
g = imnoise(img,'gaussian',0.01,0.005);
axes(handles.axes2);
imshow(g);
f = adpmedian(g,7);
axes(handles.axes3);
imshow(f);
set(handles.m_edit,'string',0.01);
set(handles.v_edit,'string',0.005);
set(handles.smax_edit,'string',7);
% Choose default command line output for adpmedian_filter
handles.output = hObject;
% Update handles structure
guidata(hObject, handles);
% UIWAIT makes adpmedian_filter wait for user response (see UIRESUME)
% uiwait(handles.figure1);
% --- Outputs from this function are returned to the command line.
function varargout = adpmedian_filter_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)
m = str2num(get(handles.m_edit,'string'));
v = str2num(get(handles.v_edit,'string'));
smax = str2num(get(handles.smax_edit,'string'));
val = get(hObject,'value');
str = get(hObject,'string');
val1 = get(handles.noise_pop_menu,'value');
str1 = get(handles.noise_pop_menu,'string');
switch str{val}
case 'Lena'
lena = [];
lena = imread('lena.bmp');
img = lena;
case 'Cameraman'
cameraman = [];
cameraman = imread('cameraman.tif');
img = cameraman;
case 'Peppers'
peppers = [];
peppers = imread('peppers.bmp');
img = peppers;
case 'Fingerprint'
fingerprint = [];
fingerprint = imread('fingerprint.jpg');
img = fingerprint;
case 'Licenceplate'
licenceplate = [];
licenceplate = imread('licenceplate.jpg');
img = licenceplate;
case 'Haze'
haze = [];
haze = imread('haze.jpg');
img = haze;
case 'Cloudy'
cloudy = [];
cloudy = imread('cloudy.tif');
img = cloudy;
end
axes(handles.axes1);
imshow(img);
switch str1{val1}
case '高斯噪声'
set(handles.m_edit,'enable','on');
set(handles.v_edit,'enable','on');
g = imnoise(img,'gaussian',m,v);
case '椒盐噪声'
set(handles.m_edit,'enable','on');
g = imnoise(img,'salt & pepper',m);
set(handles.v_edit,'enable','off');
case '乘性噪声'
set(handles.v_edit,'enable','on');
g = imnoise(img,'speckle',v);
set(handles.m_edit,'enable','off');
case '泊松噪声'
g = imnoise(img,'poisson');
set(handles.m_edit,'enable','off');
set(handles.v_edit,'enable','off');
end
axes(handles.axes2);
imshow(g);
f = adpmedian(g,smax);
axes(handles.axes3);
imshow(f);
% 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 noise_pop_menu_CreateFcn(hObject, eventdata, handles)
% hObject handle to noise_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
三、运行结果
四、备注
版本：2014a
