【图像修复】基于matlab GUI自适应空间滤波图像修复【含Matlab源码 840期】

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二、自适应滤波器简介

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。

三、部分源代码

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});
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 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 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)
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 ispcset(hObject,'BackgroundColor','white');
elseset(hObject,'BackgroundColor',get(0,'defaultUicontrolBackgroundColor'));
end

四、运行结果

五、matlab版本及参考文献

1 matlab版本
2014a

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，2020.
[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，2013.
[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，2013.
[4]刘成龙.精通MATLAB图像处理[M].清华大学出版社，2015.