?一、簡介

1 中值濾波

? ? ?中值濾波是基于排序統(tǒng)計(jì)理論的一種能有效抑制噪聲的非線性信號(hào)處理技術(shù)。它也是一種鄰域運(yùn)算，類似于卷積，但是計(jì)算的不是加權(quán)求和，而是把數(shù)字圖像或數(shù)字序列中一點(diǎn)的值用該點(diǎn)的一個(gè)鄰域中各點(diǎn)值的中值代替，讓周圍像素灰度值的差比較大的像素改取與周圍的像素值接近的值，從而可以消除孤立的噪聲點(diǎn)。它能減弱或消除傅立葉空間的高頻分量，但影響低頻分量。因?yàn)楦哳l分量對(duì)應(yīng)圖像中的區(qū)域邊緣的灰度值具有較大較快變化的部分，該濾波可將這些分量濾除，使圖像平滑。值濾波技術(shù)在衰減噪聲的同時(shí)能較好的保護(hù)圖像的邊緣。

2 均值濾波

均值濾波是指任意一點(diǎn)的像素值，都是周圍?

?個(gè)像素值的均值。例如下圖中，紅色點(diǎn)的像素值是其周圍藍(lán)色背景區(qū)域像素值之和除25，25=5

5 是藍(lán)色區(qū)域的大小。

均值濾波詳細(xì)的計(jì)算方法如下圖所示：

其中5

5的矩陣稱為核，針對(duì)原始圖像內(nèi)的像素點(diǎn)，采用核進(jìn)行處理，得到結(jié)果圖像，如下圖所示：

提取?1/25?可以將核轉(zhuǎn)換為如下形式：

3 小波變換

小波濾波原理

???????? 小波變換就是把某一基函數(shù)做位移后，求不同尺度下的小波函數(shù)與原始信號(hào)的內(nèi)積，表達(dá)式如下：

其中，a>0，是尺度因子，隱含信號(hào)的頻率信息，是平移因子，這樣信號(hào)就被分解成一系列小波函數(shù)的疊加，這就是小波分解的過程?；驹硎牵簩?duì)于信號(hào)的不同頻率部分，改變尺度值，相當(dāng)于在時(shí)間軸上對(duì)信號(hào)進(jìn)行壓縮和伸展。尺度越大，表示分析的信號(hào)區(qū)間越長，那么在頻域的分辨率就越低，這樣可以獲取信號(hào)的低頻成分；反之可以得到信號(hào)的高頻成分。小波變換可以得到一系列的小波系數(shù)，從中分析有用信號(hào)和噪聲各自對(duì)應(yīng)的部分，對(duì)小波系數(shù)進(jìn)行適當(dāng)?shù)奶幚?。小波重?gòu)就是用處理得到的新的系數(shù)來重構(gòu)信號(hào)。

???????? 小波進(jìn)行濾波就是一個(gè)小波分解和重構(gòu)的過程，其基本步驟如下：

u? 選擇合適的小波基函數(shù)

u? 對(duì)信號(hào)進(jìn)行指定層次的小波分解

u? 對(duì)各分解層進(jìn)行處理，得到新的小波系數(shù)

u? 用新得到的系數(shù)進(jìn)行小波重構(gòu)（小波逆變換）

小波基函數(shù)的選擇

???????? 對(duì)于同樣的信號(hào)，不同的基函數(shù)會(huì)得到不同的結(jié)果。在小波基函數(shù)選擇的時(shí)候要結(jié)合信號(hào)本身的特點(diǎn)，也要清楚小波基函數(shù)選取的原則：

u? 正交性：可以使分析簡便，有利于信號(hào)的精確重構(gòu)

u? 對(duì)稱性：對(duì)稱的基函數(shù)使得小波濾波呈線性相位，信號(hào)不會(huì)失真，也可以提高算法的運(yùn)行速度

u? 緊支性：緊支集的長度決定著信號(hào)局部特性的好壞，緊支集越短的小波基函數(shù)，局部時(shí)頻特征就越好，越有利于信號(hào)的瞬時(shí)檢測

u? 正則性：決定信號(hào)重構(gòu)后的平滑性，會(huì)影響頻域的分辨率，支集長度越長，正則性越好；

u? 消失矩：基函數(shù)的消失矩越高，在高頻的衰減也就越快，變換后信號(hào)的的能量越集中，可以保持良好的頻域定域性。

二、源代碼

function varargout = dsp1(varargin) % DSP1 MATLAB code for dsp1.fig % ? ? ?DSP1, by itself, creates a new DSP1 or raises the existing % ? ? ?singleton*. % % ? ? ?H = DSP1 returns the handle to a new DSP1 or the handle to % ? ? ?the existing singleton*. % % ? ? ?DSP1('CALLBACK',hObject,eventData,handles,...) calls the local % ? ? ?function named CALLBACK in DSP1.M with the given input arguments. % % ? ? ?DSP1('Property','Value',...) creates a new DSP1 or raises the % ? ? ?existing singleton*. ?Starting from the left, property value pairs are % ? ? ?applied to the GUI before dsp1_OpeningFcn gets called. ?An % ? ? ?unrecognized property name or invalid value makes property application % ? ? ?stop. ?All inputs are passed to dsp1_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 dsp1 % Last Modified by GUIDE v2.5 21-Mar-2014 21:34:03 % Begin initialization code - DO NOT EDIT gui_Singleton = 1; gui_State = struct('gui_Name', ? ? ? mfilename, ... ? ? ? ? ? ? ? ? ? 'gui_Singleton', ?gui_Singleton, ... ? ? ? ? ? ? ? ? ? 'gui_OpeningFcn', @dsp1_OpeningFcn, ... ? ? ? ? ? ? ? ? ? 'gui_OutputFcn', ?@dsp1_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 dsp1 is made visible. function dsp1_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 dsp1 (see VARARGIN) setappdata(handles.figure1,'img1',0); setappdata(handles.figure1,'img2',0); setappdata(handles.figure1,'img3',0); %set(handles.myimage_compress,'Enable', 'off'); set(handles.pushbutton_compress,'Enable', 'off'); set(handles.menu_quzaodesc, 'Enable', 'off'); set(handles.save, 'Enable', 'off'); % Choose default command line output for dsp1 handles.output = hObject; % Update handles structure guidata(hObject, handles); % UIWAIT makes dsp1 wait for user response (see UIRESUME) % uiwait(handles.figure1); % --- Outputs from this function are returned to the command line. function varargout = dsp1_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 on selection change in popupmenu. function popupmenu_Callback(hObject, eventdata, handles) % hObject ? ?handle to popupmenu (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 popupmenu contents as cell array % ? ? ? ?contents{get(hObject,'Value')} returns selected item from popupmenu val = get(hObject,'Value'); str = get(hObject, 'String'); switch str{val}; case '無' % img2=getappdata(handles.figure1,'img1'); ? ?axes(handles.axes2); ? ?imshow(img2); ? ?setappdata(handles.figure1,'img2',img2); ? ?set(handles.pushbutton_listen, 'Enable', 'off'); case '高斯噪聲' % img2=getappdata(handles.figure1,'img1'); ? ?img2 = imnoise(img2,'gaussian'); %加高斯噪聲 ? ?axes(handles.axes2); ? ?imshow(img2); ? ?setappdata(handles.figure1,'img2',img2); ? ?set(handles.menu_quzaodesc, 'Enable', 'on'); ? ?set(handles.pushbutton_listen, 'Enable', 'on'); case '椒鹽噪聲' % img2=getappdata(handles.figure1,'img1'); ? ?img2 = imnoise(img2,'salt'); ? ?axes(handles.axes2); ? ?imshow(img2); ? ?setappdata(handles.figure1,'img2',img2); ? ?set(handles.menu_quzaodesc, 'Enable', 'on'); ? ?set(handles.pushbutton_listen, 'Enable', 'on'); case '泊松噪聲' % img2=getappdata(handles.figure1,'img1'); ? ?img2 = imnoise(img2,'poisson'); ? ?axes(handles.axes2); ? ?imshow(img2); ? ?setappdata(handles.figure1,'img2',img2); ? ?set(handles.menu_quzaodesc, 'Enable', 'on'); ? ?set(handles.pushbutton_listen, 'Enable', 'on'); case '斑點(diǎn)噪聲speckle' % img2=getappdata(handles.figure1,'img1'); ? ?img2 = imnoise(img2,'speckle'); ? ?axes(handles.axes2); ? ?imshow(img2); ? ?setappdata(handles.figure1,'img2',img2); ? ?set(handles.menu_quzaodesc, 'Enable', 'on'); ? ?set(handles.pushbutton_listen, 'Enable', 'on'); end % --- Executes during object creation, after setting all properties. function popupmenu_CreateFcn(hObject, eventdata, handles) % hObject ? ?handle to popupmenu (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 myfile_Callback(hObject, eventdata, handles) % hObject ? ?handle to myfile (see GCBO) % eventdata ?reserved - to be defined in a future version of MATLAB % handles ? ?structure with handles and user data (see GUIDATA) % -------------------------------------------------------------------- function myfile_open_Callback(hObject, eventdata, handles) % hObject ? ?handle to myfile_open (see GCBO) % eventdata ?reserved - to be defined in a future version of MATLAB % handles ? ?structure with handles and user data (see GUIDATA) [filename, pathname] = uigetfile(... ? ?{'*.bmp;*.jpg; *.png; *.jpeg; ','Image Files(*.bmp,*.jpg,*.png,*.jpeg)';... ? ?'*.*', ? ? ?'All Files(*.*)' }... ? ?, 'Pick an image');%打開文件 選擇圖像 if isequal(filename,0) || isequal(pathname,0) ? ?return;%如 果點(diǎn)了“ 取 消” end axes(handles.axes1);%重要，在哪個(gè)坐標(biāo)軸顯示圖像 fpath = [pathname filename];%路徑名和文件名 img1 = imread(fpath);%讀取圖像 imshow(img1);%顯示圖像 setappdata(handles.figure1,'img1',img1); % --- Executes on selection change in popupmenu3. function popupmenu3_Callback(hObject, eventdata, handles) % hObject ? ?handle to popupmenu3 (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 popupmenu3 contents as cell array % ? ? ? ?contents{get(hObject,'Value')} returns selected item from popupmenu3 img2=getappdata(handles.figure1,'img2');%加噪圖像 img1=getappdata(handles.figure1,'img1');%原始圖像 val = get(hObject,'Value'); str = get(hObject, 'String'); switch str{val}; case '中值濾波' ? ?set(handles.uipanel_lowfilt, 'Visible', 'off'); ? ?set(handles.uipanel_gausslow, 'Visible', 'off'); ? ?set(handles.pushbutton_quzao, 'Visible', 'off'); img3 = medfilt2(img2);%中值濾波 ? ?setappdata(handles.figure1,'img3',img3); ? ?axes(handles.axes3); ? ?imshow(img3); ? ?PSNR = psnr2(img3, img1); ? ?str1 = strcat('psnr為： ' , num2str(PSNR) , 'db'); ? ?set(handles.text3, 'string', str1); %顯示PSNR值 ? ?set(handles.save, 'Enable', 'on'); ? % set(handles.myimage_compress,'Enable', 'on'); ? ?set(handles.pushbutton_compress,'Enable', 'on'); case '維納濾波' ? ?set(handles.uipanel_lowfilt, 'Visible', 'off'); ? ?set(handles.uipanel_gausslow, 'Visible', 'off'); ? ?set(handles.pushbutton_quzao, 'Visible', 'off'); img3 = wiener2(img2,[5,5]); ? ?setappdata(handles.figure1,'img3',img3); ? ?axes(handles.axes3); ? ?imshow(img3); ? ?PSNR = psnr2(img3, img1); ? ?str1 = strcat('psnr為： ' , num2str(PSNR) , 'db'); ? ?set(handles.text3, 'string', str1); ? % set(handles.myimage_compress,'Enable', 'on'); ? ?set(handles.pushbutton_compress,'Enable', 'on'); ? ?set(handles.save, 'Enable', 'on');

三、運(yùn)行結(jié)果