300字范文 > 【图像压缩】基于matlab GUI FFT图像压缩【含Matlab源码 843期】

【图像压缩】基于matlab GUI FFT图像压缩【含Matlab源码 843期】

时间：2024-01-09 01:17:21

一、简介

FFT(Fast Fourier transform)：快速傅里叶变换，是DFT的工程化实现方法。

DFT直接求解太过于复杂，FFT方法根据DFT求解过程中旋转因子的性质并引入分治算法思想，大大简化计算过程，被广泛应用在频谱分析的工程实践中，如matlab，C，C++，CUDA等底层实现

1 DFT简介

频谱分析是信号处理中的重要环节，从傅里叶变换FT，到拉普拉斯变换LT，离散时间傅里叶变换DTFT，Z变换ZT，到我们所讲的离散傅里叶变换DFT（他们之间的联系和区别见我的其他博客）。

相比于其他变换，DFT被广泛应用的原因是其输入的时域信号是离散的，输出的频域结果也是离散的。这就极大方便了我们进行基于计算机的频谱计算，存储和分析，没办法数字信号处理是大趋势。

DFT变换的公式为：

但为了分析方便，在FFT的计算过程中，我们依然使用k = 0 ∼ N − 1 k = 0 \sim N-1k=0∼N−1的选取策略。也即，如下：

2 旋转因子WWW的性质

3 FFT蝶形计算证明

4 FFT计算过程

二、源代码

function varargout = fft_encoding(varargin)% FFT_ENCODING M-file for fft_encoding.fig%FFT_ENCODING, by itself, creates a new FFT_ENCODING or raises the existing%singleton*.%%H = FFT_ENCODING returns the handle to a new FFT_ENCODING or the handle to%the existing singleton*.%%FFT_ENCODING('CALLBACK',hObject,eventData,handles,...) calls the local%function named CALLBACK in FFT_ENCODING.M with the given input arguments.%%FFT_ENCODING('Property','Value',...) creates a new FFT_ENCODING or raises the%existing singleton*. Starting from the left, property value pairs are%applied to the GUI before fft_encoding_OpeningFunction gets called. An%unrecognized property name or invalid value makes property application%stop. All inputs are passed to fft_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 fft_encoding% Last Modified by GUIDE v2.5 18-Jun- 20:05:02% Begin initialization code - DO NOT EDITgui_Singleton = 1;gui_State = struct('gui_Name', mfilename, ...'gui_Singleton', gui_Singleton, ...'gui_OpeningFcn', @fft_encoding_OpeningFcn, ...'gui_OutputFcn', @fft_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 fft_encoding is made visible.function fft_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 fft_encoding (see VARARGIN)cr = 0.5; I = imread('lena.bmp');axes(handles.axes1);imshow(I);I = double(I)/255;fftcoe = blkproc(I,[8 8],'fft2(x)');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],'ifft2(x)');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 fft_encodinghandles.output = hObject;% Update handles structureguidata(hObject, handles);% UIWAIT makes fft_encoding wait for user response (see UIRESUME)% uiwait(handles.figure1);% --- Outputs from this function are returned to the command line.function varargout = fft_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;fftcoe = blkproc(I,[8 8],'fft2(x)');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],'ifft2(x)');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);clc;% 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;fftcoe = blkproc(I,[8 8],'fft2(x)');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;endB2 = col2im(coe,[8 8],size(I),'distinct');I2 = blkproc(B2,[8,8],'ifft2(x)');axes(handles.axes2);imshow(abs(I2));e = double(I) - double(I2);[m,n]=size(e);erms = sqrt(sum(e(:).^2)/(m*n));set(handles.erms_edit,'string',erms);% --- Executes on button press in close_button.function close_button_Callback(hObject, eventdata, handles)% hObject handle to close_button (see GCBO)% eventdata reserved - to be defined in a future version of MATLAB% handles structure with handles and user data (see GUIDATA)close(fft_encoding);