数值计算方法实习报告1.docVIP

数值计算方法实习报告 实验一 1、只留导电介质的数值模拟 2、污染扩散问题的数值模拟 实验二 1、线性最小二乘的数据拟合 2、非线性最小二乘的数据拟合 以下是用有理函数和光滑样条对铜的热膨胀系数和温度进行拟合 3.插值的数据拟合 以下是用三次样条和简单函数拟合数据：x= 0:0.05:2; y = x .* sin(1./(x+eps)) 相关代码： cftool load hahn1 x=0:0.05:2; y=x.*sin(1./(x+eps)); 结果如下： 实习三 基于偏微方程（PDE）的图像降噪和还原 代码： %%% TV demo %% %%%%%%%%%%%%%%%%%%%%%%%%%%%%% % Based on: [ROF92] L. Rudin, S. Osher, E. Fatemi, % Nonlinear Total Variation based noise removal algorithms, % Physica D 60 259-268,1992. %%%%%%%%%%%%%%%%%%%%%%%%%%%%% %%%%%%%%%%%%%%%%%%%%%%%%%%%%% %%% Simple TV denoising %%% %%%%%%%%%%%%%%%%%%%%%%%%%%%%% I = imread(1.jpg); % load image I = double(I(16:270,16:270)); % cut a piece, convert to double % params iter = 80; % dt=0.2; eps=1; %%% Add noise std_n = 20; % Gaussian noise standard deviation In = randn(size(I))*std_n; % White Gaussian noise I0 = I + In; % noisy input image % show original and noisy images close all figure(1); imshow(uint8(I)); title(Original) figure(2); imshow(uint8(I0)); title(Noisy image) % denoise image by using tv for some iterations J = tv(I0,iter); figure(3); imshow(uint8(J)); title(Denoised image) %%%%%%%%%%%%%%%%%%%%%%%%%%%%% %%% TV denoising with (scalar) data fidelity term %%% %%%%%%%%%%%%%%%%%%%%%%%%%%%%% %% Here we assume the noise vaiance is known. %% Therefore we can compute lambda (instead of fixing %% iter). TV therfore can run automatically quite well. %% The process is slower. J = I0; % params ep_J = 0.01; % minimum mean change in image J lam = 0; J_old = 0; iter = 10; dt = 0.2; eps = 1; 18 var_n = std_n^2; % noise variance i = 0; while (mean(mean(abs(J - J_old))) ep_J), % iterate until convergence J_old = J; J = tv(J,iter,dt,eps,lam,I0); % scalar lam lam = calc_lam(J,I0,var_n,eps); % update lambda (fidelity term) end % for i figure(4); imshow(uint8(J)); title(Denoised image with lambda) 结果： 修改前 修改中 修改结果