This document contains code to perform image denoising using wavelet thresholding. It loads an image, adds noise, performs wavelet decomposition, applies thresholding to the coefficients, reconstructs the image, and calculates metrics like PSNR to evaluate the quality of the denoised image compared to the original. Key steps include adding noise, estimating the noise level, performing wavelet decomposition, soft-thresholding coefficients, and reconstructing the image. Metrics like PSNR and IQI are calculated to evaluate the performance of the denoising algorithm.

1. clear all;
close all;
clc;
% Filter Parameters.
sigmas=1.8; %%% Spatial (Geometric) Sigma.
mult_factor_sigmar=5; %%% Multiplication factor for SigmaR.
ksize=11; %%% Kernal Size.
%%% Wavelet Transform Parameters.
Nlevels=3; %% 3 levels.
NoOfBands=3*Nlevels+1;
wname='db8'; % data binary =8 bit
sorh='s'; % crop
x = imread('boat.png');
if(size(x,3)==3)
x=rgb2gray(x);
figure
imshow(x)
end
[M,N]=size(x);
mean_val=0;
Square_scaled_para=15
%Square_scaled_para=Square_scaled_para/10;
%for Square_scaled_para = 1:numel(Square_scaled_para) % for loop range= 1 to
length of
sizeA = size(x);
xn= imnoise(x,'speckle',0.01);
%%
figure
imshow(xn) % noisy image
title('noisy image')
xn = max(0,min(xn,255));
xn_mse=sum(sum((double(x)-double(xn)).^2))/(M*N);
xn_psnr=(10*log10(255^2./xn_mse))/3
tic
%%% Noise Level Estimation using Robust Median Estimator.
[ca,ch,cv,cd]=dwt2(xn,wname);
tt1=cd(:)';
median_hh2=median(abs(tt1));
std_dev2=(median_hh2/0.6745);
sigmar=mult_factor_sigmar*std_dev2;
[yb yg]= Linear_filt2D(xn,sigmas,sigmar,ksize);
yd=double(xn)-yb;
%%% General Wavelet Decomposition.
dwtmode('per');
[C,S]=wavedec2(yd,Nlevels,wname);
k=NoOfBands;
CW{k}=reshape(C(1:S(1,1)*S(1,2)),S(1,1),S(1,2));
k=k-1;
st_pt=S(1,1)*S(1,2);
for i=2:size(S,1)-1
slen=S(i,1)*S(i,2);
CW{k}=reshape(C(st_pt+slen+1:st_pt+2*slen),S(i,1),S(i,2));
CW{k-1}=reshape(C(st_pt+1:st_pt+slen),S(i,1),S(i,2));
CW{k-2}=reshape(C(st_pt+2*slen+1:st_pt+3*slen),S(i,1),S(i,2));
st_pt=st_pt+3*slen;
k=k-3;
end
tt2=CW{1}(:)';
median_hh2=median(abs(tt2)); %% HH1->Subband containing finest level diagonal
details.
std_dev2=(median_hh2/0.6745);

2. cw_noise_var=std_dev2^2; %% var=std^2
for i=1:NoOfBands-1
thr=bayesthf(CW{i},cw_noise_var);
yw{i}=threshf(CW{i},sorh,thr,2);
end
yw{i+1}=CW{i+1};
if(isequal(wname,'DCHWT'))
ydr=dchwtf2(yw,-Nlevels);
else
k=NoOfBands;
xrtemp=reshape(yw{k},1,S(1,1)*S(1,2));
k=k-1;
for i=2:size(S,1)-1
xrtemp=[xrtemp reshape(yw{k-1},1,S(i,1)*S(i,2))
reshape(yw{k},1,S(i,1)*S(i,2)) reshape(yw{k-2},1,S(i,1)*S(i,2))];
k=k-3;
end
ydr=(waverec2(xrtemp,S,wname));
end
%[y,map] = bin2gray(x,'qam',16);
ybw=yb+ydr;
ybwn=uint8(ybw);
yb1=yb;
yb=uint8(yb);
figure
imshow(yb) % reconstructed image
title(' reconstructed image')
toc
%%%% MSE Computation.
yb_mse=sum(sum((double(x)-double(yb)).^2))/(M*N);
ybw_mse=sum(sum((double(x)-double(ybwn)).^2))/(M*N);
%%%% PSNR Computation.
psnr_lfilt=10*log10(255^2./yb_mse);
psnr_lf_mnt=10*log10(255^2./ybw_mse);
mean_org=mean(x(:));
var_org=sum((x(:)-mean_org).^2)/(M*N-1);
mean_lfilt=mean(yb(:));
var_lfilt=sum((yb(:)-mean_lfilt).^2)/(M*N-1);
cross_var_lfilt=sum((x(:)-mean_org).*(yb(:)-mean_lfilt))/(M*N-1);
IQI_lfilt=(4*cross_var_lfilt*mean_org*mean_lfilt)/
((var_org+var_lfilt)*(mean_org^2+mean_lfilt^2));
mean_bwt=mean(ybwn(:));
var_bwt=sum((ybwn(:)-mean_bwt).^2)/(M*N-1);
cross_var_bwt=sum((x(:)-mean_org).*(ybwn(:)-mean_bwt))/(M*N-1);
IQI_bf_mnt=(4*cross_var_bwt*mean_org*mean_bwt)/
((var_org+var_bwt)*(mean_org^2+mean_bwt^2));
mse=sum(sum((double(x)-double(ybw)).^2))/(M*N);
psnr_linear=10*log10(255^2./mse)
figure
plot(Square_scaled_para,xn_psnr,'k-*')
xlabel('SQUIRED SCALE PARAMETER');
ylabel('PSNR (dB)');
hold on;
plot(Square_scaled_para,psnr_linear,'r','marker','*')
hold on;
legend('No Filter','Proposed','Location','Best');