This document contains code for denoising an image using wavelet thresholding. It performs the following steps: 1. Adds Gaussian noise of varying scale to an input image and calculates the PSNR for the noisy image. 2. Estimates the noise level using robust statistics on the wavelet coefficients and performs wavelet thresholding using Bayesian thresholding. 3. Reconstructs the image from the thresholded wavelet coefficients and calculates the PSNR. 4. Compares the performance of the proposed method to linear filtering, Wiener filtering and median filtering by plotting the PSNR for each method against the noise scale.

1. %function[] = mainnn(x)
% 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.
pairs=1;
NoOfBands=3*Nlevels+1;
wname='db8'; % data binary =8 bit
sorh='s'; % crop
x = imread('input.bmp');
if(size(x,3)==3)
x=rgb2gray(x);
end
figure
[M,N]=size(x);
mean_val=0;
Square_scaled_para=[0:0.01:0.2]
%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 = double(x) + (((Square_scaled_para)^2)*randn(sizeA)) + mean_val;
%%
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)
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);
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);

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
ybw=yb+ydr;
ybwn=uint8(ybw);
yb1=yb;
yb=uint8(yb);
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)
plot(Square_scaled_para,xn_psnr,'b-o')
xlabel('SQUIRED SCALE PARAMETER');
ylabel('PSNR (dB)');
hold on;
plot(Square_scaled_para,psnr_linear,'k','marker','*')
hold on;
%weiner
xn = double(x) + (((Square_scaled_para)^2).*randn(sizeA)) + mean_val;
xn = max(0,min(xn,255));
ab=wienerfilter(xn,[3,3],((Square_scaled_para)^2));
xn_mse=sum(sum((double(x)-double(xn)).^2))/(M*N);
xn_msee=sum(sum((double(x)-double(ab)).^2))/(M*N);
psnr_wein=10*log10((255^2)./xn_msee)
plot(Square_scaled_para,psnr_wein,'m','marker','x')
xlabel('SQUIRED SCALE PARAMETER');
ylabel('PSNR (dB)');
hold on;
%median
sizeA = size(x);
xn = double(x) + (((Square_scaled_para)^2).*randn(sizeA)) + mean_val;

3. xn = max(0,min(xn,255));
ab=medfilterr(xn,[3,3]);
xn_mse=sum(sum((double(x)-double(xn)).^2))/(M*N);
xn_psnr=10*log10((255^2)./xn_mse);
xn_msee=sum(sum((double(x)-double(ab)).^2))/(M*N);
psnr_med=10*log10((255^2)./xn_msee)
plot(Square_scaled_para,psnr_med,'r','marker','+')
%axis([0 0.2 0 60])
xlabel('SQUIRED SCALE PARAMETER');
ylabel('PSNR (dB)');
hold on;
end
legend('No Filter','Linear','wiener','median','Location','Best');
%end