function?ResIm?=?Image_Denoising_Global_Denoising（Im??trueIm）
%?Denoise?image?by?denoising?its?patches?using?a?pre-determined?dictionary.
%?Patches?are?denoised?WITHOUT?overlap.
%
%?Inputs?:?
%?Im??????:?image?to?denoise?double?[0?255]
%?trueIm??:?This?is?used?（unfairly）?to?optimize?the?parameters?for?the?algorithm
%
%?Outputs?:
%?ResIm???:?Result?Image?for?the?best?parameter

%%?Parameters
imLen?=?numel（Im）;

%%?Create?the?dictionary?-?Haar
[HaarDict??atomNorms]?=?Generate_Haar_Matrix（size（Im）??2）;
atomNorms?=?atomNorms（:）;
invAtomNorms?=?1?./?atomNorms;
%?Show_Haar_Dict（HaarDict??size（Im））;
nAtoms?=?size（HaarDict??2）;?%?=?1?+?3?*?nLevels

%%?Prepare?the?projections?of?the?image?onto?the?dictionary
projs?=?HaarDict‘?*?Im（:）;
absProjs?=?abs（projs）;

%%?Test?for?different?values?of?T
Tvalues?=?[0?:?200];
resPSNRs?=?zeros（1??length（Tvalues））;
fprintf（‘%d?T?values:?‘??length（Tvalues））;
for?Tind?=?1?:?length（Tvalues）
	
	if?mod（Tind??10）?==?0?fprintf（‘%d?‘??Tind）;?end;
	
	%?Current?threshold
	T?=?Tvalues（Tind）;
	
	%?Compute?the?hard-thresholding?result
	resProjs?=?projs?.*?（absProjs?>?（T?.*?invAtomNorms））;
	
	%?Compute?the?result?signal?by?multiplying?by?the?dictionary
	currResIm?=?HaarDict?*?resProjs;
	currResIm?=?reshape（currResIm??size（Im））;
	
	%?Compute?error?result
	resPSNRs（Tind）?=?Compute_Error_Stats（currResIm??trueIm）;
	
end
fprintf（‘\n‘）;

%%?Find?the?best?value?and?plot?the?results
[~?maxPSNRind]?=?max（resPSNRs）;
bestT?=?Tvalues（maxPSNRind）;
if?1
	figure;
	plot（Tvalues??resPSNRs??‘+r‘）;
	title（‘PSNR?as?a?function?of?T‘）;
end

%%?Reconstruct?the?image?for?the?best?value?of?T
resProjs?=?projs?.*?（absProjs?>?（bestT?.*?invAtomNorms））;
ResIm?=?HaarDict?*?resProjs;
ResIm?=?reshape（ResIm??size（Im））;

%%
return;

%?[nm]=size（Haar）;
%?W=[0.25*ones（n*41）;?0.5*ones（n*31）];




function?[HaarDict??atomNorms]?=?Generate_Haar_Matrix（imSize??nLevels）

atomNorms?=?[];

%?Prepare?the?first?level?bands
basicH?=?[1?-1];
basicL?=?[1?1];
HH1?=?kron（basicH‘??basicH）;?
HaarDict?=?Construct_One_Haar_Band（imSize??HH1）;
atomNorms?=?[atomNorms?ones（1??prod（imSize））?*?sqrt（sum（HH1（:）.^2））];

LH1?=?kron（basicL‘??basicH）;?
HaarDict?=?[HaarDict?Construct_One_Haar_Band（imSize??LH1）];
atomNorms?=?[atomNorms?ones（1??prod（imSize））?*?sqrt（sum（LH1（:）.^2））];

HL1?=?kron（basicH‘??basicL）;?
HaarDict?=?[HaarDict?Construct_One_Haar_Band（imSize?