小波实验报告双树复小波变换Word文档格式.docx

小波实验报告双树复小波变换Word文档格式.docx

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x=round（（drawcirc（64,1,0,0,256）-*200）;

setfig

（1）;

colormap（gray（256））

image（min（max（x+128,1）,256））;

set（gca,'

position'

[.25.5]）;

axis（'

off'

）;

image'

%draw（xx）;

title（'

Input（256x256）'

'

FontSize'

14）;

drawnow

%Do4levelsofCWT.

[Yl,Yh]=dtwavexfm2（x,4,'

near_sym_b'

qshift_b'

%Looptoreconstructoutputfromcoefsateachlevelinturn.

%Startswiththefinestlevel.

titl=['

1st'

;

'

2nd'

3rd'

4th'

Low'

];

yy=zeros（size（x）.*[23]）;

yt1=1:

size（x,1）;

yt2=1:

size（x,2）;

formlev=1:

5,

mask=zeros（6,5）;

mask（:

mlev）=1;

z=dtwaveifm2（Yl*mask（1,5）,Yh,'

mask）;

figure;

draw（z）;

drawnow

yy（yt1,yt2）=z;

yt2=yt2+size（x,2）/2;

end

%disp（'

Pressakey...'

）

%pause

%NowdosamewithDWT.

%Do4levelsofRealDWTusing'

antonini'

（9,7）-tapfilters.

[Yl,Yh]=wavexfm2（x,4,'

yt1=[1:

size（x,1）]+size（x,1）;

mask=zeros（3,5）;

z=waveifm2（Yl*mask（1,5）,Yh,'

figure;

setfig（gcf）;

image（min（max（yy+128,1）,256））;

[.8.8]）;

holdon

plot（128*[[1;

1]*[1:

4][0;

6]]+1,128*[[0;

4]*[1111][2;

2]]+1,'

-k'

holdoff

Componentsofreconstructed'

disc'

images'

text*size（yy,2）,*size（yy,1）,'

DTCWT'

horiz'

r'

wavelets:

vert'

t'

DWT'

fork=1:

4,text（k*128-63,size（yy,1）*,sprintf（'

level%d'

k）,'

14,'

c'

end

text（5*128+1,size（yy,1）*,'

level4scalingfn.'

%print-deps

disp（'

Pressakeytoseeperfectreconstructionproperty...'

pause

%Accumulatetheimagesfromlowbandupwardstoshowperfectreconstruction.

sy=size（x,2）/2;

formlev=4:

-1:

1,

yt2=[1:

sy]+（mlev-1）*sy;

yy（:

yt2）=yy（:

yt2）+yy（:

yt2+sy）;

AccumulatedreconstructionsfromeachlevelofDTCWT'

text（size（yy,2）*,size（yy,1）*,'

AccumulatedreconstructionsfromeachlevelofDWT'

hor'

return

（2）functionp=drawcirc（r,w,dx,dy,N）

%functionp=drawcirc（r,w,dx,dy,N）

%GenerateanimageofsizeN*Npels,containingacircle

%radiusrpelsandcentredatdx,dyrelative

%tothecentreoftheimage.Theedgeofthecircleisacosineshaped

%edgeofwidthw（from10to90%points）.

x=ones（N,1）*（（[1:

N]-（N+1）/2-dx）/r）;

y=（（[1:

N]'

-（N+1）/2-dy）/r）*ones（1,N）;

p=+*sin（min（max（（exp*（x+y））-exp）*（r*3/w）,-pi/2）,pi/2））;

（3）functionZ=dtwaveifm2（Yl,Yh,biort,qshift,gain_mask）;

%Functiontoperformann-leveldual-treecomplexwavelet（DTCWT）

%2-Dreconstruction.

%Z=dtwaveifm2（Yl,Yh,biort,qshift,gain_mask）;

%Yl->

Thereallowpassimagefromthefinallevel

%Yh->

Acellarraycontainingthe6complexhighpasssubimagesforeachlevel.

%biort->

'

=>

Antonini9,7tapfilters.

%'

legall'

LeGall5,3tapfilters.

near_sym_a'

Near-Symmetric5,7tapfilters.

Near-Symmetric13,19tapfilters.

%qshift->

qshift_06'

QuarterSampleShiftOrthogonal（Q-Shift）10,10tapfilters,

%（only6,6non-zerotaps）.

qshift_a'

Q-shift10,10tapfilters,

%（with10,10non-zerotaps,unlikeqshift_06）.

Q-Shift14,14tapfilters.

qshift_c'

Q-Shift16,16tapfilters.

qshift_d'

Q-Shift18,18tapfilters.

%gain_mask->

Gaintobeappliedtoeachsubband.

%gain_mask（d,l）isgainforsubbandwithdirectiondatlevell.

%Ifgain_mask（d,l）==0,nocomputationisperformedforband（d,l）.

%Defaultgain_mask=ones（6,length（Yh））.

%Z->

Reconstructedrealimagematrix

%Forexample:

Z=dtwaveifm2（Yl,Yh,'

%performsa3-levelreconstructionfromYl,Yhusingthe13,19-tapfilters

%forlevel1andtheQ-shift14-tapfiltersforlevels>

=2.

%NickKingsburyandCianShaffrey

%CambridgeUniversity,May2002

a=length（Yh）;

%Nooflevels.

ifnargin<

5,gain_mask=ones（6,a）;

end%Defaultgain_mask.

ifisstr（biort）&

isstr（qshift）%Checkiftheinputsarestrings

biort_exist=exist（[biort'

.mat'

]）;

qshift_exist=exist（[qshift'

ifbiort_exist==2&

qshift_exist==2;

%Checktoseeiftheinputsexistas.matfiles

load（biort）;

load（qshift）;

else

error（'

PleaseenterthecorrectnamesoftheBiorthogonalorQ-ShiftFilters,seehelpDTWAVEIFM2fordetails.'

else

PleaseenterthenamesoftheBiorthogonalorQ-ShiftFiltersasshowninhelpDTWAVEIFM2.'

current_level=a;

Z=Yl;

whilecurrent_level>

=2;

;

%thisensuresthatforlevel-1weneverdothefollowing

lh=c2q（Yh{current_level}（:

:

[16]）,gain_mask（[16],current_level））;

hl=c2q（Yh{current_level}（:

[34]）,gain_mask（[34],current_level））;

hh=c2q（Yh{current_level}（:

[25]）,gain_mask（[25],current_level））;

%DoevenQshiftfiltersoncolumns.

y1=colifilt（Z,g0b,g0a）+colifilt（lh,g1b,g1a）;

y2=colifilt（hl,g0b,g0a）+colifilt（hh,g1b,g1a）;

%DoevenQshiftfiltersonrows.

Z=（colifilt（y1.'

g0b,g0a）+colifilt（y2.'

g1b,g1a））.'

%ChecksizeofZandcropasrequired

[row_sizecol_size]=size（Z）;

S=2*size（Yh{current_level-1}）;

ifrow_size~=S

（1）%checktoseeifthisresultneedstobecroppedfortherows

Z=Z（2:

row_size-1,:

end

ifcol_size~=S

（2）%checktoseeifthisresultneedstobecroppedforthecols

Z=Z（:

2:

col_size-1）;

ifany（size（Z）~=S（1:

2））,

SizesofsubbandsarenotvalidforDTWAVEIFM2'

current_level=current_level-1;

ifcurrent_level==1;

%Dooddtop-levelfiltersoncolumns.

y1=colfilter（Z,g0o）+colfilter（lh,g1o）;

y2=colfilter（hl,g0o）+colfilter（hh,g1o）;

%Dooddtop-levelfiltersonrows.

Z=（colfilter（y1.'

g0o）+colfilter（y2.'

g1o））.'

%==========================================================================================

%**********INTERNALFUNCTION**********

functionx=c2q（w,gain）

%functionz=c2q（w,gain）

%Scalebygainandconvertfromcomplexw（:

1:

2）torealquad-numbersinz.

%Arrangepixelsfromtherealandimagpartsofthe2subbands

%into4separatesubimages.

%A----BReImofw（:

1）

%||

%C----DReImofw（:

2）

sw=size（w）;

x=zeros（2*sw（1:

2））;

ifany（w（:

））&

any（gain）

sc=sqrt*gain;

P=w（:

1）*sc

（1）+w（:

2）*sc

（2）;

Q=w（:

1）*sc

（1）-w（:

t1=1:

2:

t2=1:

%Recovereachofthe4cornersofthequads.

x（t1,t2）=real（P）;

%a=（A+C）*sc;

x（t1,t2+1）=imag（P）;

%b=（B+D）*sc;

x（t1+1,t2）=imag（Q）;

%c=（B-D）*sc;

x（t1+1,t2+1）=-real（Q）;

%d=（C-A）*sc;

（3）function[Yl,Yh,Yscale]=dtwavexfm2（X,nlevels,biort,qshift）;

%Functiontoperforman-levelDTCWT-2Ddecompostionona2DmatrixX

%[Yl,Yh,Yscale]=dtwavexfm2（X,nlevels,biort,qshift）;

%X->

2Drealmatrix/Image

%nlevels->

No.oflevelsofwaveletdecomposition

%Yscale->

ThisisanOPTIONALoutputargument,thatisacellarraycontaining

%reallowpasscoefficientsforeveryscale.

%Example:

[Yl,Yh]=dtwavexfm2（X,3,'

%performsa3-leveltransformontherealimageXusingthe13,19-tapfilters

%CambridgeUniversity,Sept2001

%Checktoseeiftheinputsexistas.matfiles

PleaseenterthecorrectnamesoftheBiorthogonalorQ-ShiftFilters,seehelpDTWAVEXFM2fordetails.'

PleaseenterthenamesoftheBiorthogonalorQ-ShiftFiltersasshowninhelpDTWAVEXFM2.'

end

orginal_size=size（X）;

ifndims（X）>

=3;

error（sprintf（'

Theenteredimageis%dx%dx%d,pl