1、-()0 td t*-1(,),()()()*()stuWf u sftf tdtfuss*1()()sttss*()()sss/2()2(2)jjnxxk2jnk21j111fiddf0ixMx 0iyMy ifdMd(,)ooxyThe truncated spherical exit wave)(2)(222),(),(aayyxxjaiaiyxdkjiiidydxeydxdpejyxuaiaiiiiooooooioiiiidydxMyMxuyyxxhyxu),(),(),(,)(,)iaiah x ypd xd y),(oooyxu),(oooMyMxu),(),(vdudpvuHii
2、),(iiyxooooooioiiidydxMyMxIyyxxhyxI),(),(),(2Part 3 Technology and Part 3 Technology and ApplicationsApplications10 Image Restoration10 Image RestorationChapter16 Chapter16 Image Restoration Image Restoration 16.2 Classical restoration16.3 Linear algebraic restoration16.4 restoration of less restric
3、ted degradations16.5 Superresolution16.6 System identification16.7Noise modeling16.8 Implementation16.2 Classical RestorationClassification of filtersClassification of filters lowpass Basic filter types bandpass,bandstophighpass Wiener estimator design of two linear filters the matched detector nonl
4、inear filter),(),(),(),(),(),(2vuPvuPvuHvuPvuHvuGnfffP and are the power spectra of the signal and noise,respectivelynP)()()(tytstedtteteMSE)()(22Points：Given the power spectra of Given the power spectra of that minimizes the mean square that minimizes the mean square error;error;is positive for bot
5、h positive and negative errors.Squaring the error causes large errors to be “penalized”more severely than small errors。2()e t()()()()s t n ts tn t00()()()()()()snnsnP s P sMSEdsP s Hs dsP sP sBased on formula(2),we can derive and prove the Based on formula(2),we can derive and prove the conclusions
6、belowconclusions below：0s 0()()()()ssnP sHsP sP sFigure 5 Wiener deconvolutionFigure 5 Wiener deconvolution0()()1()()()()()ssnHsP sG sF sF sP sP sThe transfer function of the optimal deconvolution filter in the mean square sense is:S(t)w(t)x(t)n(t)y(t)z(t)F(s)1/F(s)0()Hs+G(s)12*2),(/),(),(),(),(),()
7、,(vuPvuPvuHvuHvuHvuHvuGfn),(/),(),(),(),(2vuPvuPvuHvuHvuGfn16.2 Classical Restoration16.3 Linear Algebraic Restoration22nfHg222)(nfHgfQfW0)(22)(HfgHQfQffWgHQQHHfttt1)(1,gHIHHftt1)(2121nfRRQf16.2 Classical Restoration16.3 Linear Algebraic Restoration16.4 restoration of less restricted degradations),(
8、yxw),(2yxw),(),(),0,0(),(02yxNyxyxpyxvuPwnnn0NW(,)x y(,)x y12*2*),(),(),(),(),(NSsPPvuFPvuFvuFvuFyxvuG),(yxw),(2yxw),(),(),(),(),(),(),(),(2yxNPRvuPNRyxNyxyxvuPNRyxvuPyxvnPOOOwowwooosn16.2 Classical Restoration16.3 Linear Algebraic Restoration16.4 restoration of less restricted degradations16.5 Supe
9、rresolutionUse the sample values of f(t)to compute points on its spectrum F(s).Figure Computing spectraThe input signal and its spectrumatatasA22210)(xf16.2Classical Restoration16.3 Linear Algebraic Restoration16.4 restoration of less restricted degradations16.5 Superresolution16.6 System Identifica
10、tion h(x,y)f(x,y)g(x,y),(),(),(vuFvuGvuHPoint Source Targets If it were possible to input an impulse(PSF),the output would be the impulse response.While an impulse is physically impossible,we could get by with a pulse that is narrow compared to the PSF itself.)2cos(),(0 xsyxf0su)(),(xyxf)(),(xuyxf)2
11、()()(axHxfxg22)(axjexfax)()()(sPsHsZf)(sPf)(xf16.2 16.2Classical Restoration16.3 Linear Algebraic Restoration16.4 restoration of less restricted degradations16.5 Superresolution16.6 System Identification16.7Noise Modeling 16.2 16.2Classical Restoration16.3 Linear Algebraic Restoration16.4 restoratio
12、n of less restricted degradations16.5 Superresolution16.6System Identification16.7Noise Modeling16.8 Implementation1010,NiNkkinmnmkiFGwfF Fwft*NkijkieNw2,11,10,11,00,0.NNNNwwwwwFwG ttGwwF*Nxh10 其它ppppqqqqppkxxNxh222122121220221220000000022000000002200000000222222000000002222111111111111111181rHFWWWg
13、*1*yhxfgx*hfg()()()H zF z G z 421211212000000ffggF z G zf g zzzzzffgg 44321123400000hhhhH zh zzzzzhhhh1oofg1 1 1tf 1 1 1tg 1 1 11 1 11 1 11 1 11 1 11 1 1xy1232124642369632464212321xy4321212112120000002321ffggzzzzf gzzzzffgg1454141620164520202054162016414541xy13.15110.8513.159.923.150.850.720.8513.15110.851xy 16.2 16.2Classical Restoration16.3 Linear Algebraic Restoration16.4 restoration of less restricted degradations16.5 Superresolution16.6System Identification16.7Noise Modeling16.8 Implementation
