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f(2-D)g(con)n(v)n(olu-)-186 3430 y(tion)23 b(of)g(image)g(with)g (non-causal)g(p)r(oin)n(t-spread)g(function)f(\(PSF\).)-186 3517 y(Blur)31 b(iden)n(ti\014cation)f(is)h(determination)e(of)i(unkno) n(wn)e(PSF,)i(and)-186 3603 y(is)24 b(the)e(most)h(imp)r(ortan)n(t)f (step)h(to)n(w)n(ards)h(successful)g(digital)g(image)-186 3690 y(restoration.)-61 3777 y(Early)29 b(approac)n(hes)h(to)g(blur)f (iden)n(ti\014cation)g(tak)n(e)g(adv)l(an)n(tage)-186 3864 y(of)37 b(2-D)f(p)r(o)n(w)n(er)g(cepstrum)f(of)i(degraded)f(image) h([1].)67 b(P)n(erio)r(dic-)-186 3950 y(it)n(y)26 b(in)h(logarithm)g (of)g(sp)r(ectrum)f(enables)h(iden)n(ti\014cation)g(of)g(blurs)-186 4037 y(that)33 b(ha)n(v)n(e)g(zeros)i(on)e(the)g(unit)g(bicircle)i (\(motion)e(blur,)i(out-of-)-186 4124 y(fo)r(cus)29 b(blur\).)42 b(More)29 b(recen)n(t)f(approac)n(hes)h(are)f(based)h(on)f(the)g(2-D) -186 4211 y(autoregressiv)n(e)d(mo)n(ving)d(a)n(v)n(erage)i(\(ARMA\))e (mo)r(del)h(of)h(degraded)-186 4297 y(image.)74 b(AR)38 b(part)g(of)i(the)e(mo)r(del)h(represen)n(ts)g(original)h(image)-186 4384 y(mo)r(del,)d(and)e(MA)g(part)g(represen)n(ts)g(non-causal)h(PSF)f ([2].)63 b(Es-)-186 4471 y(timation)36 b(of)i(unkno)n(wn)d(mo)r(del)h (parameters)h(is)g(p)r(erformed)f(us-)-186 4558 y(ing)g(maximization)f (of)h(lik)n(eliho)r(o)r(d)h(function.)65 b(This)36 b(metho)r(d)f(is) -186 4645 y(extended)27 b(to)i(more)f(general)i(case,)g(using)f(sp)r (ectrally)g(equiv)l(alen)n(t)-186 4731 y(minim)n(um)e(phase)k(\(SEMP\)) f(system)f(represen)n(tation)i([3)q(].)49 b(In)29 b([4)q(])-186 4818 y(2-D)19 b(ARMA)f(mo)r(del)h(iden)n(ti\014cation)h(is)g(decomp)r (osed)e(in)n(to)i(parallel)-186 4905 y(1-D)25 b(complex)g(ARMA)g(mo)r (del)g(iden)n(ti\014cation.)-61 4992 y(Iterativ)n(e)34 b(algorithms,)j(where)e(iden)n(ti\014cation)g(and)f(restora-)-186 5078 y(tion)f(steps)g(are)g(p)r(erformed)g(one)f(after)i(another,)h (are)e(describ)r(ed)-186 5165 y(in)26 b([5)q(])h(and)f([6)q(].)37 b(In)26 b([7)q(])h(the)f(PSF)g(is)h(c)n(hosen)g(from)g(a)f(collection)j (of)-186 5252 y(a)j(candidate)h(PSFs)f(to)g(pro)n(vide)g(the)g(b)r(est) g(matc)n(h)f(b)r(et)n(w)n(een)h(the)-186 5339 y(restoration)22 b(residual)g(p)r(o)n(w)n(er)f(sp)r(ectrum)f(and)h(its)g(exp)r(ected)f (v)l(alue.)1975 1493 y(Unkno)n(wn)31 b(PSF)g(parameter)h(estimation)g (based)f(on)h(con)n(tin)n(uous)1975 1579 y(blur)26 b(mo)r(del)f(is)h (describ)r(ed)g(in)g([8].)2100 1666 y(Our)31 b(blur)h(iden)n (ti\014cation)g(algorithm)g(op)r(erates)h(on)f(singular)1975 1753 y(v)n(ectors)21 b(of)h(degraded)e(image.)33 b(W)-6 b(e)20 b(iden)n(tify)h(comp)r(onen)n(ts)f(of)h(SVD)1975 1840 y(decomp)r(osition)31 b(of)g(the)e(unkno)n(wn)g(PSF.)i(First)f (\(left)h(and)f(righ)n(t\))1975 1926 y(singular)24 b(v)n(ectors)f(of)g (PSF)g(can)f(b)r(e)h(estimated)f(using)h(corresp)r(ond-)1975 2013 y(ing)f(\014rst)f(few)i(singular)g(v)n(ectors)e(of)h(degraded)g (image.)33 b(When)21 b(S/N)1975 2100 y(ratio)27 b(is)g(high,)g(it)f(is) g(p)r(ossible)i(to)e(estimate)g(second)g(singular)i(v)n(ec-)1975 2187 y(tors)f(of)f(PSF.)2100 2273 y(This)g(pap)r(er)f(is)h(organized)g (as)g(follo)n(ws.)37 b(In)24 b(Section)i(2)f(w)n(e)h(dis-)1975 2360 y(cuss)36 b(c)n(hanges)f(in)g(singular)h(v)n(ectors)f(of)h (original)h(image)e(due)g(to)1975 2447 y(degradation.)51 b(In)30 b(Section)h(3)g(w)n(e)h(describ)r(e)f(our)g(blur)f(iden)n (ti\014ca-)1975 2534 y(tion)22 b(algorithm.)33 b(Section)21 b(4)g(con)n(tains)h(iden)n(ti\014cation)f(results)g(and)1975 2620 y(discussion,)26 b(while)e(in)f(Section)g(5)h(w)n(e)g(summarize)e (prop)r(osed)i(algo-)1975 2707 y(rithm.)2000 2905 y Fl(2.)53 b(DEGRAD)n(A)-7 b(TION)29 b(OF)g(SINGULAR)i(VECTORS)1975 3066 y Fk(Blur)h(iden)n(ti\014cation)f(is)h(p)r(ossible)h(from)e(ph)n (ysical)g(mo)r(deling)g(and)1975 3153 y(measuremen)n(t)39 b(of)i(imaging)g(system)e(\(test)h(images\),)45 b(but)39 b(it)h(is)1975 3239 y(frequen)n(tly)29 b(necessary)h(to)g(iden)n(tify)f (blur)h(from)f(degraded)h(image)1975 3326 y(only)-6 b(.)40 b(Standard)27 b(linear)h(discrete)h(mo)r(del)e(of)h(image)g (degradation)1975 3413 y(is)f(describ)r(ed)e(using)h(follo)n(wing)j (equation:)2093 3643 y Fj(g)s Fk(\()p Fj(i;)12 b(j)t Fk(\))22 b(=)2454 3541 y Fi(K)2422 3566 y Fh(X)2390 3740 y Fi(k)q Fg(=)p Ff(\000)p Fi(K)2643 3541 y(L)2604 3566 y Fh(X)2586 3740 y Fi(l)p Fg(=)p Ff(\000)p Fi(L)2755 3643 y Fj(h)p Fk(\()p Fj(k)r(;)14 b(l)q Fk(\))p Fj(f)8 b Fk(\()p Fj(i)18 b Fe(\000)e Fj(k)r(;)e(j)21 b Fe(\000)c Fj(l)q Fk(\))g(+)g Fj(n)p Fk(\()p Fj(i;)d(j)t Fk(\))p Fj(;)118 b Fk(\(1\))1975 3879 y(where)26 b Fj(i)g Fk(and)f Fj(k)j Fk(represen)n(t)d(discrete)h(v)l(ariables)g(in)g(v)n(ertical)g (direc-)1975 3966 y(tion,)35 b Fj(j)i Fk(and)32 b Fj(l)h Fk(represen)n(t)f(discrete)h(v)l(ariables)g(in)f(horizon)n(tal)h(di-) 1975 4053 y(rection,)e Fj(f)8 b Fk(\()p Fj(i;)13 b(j)t Fk(\))30 b(is)f(original)h(image,)g Fj(g)s Fk(\()p Fj(i;)13 b(j)t Fk(\))29 b(is)g(degraded)g(image,)1975 4139 y Fj(n)p Fk(\()p Fj(i;)14 b(j)t Fk(\))36 b(is)f(Gaussian)h(white)g(noise)g (\014eld,)h(and)e Fj(h)p Fk(\()p Fj(k)r(;)13 b(l)q Fk(\))35 b(is)h(space-)1975 4226 y(in)n(v)l(arian)n(t)29 b(PSF)h(of)g(size)g (\(2)p Fj(K)25 b Fk(+)20 b(1\)\(2)p Fj(L)g Fk(+)f(1\).)46 b(If)30 b(w)n(e)f(lo)r(ok)i(at)e(the)1975 4313 y(images)c(in)e(the)g (equation)h(\(1\))g(as)g Fj(N)d Fe(\002)13 b Fj(N)32 b Fk(matrices,)24 b(than)g(w)n(e)g(can)1975 4400 y(analyze)37 b(c)n(hanges)g(in)g(SVD)e(represen)n(tation)i(of)g(original)i(image) 1975 4486 y(matrix)27 b Fl(F)g Fk(due)g(to)g(degradation.)41 b(Original)28 b(image)g(is)g(blurred)f(in)1975 4573 y(suc)n(h)32 b(a)g(w)n(a)n(y)h(that)e(original)j(image)f(is)f(displaced)h(b)n(y)e (\()p Fj(k)r(;)13 b(l)q Fk(\),)34 b(and)1975 4660 y(linear)h(com)n (bination)e(using)h(w)n(eigh)n(ting)h(factors)g Fj(h)p Fk(\()p Fj(k)r(;)13 b(l)q Fk(\))34 b(is)g(com-)1975 4747 y(puted:)2132 4875 y Fi(R)2178 4886 y Fd(G)2120 4904 y Fh(X)2126 5078 y Fi(r)r Fg(=1)2252 4980 y Fj(s)2288 4988 y Fi(r)r(G)2370 4980 y Fl(u)2419 4988 y 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b(depicted)e(in)f(Fig.)-186 5165 y(1\(a\))22 b(and)g(1\(b\))f(are)h (result)g(of)h(a)n(v)n(eraging)g(on)e(a)i(n)n(um)n(b)r(er)c(of)k (images)-186 5252 y(of)i(v)l(arious)g(scenes.)35 b(Fig.)g(1\(a\))25 b(depicts)f(v)l(alue)h(of)g(one-step)f(corre-)-186 5339 y(lation)g(for)g(non-degraded)f(images,)i Fj(N)k Fk(=)21 b(256.)35 b(As)23 b Fj(r)i Fk(mo)n(v)n(es)e(from)2135 1319 y @beginspecial 53 @llx 199 @lly 542 @urx 589 @ury 1984 @rwi @setspecial %%BeginDocument: kare1.eps %!PS-Adobe-2.0 EPSF-1.2 %%Creator: MATLAB, The Mathworks, Inc. %%Title: kare1.eps %%CreationDate: 10/28/99 14:34:55 %%DocumentNeededFonts: Helvetica %%DocumentProcessColors: Cyan Magenta Yellow Black %%Pages: 1 %%BoundingBox: 53 199 542 589 %%EndComments %%BeginProlog % MathWorks dictionary /MathWorks 160 dict begin % definition operators /bdef {bind def} bind def /ldef {load def} bind def /xdef {exch def} bdef /xstore {exch store} bdef % operator abbreviations /c /clip ldef /cc /concat ldef /cp /closepath ldef /gr /grestore ldef /gs /gsave ldef /mt /moveto ldef /np /newpath ldef /cm /currentmatrix ldef /sm /setmatrix ldef /rc {rectclip} bdef /rf {rectfill} bdef /rm /rmoveto ldef /rl /rlineto ldef /s /show ldef /sc {setcmykcolor} bdef /sr /setrgbcolor ldef /sg /setgray ldef /w /setlinewidth ldef /j /setlinejoin ldef /cap /setlinecap ldef % page state control /pgsv () def /bpage {/pgsv save def} bdef /epage {pgsv restore} bdef /bplot /gsave ldef /eplot {stroke grestore} bdef % orientation switch /portraitMode 0 def /landscapeMode 1 def % coordinate system mappings /dpi2point 0 def % font control /FontSize 0 def /FMS { /FontSize xstore %save size off stack findfont [FontSize 0 0 FontSize neg 0 0] makefont setfont }bdef /ISOLatin1Encoding where {pop /WindowsLatin1Encoding 256 array bdef ISOLatin1Encoding WindowsLatin1Encoding copy pop /.notdef/.notdef/quotesinglbase/florin/quotedblbase/ellipsis/dagger/daggerdbl /circumflex/perthousand/Scaron/guilsinglleft/OE/.notdef/.notdef/.notdef 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objects /L { lineto stroke } bdef /MP { 3 1 roll moveto 1 sub {rlineto} repeat } bdef /AP { {rlineto} repeat } bdef /PP { closepath eofill } bdef /DP { closepath stroke } bdef /MR { 4 -2 roll moveto dup 0 exch rlineto exch 0 rlineto neg 0 exch rlineto closepath } bdef /FR { MR stroke } bdef /PR { MR fill } bdef /L1i { { currentfile picstr readhexstring pop } image } bdef /tMatrix matrix def /MakeOval { newpath tMatrix currentmatrix pop translate scale 0 0 1 0 360 arc tMatrix setmatrix } bdef /FO { MakeOval stroke } bdef /PO { MakeOval fill } bdef /PD { currentlinecap 1 setlinecap 3 1 roll 2 copy moveto lineto stroke setlinecap } bdef /FA { newpath tMatrix currentmatrix pop translate scale 0 0 1 5 -2 roll arc tMatrix setmatrix stroke } bdef /PA { newpath tMatrix currentmatrix pop translate 0 0 moveto scale 0 0 1 5 -2 roll arc closepath tMatrix setmatrix fill } bdef /FAn { newpath tMatrix currentmatrix pop translate scale 0 0 1 5 -2 roll arcn tMatrix setmatrix stroke } bdef /PAn { newpath tMatrix currentmatrix pop translate 0 0 moveto scale 0 0 1 5 -2 roll arcn closepath tMatrix setmatrix fill } bdef /MRR { /vradius xdef /hradius xdef /lry xdef /lrx xdef /uly xdef /ulx xdef newpath tMatrix currentmatrix pop ulx hradius add uly vradius add translate hradius vradius scale 0 0 1 180 270 arc tMatrix setmatrix lrx hradius sub uly vradius add translate hradius vradius scale 0 0 1 270 360 arc tMatrix setmatrix lrx hradius sub lry vradius sub translate hradius vradius scale 0 0 1 0 90 arc tMatrix setmatrix ulx hradius add lry vradius sub translate hradius vradius scale 0 0 1 90 180 arc tMatrix setmatrix closepath } bdef /FRR { MRR stroke } bdef /PRR { MRR fill } bdef /MlrRR { /lry xdef /lrx xdef /uly xdef /ulx xdef /rad lry uly sub 2 div def newpath tMatrix currentmatrix pop ulx rad add uly rad add translate rad rad scale 0 0 1 90 270 arc tMatrix setmatrix lrx rad sub lry rad sub translate rad rad scale 0 0 1 270 90 arc tMatrix setmatrix closepath } bdef /FlrRR { MlrRR stroke } bdef /PlrRR { MlrRR fill } bdef /MtbRR { /lry xdef /lrx xdef /uly xdef /ulx xdef /rad lrx ulx sub 2 div def newpath tMatrix currentmatrix pop ulx rad add uly rad add translate rad rad scale 0 0 1 180 360 arc tMatrix setmatrix lrx rad sub lry rad sub translate rad rad scale 0 0 1 0 180 arc tMatrix setmatrix closepath } bdef /FtbRR { MtbRR stroke } bdef /PtbRR { MtbRR fill } bdef currentdict end def %%EndProlog %%BeginSetup MathWorks begin 0 cap end %%EndSetup %%Page: 1 1 %%BeginPageSetup %%PageBoundingBox: 53 199 542 589 MathWorks begin bpage %%EndPageSetup %%BeginObject: obj1 bplot /dpi2point 12 def portraitMode 0204 7344 csm 433 272 5871 4681 MR c np 85 dict begin %Colortable dictionary /c0 { 0 0 0 sr} bdef /c1 { 1 1 1 sr} bdef /c2 { 1 0 0 sr} bdef /c3 { 0 1 0 sr} bdef /c4 { 0 0 1 sr} bdef /c5 { 1 1 0 sr} bdef /c6 { 1 0 1 sr} bdef /c7 { 0 1 1 sr} bdef 1 j 1 sg 0 0 6913 5185 PR 6 w 0 4224 5356 0 0 -4224 898 4612 4 MP PP -5356 0 0 4224 5356 0 0 -4224 898 4612 5 MP stroke 4 w DO 0 sg 1927 4612 mt 1927 388 L 1927 388 mt 1927 388 L 2977 4612 mt 2977 388 L 2977 388 mt 2977 388 L 4028 4612 mt 4028 388 L 4028 388 mt 4028 388 L 5078 4612 mt 5078 388 L 5078 388 mt 5078 388 L 6128 4612 mt 6128 388 L 6128 388 mt 6128 388 L 898 4612 mt 6254 4612 L 6254 4612 mt 6254 4612 L 898 4084 mt 6254 4084 L 6254 4084 mt 6254 4084 L 898 3556 mt 6254 3556 L 6254 3556 mt 6254 3556 L 898 3028 mt 6254 3028 L 6254 3028 mt 6254 3028 L 898 2500 mt 6254 2500 L 6254 2500 mt 6254 2500 L 898 1972 mt 6254 1972 L 6254 1972 mt 6254 1972 L 898 1444 mt 6254 1444 L 6254 1444 mt 6254 1444 L 898 916 mt 6254 916 L 6254 916 mt 6254 916 L 898 388 mt 6254 388 L 6254 388 mt 6254 388 L SO 6 w 898 388 mt 6254 388 L 898 4612 mt 6254 4612 L 6254 4612 mt 6254 388 L 898 4612 mt 898 388 L 898 4612 mt 6254 4612 L 898 4612 mt 898 388 L 1927 4612 mt 1927 4558 L 1927 388 mt 1927 442 L %%IncludeResource: font Helvetica /Helvetica /WindowsLatin1Encoding 120 FMSR 1861 4758 mt (50) s 2977 4612 mt 2977 4558 L 2977 388 mt 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21 -37 21 0 21 -31 21 5 21 53 21 -9 21 31 21 -8 21 -16 21 60 21 -84 21 72 21 36 21 -69 21 5 21 16 21 22 21 -30 21 33 21 -16 21 -75 21 86 21 -60 21 115 21 -35 21 -31 21 86 21 -131 21 23 21 55 21 -2 21 164 21 -23 21 -25 21 -33 21 110 21 28 21 -78 21 25 21 24 21 -14 21 -20 21 43 21 -49 21 -7 21 -3 21 89 21 7 21 -2 21 -28 21 5 21 129 21 -168 21 45 21 28 21 68 21 8 21 -73 21 61 21 6 21 -1 21 -44 21 68 21 -69 21 37 21 22 21 -46 21 76 21 -31 21 70 21 -64 21 101 21 -34 21 -27 21 22 21 15 21 -59 21 186 21 -129 21 7 21 32 21 26 21 18 21 20 21 -39 21 35 21 38 21 -56 21 65 21 -4 21 -35 21 62 21 -41 4175 3681 100 MP stroke 21 22 21 37 21 78 21 21 21 -37 21 -8 21 60 21 4 21 -6 21 -23 21 97 21 -108 21 75 21 -108 21 183 21 -62 21 -28 21 101 21 -30 21 -8 21 19 21 15 21 -46 21 70 21 13 21 67 21 -52 21 72 22 -39 21 -9 21 32 21 6 21 42 21 -86 21 117 21 -21 21 30 21 76 21 -76 21 31 21 11 21 22 21 23 21 35 21 -52 21 18 21 64 21 -1 21 -3 21 54 21 -47 21 -13 21 81 21 4 21 -20 21 79 21 82 21 -38 21 -20 21 41 21 18 21 -89 21 66 21 136 21 -61 21 27 21 -33 21 137 21 -98 21 -30 21 95 21 46 21 -117 21 48 21 174 21 -25 21 -65 21 65 21 -67 21 139 21 -34 21 -8 21 48 21 51 21 8 21 42 21 -44 21 -9 21 66 21 5 21 -10 21 40 21 26 21 73 21 -21 21 46 21 1 21 6 21 26 2095 2162 100 MP stroke 21 60 21 70 21 -4 21 13 21 25 21 24 21 -15 21 84 21 9 21 -24 21 97 21 -89 21 104 21 11 21 31 21 44 21 44 21 -74 21 120 21 5 21 -11 21 73 21 -29 21 36 21 13 21 121 21 -105 21 101 21 -43 21 131 21 55 21 -7 21 -47 21 45 21 91 21 35 21 56 21 -40 21 95 21 -15 21 84 21 -12 21 73 21 18 21 -28 21 97 21 18 21 -6 21 27 21 71 21 53 21 25 21 36 21 73 21 11 21 72 21 61 898 399 58 MP stroke 21 0 21 0 21 0 21 0 21 0 21 0 21 0 21 0 21 0 21 0 21 0 21 0 21 0 21 0 21 0 21 0 21 0 21 0 21 0 21 0 21 0 21 0 21 0 21 0 21 0 21 0 21 0 21 0 21 0 21 0 21 0 21 0 21 0 21 0 21 0 21 0 21 0 21 0 21 0 21 0 21 0 21 0 21 0 21 0 21 0 21 0 21 0 21 0 21 0 21 0 21 0 21 0 21 0 21 0 21 0 21 0 21 0 21 0 21 0 21 0 21 0 21 0 21 0 21 0 21 0 21 0 21 0 21 0 21 0 21 0 21 0 21 0 21 0 21 0 21 0 21 0 21 0 21 0 21 0 21 0 21 0 21 0 21 0 21 0 21 0 21 0 21 0 21 0 21 0 21 0 21 0 21 0 21 0 21 0 21 0 21 0 21 0 21 0 21 0 4175 3028 100 MP stroke 21 0 21 0 21 0 21 0 21 0 21 0 21 0 21 0 21 0 21 0 21 0 21 0 21 0 21 0 21 0 21 0 21 0 21 0 21 0 21 0 21 0 21 0 21 0 21 0 21 0 21 0 21 0 21 0 22 0 21 0 21 0 21 0 21 0 21 0 21 0 21 0 21 0 21 0 21 0 21 0 21 0 21 0 21 0 21 0 21 0 21 0 21 0 21 0 21 0 21 0 21 0 21 0 21 0 21 0 21 0 21 0 21 0 21 0 21 0 21 0 21 0 21 0 21 0 21 0 21 0 21 0 21 0 21 0 21 0 21 0 21 0 21 0 21 0 21 0 21 0 21 0 21 0 21 0 21 0 21 0 21 0 21 0 21 0 21 0 21 0 21 0 21 0 21 0 21 0 21 0 21 0 21 0 21 0 21 0 21 0 21 0 21 0 21 0 21 0 2095 3028 100 MP stroke 21 0 21 0 21 0 21 0 21 0 21 0 21 0 21 0 21 0 21 0 21 0 21 0 21 0 21 0 21 0 21 0 21 0 21 0 21 0 21 0 21 0 21 0 21 0 21 0 21 0 21 0 21 0 21 0 21 0 21 0 21 0 21 0 21 0 21 0 21 0 21 0 21 0 21 0 21 0 21 0 21 0 21 0 21 0 21 0 21 0 21 0 21 0 21 0 21 0 21 0 21 0 21 0 21 0 21 0 21 0 21 0 21 0 898 3028 58 MP stroke gr %%IncludeResource: font Helvetica /Helvetica /WindowsLatin1Encoding 144 FMSR 2708 4919 mt (Singular vector number - r ) s 572 3512 mt -90 rotate (One-step correlation coefficient) s 90 rotate end eplot %%EndObject epage end showpage %%Trailer %%EOF %%EndDocument @endspecial 2988 1406 a(a\))2135 2757 y @beginspecial 55 @llx 199 @lly 542 @urx 589 @ury 1984 @rwi @setspecial %%BeginDocument: kare2.eps %!PS-Adobe-2.0 EPSF-1.2 %%Creator: MATLAB, The Mathworks, Inc. %%Title: kare2.eps %%CreationDate: 10/28/99 14:35:13 %%DocumentNeededFonts: Helvetica %%DocumentProcessColors: Cyan Magenta Yellow Black %%Pages: 1 %%BoundingBox: 55 199 542 589 %%EndComments %%BeginProlog % MathWorks dictionary /MathWorks 160 dict begin % definition operators /bdef {bind def} bind def /ldef {load def} bind def /xdef {exch def} bdef /xstore {exch store} bdef % operator abbreviations /c /clip ldef /cc /concat ldef /cp /closepath ldef /gr /grestore ldef /gs /gsave ldef /mt /moveto ldef /np /newpath ldef /cm /currentmatrix ldef /sm /setmatrix ldef /rc {rectclip} bdef /rf {rectfill} bdef /rm /rmoveto ldef /rl /rlineto ldef /s /show ldef /sc {setcmykcolor} bdef /sr /setrgbcolor ldef /sg /setgray ldef /w /setlinewidth ldef /j /setlinejoin ldef /cap /setlinecap ldef % page state control /pgsv () def /bpage {/pgsv save def} bdef /epage {pgsv restore} bdef /bplot /gsave ldef /eplot {stroke grestore} bdef % orientation switch /portraitMode 0 def /landscapeMode 1 def % coordinate system mappings /dpi2point 0 def % font control /FontSize 0 def /FMS { /FontSize xstore %save size off stack findfont [FontSize 0 0 FontSize neg 0 0] makefont setfont }bdef /ISOLatin1Encoding where {pop /WindowsLatin1Encoding 256 array bdef ISOLatin1Encoding WindowsLatin1Encoding copy pop /.notdef/.notdef/quotesinglbase/florin/quotedblbase/ellipsis/dagger/daggerdbl /circumflex/perthousand/Scaron/guilsinglleft/OE/.notdef/.notdef/.notdef /.notdef/quoteleft/quoteright/quotedblleft/quotedblright/bullet/endash/emdash /tilde/trademark/scaron/guilsinglright/oe/.notdef/.notdef/Ydieresis WindowsLatin1Encoding 128 32 getinterval astore pop} {/WindowsLatin1Encoding StandardEncoding bdef} ifelse /reencode { exch dup where {pop load} {pop StandardEncoding} ifelse exch dup 3 1 roll findfont dup length dict begin { 1 index /FID ne {def}{pop pop} ifelse } forall /Encoding exch def currentdict end definefont pop } bdef /isroman { findfont /CharStrings get /Agrave known } bdef /FMSR { 3 1 roll 1 index dup isroman {reencode} {pop pop} ifelse exch FMS } bdef /csm { 1 dpi2point div -1 dpi2point div scale neg translate landscapeMode eq {90 rotate} if } bdef % line types: solid, dotted, dashed, dotdash /SO { [] 0 setdash } bdef /DO { [.5 dpi2point mul 4 dpi2point mul] 0 setdash } bdef /DA { [6 dpi2point mul] 0 setdash } bdef /DD { [.5 dpi2point mul 4 dpi2point mul 6 dpi2point mul 4 dpi2point mul] 0 setdash } bdef % macros for lines and objects /L { lineto stroke } bdef /MP { 3 1 roll moveto 1 sub {rlineto} repeat } bdef /AP { {rlineto} repeat } bdef /PP { closepath eofill } bdef /DP { closepath stroke } bdef /MR { 4 -2 roll moveto dup 0 exch rlineto exch 0 rlineto neg 0 exch rlineto closepath } bdef /FR { MR stroke } bdef /PR { MR fill } bdef /L1i { { currentfile picstr readhexstring pop } image } bdef /tMatrix matrix def /MakeOval { newpath tMatrix currentmatrix pop translate scale 0 0 1 0 360 arc tMatrix setmatrix } bdef /FO { MakeOval stroke } bdef /PO { MakeOval fill } bdef /PD { currentlinecap 1 setlinecap 3 1 roll 2 copy moveto lineto stroke setlinecap } bdef /FA { newpath tMatrix currentmatrix pop translate scale 0 0 1 5 -2 roll arc tMatrix setmatrix stroke } bdef /PA { newpath tMatrix currentmatrix pop translate 0 0 moveto scale 0 0 1 5 -2 roll arc closepath tMatrix setmatrix fill } bdef /FAn { newpath tMatrix currentmatrix pop translate scale 0 0 1 5 -2 roll arcn tMatrix setmatrix stroke } bdef /PAn { newpath tMatrix currentmatrix pop translate 0 0 moveto scale 0 0 1 5 -2 roll arcn closepath tMatrix setmatrix fill } bdef /MRR { /vradius xdef /hradius xdef /lry xdef /lrx xdef /uly xdef /ulx xdef newpath tMatrix currentmatrix pop ulx hradius add uly vradius add translate hradius vradius scale 0 0 1 180 270 arc tMatrix setmatrix lrx hradius sub uly vradius add translate hradius vradius scale 0 0 1 270 360 arc tMatrix setmatrix lrx hradius sub lry vradius sub translate hradius vradius scale 0 0 1 0 90 arc tMatrix setmatrix ulx hradius add lry vradius sub translate hradius vradius scale 0 0 1 90 180 arc tMatrix setmatrix closepath } bdef /FRR { MRR stroke } bdef /PRR { MRR fill } bdef /MlrRR { /lry xdef /lrx xdef /uly xdef /ulx xdef /rad lry uly sub 2 div def newpath tMatrix currentmatrix pop ulx rad add uly rad add translate rad rad scale 0 0 1 90 270 arc tMatrix setmatrix lrx rad sub lry rad sub translate rad rad scale 0 0 1 270 90 arc tMatrix setmatrix closepath } bdef /FlrRR { MlrRR stroke } bdef /PlrRR { MlrRR fill } bdef /MtbRR { /lry xdef /lrx xdef /uly xdef /ulx xdef /rad lrx ulx sub 2 div def newpath tMatrix currentmatrix pop ulx rad add uly rad add translate rad rad scale 0 0 1 180 360 arc tMatrix setmatrix lrx rad sub lry rad sub translate rad rad scale 0 0 1 0 180 arc tMatrix setmatrix closepath } bdef /FtbRR { MtbRR stroke } bdef /PtbRR { MtbRR fill } bdef currentdict end def %%EndProlog %%BeginSetup MathWorks begin 0 cap end %%EndSetup %%Page: 1 1 %%BeginPageSetup %%PageBoundingBox: 55 199 542 589 MathWorks begin bpage %%EndPageSetup %%BeginObject: obj1 bplot /dpi2point 12 def portraitMode 0204 7344 csm 466 272 5838 4681 MR c np 85 dict begin %Colortable dictionary /c0 { 0 0 0 sr} bdef /c1 { 1 1 1 sr} bdef /c2 { 1 0 0 sr} bdef /c3 { 0 1 0 sr} bdef /c4 { 0 0 1 sr} bdef /c5 { 1 1 0 sr} bdef /c6 { 1 0 1 sr} bdef /c7 { 0 1 1 sr} bdef 1 j 1 sg 0 0 6913 5185 PR 6 w 0 4224 5356 0 0 -4224 898 4612 4 MP PP -5356 0 0 4224 5356 0 0 -4224 898 4612 5 MP stroke 4 w DO 0 sg 1927 4612 mt 1927 388 L 1927 388 mt 1927 388 L 2977 4612 mt 2977 388 L 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(motion)f(blur,)h(spik)n(es)g(in)f(cepstrum)f([1)q(])1975 2850 y(w)n(ere)25 b(visible)f(up)f(to)h(S/N)f(ratios)i(of)f(20)h(dB.)f (Prop)r(osed)g(algorithm)1975 2937 y(is)37 b(an)f(addition)h(to)f (metho)r(ds)f(describ)r(ed)i(in)f([9)q(].)66 b(F)-6 b(or)36 b(uniform)1975 3023 y(PSFs)26 b(w)n(e)g(estimated)f(all)i(v)l(alues,)f (not)f(just)h(PSF)g(supp)r(ort.)34 b(Some)1975 3110 y(ringing)e(w)n(as) f(presen)n(t)f(in)g(the)g(restored)h(images.)49 b(When)30 b(PSF)g(is)1975 3197 y(iden)n(ti\014ed)h(from)g(degraded)g(image)g (only)-6 b(,)32 b(than)f(unkno)n(wn)f(origi-)1975 3284 y(nal)d(image)g(is)g(test)g(signal)h(for)f(iden)n(ti\014cation)g(pro)r (cedure.)37 b(Lo)n(w)n(er)1975 3370 y(p)r(o)n(w)n(er)20 b(in)f(high-frequency)f(comp)r(onen)n(ts)h(of)h(test)f(signal)i (implicate)1975 3457 y(less)33 b(accurate)g(iden)n(ti\014cation)f(of)g (degradation)h(system)e(transfer)1975 3544 y(function)26 b(in)g(that)f(frequency)g(range.)2100 3631 y(Imp)r(ortan)n(t)k(p)r(oin) n(t)i(is)g(determination)f(of)i(PSF)f(supp)r(ort.)49 b(As)1975 3718 y(w)n(e)31 b(already)g(said,)i(PSF)d(supp)r(ort)g(is)h (determined)f(directly)g(from)1975 3805 y(the)g(sequences)h(where)f (PSF)h(comp)r(onen)n(ts)e(are)i(estimated.)48 b(Ap-)1975 3891 y(p)r(earance)33 b(of)h(v)n(ery)d(small)i(or)g(negativ)n(e)f(v)l (alues)h(is)g(a)f(signal)i(that)1975 3978 y(PSF)c(b)r(oundaries)f(are)h (reac)n(hed.)45 b(In)29 b(the)g(cases)h(when)f(PSF)h(sup-)1975 4065 y(p)r(ort)k(w)n(as)g(not)f(prop)r(erly)g(estimated,)j(restoration) e(results)g(w)n(ere)1975 4152 y(also)27 b(go)r(o)r(d.)2100 4239 y(Using)k(describ)r(ed)g(pro)r(cedure)f(w)n(e)i(can)e(accurately)i (estimate)1981 4324 y(^)1975 4325 y Fl(u)2025 4334 y Fg(1)p Fi(h)2117 4325 y Fk(and)2267 4324 y(^)2263 4325 y Fl(v)2309 4334 y Fg(1)p Fi(h)2380 4325 y Fk(.)h(That)23 b(is)f(a)g(separable)h(appro)n(ximation)f(of)h(the)e(true)1975 4412 y(PSF.)36 b(In)g(fact,)j(among)d(all)g(separable)h(appro)n (ximations)f(of)g(the)1975 4499 y(true)22 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/rm /rmoveto ldef /rl /rlineto ldef /s /show ldef /sc {setcmykcolor} bdef /sr /setrgbcolor ldef /sg /setgray ldef /w /setlinewidth ldef /j /setlinejoin ldef /cap /setlinecap ldef % page state control /pgsv () def /bpage {/pgsv save def} bdef /epage {pgsv restore} bdef /bplot /gsave ldef /eplot {stroke grestore} bdef % orientation switch /portraitMode 0 def /landscapeMode 1 def % coordinate system mappings /dpi2point 0 def % font control /FontSize 0 def /FMS { /FontSize xstore %save size off stack findfont [FontSize 0 0 FontSize neg 0 0] makefont setfont }bdef /ISOLatin1Encoding where {pop /WindowsLatin1Encoding 256 array bdef ISOLatin1Encoding WindowsLatin1Encoding copy pop /.notdef/.notdef/quotesinglbase/florin/quotedblbase/ellipsis/dagger/daggerdbl /circumflex/perthousand/Scaron/guilsinglleft/OE/.notdef/.notdef/.notdef /.notdef/quoteleft/quoteright/quotedblleft/quotedblright/bullet/endash/emdash /tilde/trademark/scaron/guilsinglright/oe/.notdef/.notdef/Ydieresis WindowsLatin1Encoding 128 32 getinterval astore pop} {/WindowsLatin1Encoding StandardEncoding bdef} ifelse /reencode { exch dup where {pop load} {pop StandardEncoding} ifelse exch dup 3 1 roll findfont dup length dict begin { 1 index /FID ne {def}{pop pop} ifelse } forall /Encoding exch def currentdict end definefont pop } bdef /isroman { findfont /CharStrings get /Agrave known } bdef /FMSR { 3 1 roll 1 index dup isroman {reencode} {pop pop} ifelse exch FMS } bdef /csm { 1 dpi2point div -1 dpi2point div scale neg translate landscapeMode eq {90 rotate} if } bdef % line types: solid, dotted, dashed, dotdash /SO { [] 0 setdash } bdef /DO { [.5 dpi2point mul 4 dpi2point mul] 0 setdash } bdef /DA { [6 dpi2point mul] 0 setdash } bdef /DD { [.5 dpi2point mul 4 dpi2point mul 6 dpi2point mul 4 dpi2point mul] 0 setdash } bdef % macros for lines and objects /L { lineto stroke } bdef /MP { 3 1 roll moveto 1 sub {rlineto} repeat } bdef /AP { {rlineto} repeat } bdef /PP { closepath eofill } bdef /DP { closepath stroke } bdef /MR { 4 -2 roll moveto dup 0 exch rlineto exch 0 rlineto neg 0 exch rlineto closepath } bdef /FR { MR stroke } bdef /PR { MR fill } bdef /L1i { { currentfile picstr readhexstring pop } image } bdef /tMatrix matrix def /MakeOval { newpath tMatrix currentmatrix pop translate scale 0 0 1 0 360 arc tMatrix setmatrix } bdef /FO { MakeOval stroke } bdef /PO { MakeOval fill } bdef /PD { currentlinecap 1 setlinecap 3 1 roll 2 copy moveto lineto stroke setlinecap } bdef /FA { newpath tMatrix currentmatrix pop translate scale 0 0 1 5 -2 roll arc tMatrix setmatrix stroke } bdef /PA { newpath tMatrix currentmatrix pop translate 0 0 moveto scale 0 0 1 5 -2 roll arc closepath tMatrix setmatrix fill } bdef /FAn { newpath tMatrix currentmatrix pop translate scale 0 0 1 5 -2 roll arcn tMatrix setmatrix stroke } bdef /PAn { newpath tMatrix currentmatrix pop translate 0 0 moveto scale 0 0 1 5 -2 roll arcn closepath tMatrix setmatrix fill } bdef /MRR { /vradius xdef /hradius xdef /lry xdef /lrx xdef /uly xdef /ulx xdef newpath tMatrix currentmatrix pop ulx hradius add uly vradius add translate hradius vradius scale 0 0 1 180 270 arc tMatrix setmatrix lrx hradius sub uly vradius add translate hradius vradius scale 0 0 1 270 360 arc tMatrix setmatrix lrx hradius sub lry vradius sub translate hradius vradius scale 0 0 1 0 90 arc tMatrix setmatrix ulx hradius add lry vradius sub translate hradius vradius scale 0 0 1 90 180 arc tMatrix setmatrix closepath } bdef /FRR { MRR stroke } bdef /PRR { MRR fill } bdef /MlrRR { /lry xdef /lrx xdef /uly xdef /ulx xdef /rad lry uly sub 2 div def newpath tMatrix currentmatrix pop ulx rad add uly rad add translate rad rad scale 0 0 1 90 270 arc tMatrix setmatrix lrx rad sub lry rad sub translate rad rad scale 0 0 1 270 90 arc tMatrix setmatrix closepath } bdef /FlrRR { MlrRR stroke } bdef /PlrRR { MlrRR fill } bdef /MtbRR { /lry xdef /lrx xdef /uly xdef /ulx xdef /rad lrx ulx sub 2 div def newpath tMatrix currentmatrix pop ulx rad add uly rad add translate rad rad scale 0 0 1 180 360 arc tMatrix setmatrix lrx rad sub lry rad sub translate rad rad scale 0 0 1 0 180 arc tMatrix setmatrix closepath } bdef /FtbRR { MtbRR stroke } bdef /PtbRR { MtbRR fill } bdef currentdict end def %%EndProlog %%BeginSetup MathWorks begin 0 cap end %%EndSetup %%Page: 1 1 %%BeginPageSetup %%PageBoundingBox: 101 199 485 581 MathWorks begin bpage %%EndPageSetup %%BeginObject: obj1 bplot /dpi2point 12 def portraitMode 0204 7344 csm 1008 362 4609 4585 MR c np 277 dict begin %Colortable dictionary /c0 { 0 0 0 sr} bdef /c1 { 1 1 1 sr} bdef /c2 { 1 0 0 sr} bdef /c3 { 0 1 0 sr} bdef /c4 { 0 0 1 sr} bdef /c5 { 1 1 0 sr} bdef /c6 { 1 0 1 sr} bdef /c7 { 0 1 1 sr} bdef 1 j 1 sg 0 0 6913 5185 PR 6 w gs 1342 478 4227 4227 MR c np gs np 1342 478 mt 0 4227 rl 4227 0 rl 0 -4227 rl cp c np [4227 0 0 4227 1342 478] cc /picstr 256 string def 256 256 8 [256.000000 0 0 256.000000 0 0] L1i 6268635A555B676E71716C706E7682785F404E646A604A4C4843454860738F8F8D7635396C87A1A9 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y(First)h(singular)g(v)n(ectors)f(\(left)g (and)g(righ)n(t\))g(of)h(the)e(unkno)n(wn)g(PSF)1975 504 y(are)35 b(estimated)e(using)i(corresp)r(onding)g(singular)g(v)n (ectors)f(of)g(de-)1975 591 y(graded)25 b(image.)34 b(Estimated)24 b(PSF)g(is)h(almost)f(constan)n(t)h(in)f(a)g(wide)1975 678 y(range)32 b(of)g(S/N)e(ratios)i(of)g(in)n(terest.)50 b(Main)32 b(part)e(of)i(the)e(error)i(in)1975 764 y(PSF)25 b(estimation)h(is)f(due)g(to)g(simpli\014ed)g(mo)r(del)f(of)i (non-degraded)1975 851 y(image)j(singular)h(v)n(ectors.)43 b(Estimation)29 b(algorithm)g(do)r(es)g(not)f(re-)1975 938 y(quire)33 b(n)n(umerical)f(optimization,)i(what)f(implicates)g (fast)g(op)r(era-)1975 1025 y(tion.)47 b(Prop)r(osed)31 b(pro)r(cedure)f(is)g(esp)r(ecially)h(applicable)g(at)f(lo)n(w)n(er) 1975 1111 y(S/N)21 b(ratios.)34 b(Restoration)22 b(results)f(on)g(sim)n (ulated)g(and)f(real)i(w)n(orld)1975 1198 y(images)27 b(pro)n(v)n(e)e(the)g(v)l(alidit)n(y)g(of)i(the)e(approac)n(h.)2600 1392 y Fl(6.)52 b(REFERENCES)2014 1553 y Fk([1])42 b(M.)28 b(Cannon,)f(\\Blind)h(Decon)n(v)n(olution)e(of)i(Spatially)f(In)n(v)l (ari-)2136 1640 y(an)n(t)k(Image)f(Blurs)i(with)f(Phase,")h Fa(IEEE)g(T)-6 b(r)l(ansactions)35 b(on)2136 1727 y(A)l(c)l(oustics,)h (Sp)l(e)l(e)l(ch)e(and)g(Signal)e(Pr)l(o)l(c)l(essing)p Fk(,)k(V)-6 b(ol.)31 b(24,)j(pp.)2136 1814 y(58-63,)28 b(F)-6 b(ebruary)24 b(1976.)2014 1921 y([2])42 b(A.)55 b(M.)h(T)-6 b(ek)l(alp,)63 b(H.)55 b(Kaufman,)62 b(and)55 b(J.)h(W.)f(W)-6 b(o)r(o)r(ds,)2136 2007 y(\\Iden)n(ti\014cation)31 b(of)h(Image)e(and)g(Blur)h(P)n(arameters)h(for)f(the)2136 2094 y(Restoration)j(of)f(Noncausal)g(Blurs,")h Fa(IEEE)g(T)-6 b(r)l(ansactions)2136 2181 y(on)37 b(A)l(c)l(oustics,)i(Sp)l(e)l(e)l (ch)f(and)e(Signal)g(Pr)l(o)l(c)l(essing)p Fk(,)k(V)-6 b(ol.)35 b(34,)2136 2268 y(pp.)26 b(963-972,)i(August)d(1986.)2014 2375 y([3])42 b(A.)30 b(M.)f(T)-6 b(ek)l(alp)30 b(and)e(H.)i(Kaufman,)f (\\On)g(Statistical)i(Iden-)2136 2462 y(ti\014cation)47 b(of)g(a)f(Class)i(of)f(Linear)g(Space-In)n(v)l(arian)n(t)e(Im-)2136 2548 y(age)d(Blurs)g(Using)f(Non-minim)n(um-Phase)d(ARMA)i(Mo)r(d-)2136 2635 y(els,")24 b Fa(IEEE)g(T)-6 b(r)l(ansactions)26 b(on)f(A)l(c)l(oustics,)h(Sp)l(e)l(e)l(ch)g(and)e(Sig-)2136 2722 y(nal)k(Pr)l(o)l(c)l(essing)p Fk(,)g(V)-6 b(ol.)26 b(36,)g(pp.)g(1360-1363,)i(August)d(1988.)2014 2829 y([4])42 b(J.)32 b(Biemond,)g(F.)g(G.)f(Putten,)h(and)f(J.)g(W.)h(W)-6 b(o)r(o)r(ds,)33 b(\\Iden-)2136 2916 y(ti\014cation)g(and)g (Restoration)g(of)g(Images)f(with)h(Symmetric)2136 3002 y(Noncausal)25 b(Blurs,")f Fa(IEEE)h(T)-6 b(r)l(ansactions)28 b(on)d(Cir)l(cuits)h(and)2136 3089 y(Systems)p Fk(,)i(V)-6 b(ol.)26 b(35,)g(pp.)g(385-392,)i(April)d(1988.)2014 3196 y([5])42 b(R.)21 b(L.)g(Lagendijk,)h(J.)g(Biemond,)f(and)f(D.)h (E.)g(Bo)r(ek)n(ee,)i(\\Iden-)2136 3283 y(ti\014cation)f(and)f (Restoration)h(of)g(Noisy)f(Blurred)g(Images)g(Us-)2136 3370 y(ing)31 b(the)f(Exp)r(ectation-Maximization)h(Algorithm,")f Fa(IEEE)2136 3457 y(T)-6 b(r)l(ansactions)28 b(on)e(A)l(c)l(oustics,)h (Sp)l(e)l(e)l(ch)f(and)g(Signal)f(Pr)l(o)l(c)l(ess-)2136 3543 y(ing)p Fk(,)h(V)-6 b(ol.)26 b(38,)h(pp.)e(1180-1191,)k(July)c (1990.)2014 3650 y([6])42 b(A.)36 b(K.)g(Katsaggelos)i(and)d(K.)h(T.)g (La)n(y)-6 b(,)38 b(\\Maxim)n(um)c(Lik)n(e-)2136 3737 y(liho)r(o)r(d)e(Blur)e(Iden)n(ti\014cation)g(and)g(Image)f (Restoration)i(Us-)2136 3824 y(ing)25 b(the)f(EM)h(Algorithm,")g Fa(IEEE)h(T)-6 b(r)l(ansactions)28 b(on)f(Signal)2136 3911 y(Pr)l(o)l(c)l(essing)p Fk(,)h(V)-6 b(ol.)26 b(39,)h(pp.)e (729-733,)j(Marc)n(h)e(1991.)2014 4018 y([7])42 b(A.)33 b(E.)f(Sa)n(v)l(akis)h(and)f(H.)g(J.)h(T)-6 b(russel,)35 b(\\Blur)e(Iden)n(ti\014cation)2136 4105 y(b)n(y)i(Residual)h(Sp)r (ectral)g(Matc)n(hing,")g Fa(IEEE)h(T)-6 b(r)l(ansactions)2136 4191 y(on)28 b(Image)g(Pr)l(o)l(c)l(essing)p Fk(,)g(V)-6 b(ol.)25 b(2,)i(pp.)e(141-151,)j(April)e(1993.)2014 4298 y([8])42 b(G.)27 b(P)n(a)n(vlo)n(vi)n(\023)-36 b(c)27 b(and)f(A.)g(M.)h(T)-6 b(ek)l(alp,)26 b(\\Maxim)n(um)f(Lik)n(eliho)r(o) r(d)2136 4385 y(P)n(arametric)h(Blur)f(Iden)n(ti\014cation)g(Based)g (on)g(a)h(Con)n(tin)n(uous)2136 4472 y(Spatial)e(Domain)f(Mo)r(del,")i Fa(IEEE)g(T)-6 b(r)l(ansactions)28 b(on)e(Image)2136 4559 y(Pr)l(o)l(c)l(essing)p Fk(,)i(V)-6 b(ol.)26 b(1,)h(pp.)e (496-503,)j(Octob)r(er)d(1992.)2014 4666 y([9])42 b(M.)28 b(M.)f(Chang,)g(A.)f(M.)i(T)-6 b(ek)l(alp,)26 b(and)g(A.)h(T.)g(Erdem,) f(\\Blur)2136 4753 y(Iden)n(ti\014cation)j(Using)g(the)g(Bisp)r (ectrum,")h Fa(IEEE)g(T)-6 b(r)l(ansac-)2136 4839 y(tions)25 b(on)f(Signal)g(Pr)l(o)l(c)l(essing)p Fk(,)h(V)-6 b(ol.)22 b(39,)i(pp.)e(2323-2325,)j(Oc-)2136 4926 y(tob)r(er)h(1991.)1975 5033 y([10])43 b(A.)37 b(E.)g(Sa)n(v)l(akis)f(and)g(H.)h(J.)g(T)-6 b(russel,)41 b(\\On)36 b(the)g(Accuracy)2136 5120 y(of)f(PSF)e (Represen)n(tation)g(in)g(Image)g(Restoration,")i Fa(IEEE)2136 5207 y(T)-6 b(r)l(ansactions)26 b(on)d(Image)g(Pr)l(o)l(c)l(essing)p Fk(,)h(V)-6 b(ol.)22 b(2,)g(pp.)f(252-259,)2136 5294 y(April)26 b(1993.)p eop %%Trailer end userdict /end-hook known{end-hook}if %%EOF