Some Computer Experiments in Picture Processing for Bandwidth Rednetion By H. J. LANDAL and D. SLEPIAN (Minne reed Fenny 6280 Some sonputer exponents in pesvssey 098 pistaves for finn width reduction wre deserted. In tie sekeme ated, « piture %& Durlihimed sine swipes sank of which ty raced eoparaely, A alist in expres “wntion of a Rote act af peraly chosen basis subpitires. Quantized versions of the cooht- ° a oe biary agit, Cinq thie prove ceo} geal pty wig ep Drexiwaiely 2 bie per peluveclemeut; tee were wonble fo ne 0 at tonae itr ‘Sone gerd rowenta ca Re en oof pirtares ave inched, This poper esr some oxptesexpatinvnte i yet pean sng carne oe we cans the incor of TG aval the sing YM (hur geal was te eaplore a partiulr wethed (er the ork ceding af tyne] Bistaeephane® sores in Diva gts, The expericents nyu ah ies ey. We Get descr tae experinents as their results, hen follow with seine gezcal sonuient= a she ene! Dstaors. These coments nev ince, fo expe our siete Sor The patel ssetigtine elertn Fy means Phe TADBN sins ot Meare ALLA « photog! a erm in egal fons stele sor waning by the GEASS onspater, Spefeally the pietire is srasnr om try felony logy serizons cis, the liga inert ge seas my Gime flong eseh fine; ery semple i son eatin! to Tis newest one 8 2 cpaliy spaced pli feels, anal road 91 digital tape 125 eae ga sonoear wRcwvteaL JOURNAL, seNsUAD 0P) se singe Ait inte, Converele, sive the digax! tape, each kit Iteger "+ replueod by is eageeyoming meplizne value, shir ‘hen regarded sary aon ge te Nyaa rata of ¢ Beco ‘ruveforr The eesnnicustedaveforn conteale Ue bese intensity 0 Sreeceive lines traced by storming cathode-rap oxcillneupe. The (Guloseope fore is phntogrs be, ‘nal our experinwnle,the vases usd for (he above qunntties wore ‘iy = me — Boy and J = 10, Figure Ze is an urinal photogs Wi Th is the sesule of eosvesting the pieare it bivy sigs on cape sind aesrustructing i TAPON, marion ehows that, with the Savemetars ne choc, te liga tepaesetatant is of eustateare tele Vision quali, Wns, af conse the inevitable rer Have Tr pressing a picture, we fin eoaverten seelB-bape of bine ditto Ue eoeeesponding incege, and sul uel 2°", Tha nelle Ine inter ing in Ue eur (9°, 2? —1), are called pete flewent, end we denote Ly 3u che piezo eemensbisived trom the JH stuple oF the ithe ofthe petare. Por ennpurer processing, we ezatd © path aa git my % ae teats of pietno-eenerts. Experiments, ws farts partons he my x eesleent pete by a fmnare gid fos it Piz) inta my 2 na/m equaze eubprtures, eoh Tesving m pitse-oleenes on » sie. These subpiceures vere ere Independerty, swe at a ime, by tw cheme aesesed below, ‘We view the M =m? pleturoleents ala subpictur whow reed cont tow by row Tron let to rsh, a be eusaponents of 1 Fn Fal reer ¥, which represents the eubpletuce. Por example fa Ee ¥-| ion is the vector representing the topett vbpieture of Fig. 2 ‘To deseribe fick vootoey iis nasi ta irtvoduer a asa. We tacefore aicose frthonormal H-dinnsiona Base vetare by o-~ «Bye. Taeso romein fi, and detormine Ihe partralar sending vere tade® discussion i in ot) the nts oof ge eda el Boa feolasrsie Copies af Uwe nelogmpis wil hr ay rec pees rezone ewer way Jo) We ees row exp Yin terms of she si vector, to bas y wi sess, by orthacr ality th Baby, Fah e We then quantie ¢; to one nfs liflerent values denoting by é the ‘usutiand versen of e.. To srt Heese utignd eoefbients of fubpietive in the simplest possible seas, hey by encoding te ie Apencer‘iy sith expliting the statietien, cetinution of thie wales ruins ¢ = Dos Theo] bivary ete, We ssh te ember Tig 1Pacs a islam in arise, 1398 rue sts sYsHRBE AZEHSIOWT SOTRVAL, O68 VN B= wm", whi the munabor of bite es par potureeeroant, a neces ofthe fieney (or band) of th enc ere ‘Pp reomnetrnt a peso, we sapace the enrtised eoeflents sre know, and obtain & reeunsimetedsubpieture ene vetoe ¥ from the recipe Y=Een ‘The components of Bane quand to the ener inteace value in he range [oP 2" =f The arp the pletureatenonts &,, of the Teomneitnend iets, A photogrgle ocd from the values using {he TAPE use in tie tamer azeady deserted. ty tee amyl to aon of conmmrren nietonm oneness 1520 Our expevinent consisted of ehsoning vurlous bask veetom and ‘avin tinnvon owes “ur the expoasien eoceints ©). We also fsovriencel sith soe nonlinea® tramtonnatinas on the tite: Fons beta ta rr bith eamogeesion procseing, None of Ine various cypee of eompanding we tet psided beter eels at veers otzined thon resysuting Te abuse 9: vue work, sabpitares Of A= 16 piotoreclements Hie — 4} more net a Fn experi ic wi vith = 8 We won abe ta ublaiy pirtoren goal usb will a ele = 2 hits per Bicrv-ciemenl, uc meres inva homer res Figure fa sepeate the 10 bit yo" penee-slemsent logs of Fi be Figuze ah stow a roeonstcced sure with 2 We jt ietuvorkrest oltaiiel will seem using an = 4 ad the: Hasty tard hasie dees! below, We alen stam the eampatir the Hilfewntian CAL selene emplopt! in Ectarephome cong wih aes bite per pietun-cccment Hague Be shows che raul» on; A colapanes Leverahly vita Fig. 8b. Two Ailes abjeee wm seated anzlogouely tn Flas. 4 ab 5 Although the supietans caeolirg cca somethin seerense 4 rato, she difoonral PUM selanve i far niet iatrwuent, Fra four experi it serie nPly sgt poe ec ean be oliine Seal re shine aehenie av sr nti ee Uh 2 bite pe paste event ‘To oewid nee easton, 2 al that follows ww sll think of a pictoss ie viuente teow te. ae fine colection of qucave Hltea,ezele nf whieh eat este Hoey many diferent ales, Leow ticny ite syst one ase 20 transit the 3iethte of Hig. 1? rhe arswer is of course. ave. It ist single stare. "The question ie uot an inceretisg one Mors pertswatly, we ssh le ow iy hits rer plete are arsited on he average to transmit ln stings af Pilates dwn, dio @ given amend of yslarns, Since ielare Soutes van be rogue as praiueing.sequstnos pee ele elo wbieh een tasuine aie oF K aifeeat vals, wvdatiy we eum Trsunat all posible pletaree porietly Uy ing flex K] bite per pecunecnaett. To) sip aster of tas Int nate enw this yh ‘We must eapitlize om or oF hoth af these Z's 6) nor all potuses are prouced th equal probability by the frie, Wer ate he puto intl i) Te beerser doe asin all etn to by eeproded at 1580 un geuu everew mmewent soar, sas-sus 18m) Fig (lo) 0 a per ‘rae quetiow oI to take avantege oF sul sousssacons sas Toes mach sts? Sn inforaton thor, end melds wre eo a Priveiple for eon piling the anewcr, & ralelacion cf the ti La piceure eure dosemins ow fae iti Viet, anti oalsaia peter mome:ruction, by exploiting source Tedhadanelay thik rinnnant te fe elerined solely by th ST the eneembie, wl se netzing ts do mE the sate of poms, ‘vision of tho obeerer Durvemizaton of the encopy af a pistuse sneer dose not golve the run af zeal tates to warkete th peeve tanemesions for pit= arene they are uevlly presented by sare, hve wore decal) acl revuutin {van he obeersur sa ae, The ile that ste course conmns nerese aaooRssis fa fofenent in the souren emcile sug be ndings £0 the Voor wag wire ta vewslruet tea ong so nine sellin of ecuraey, Le. achieve sun “level of Behty”. The mina bite ce, piven as a tion of Hoth the perveular floaty einer flop aad Uae sauce etststns vay hd he eoraputes, and i ale Use mle Satortion function, As wit enh reiozatne sry Bn the Tait wre ad Coneentally este distortion Ins feral ly aia uplely Ue ancmst question i she LV eos wal: "Ho o Trae?" In somes! ty, it foe's da wasy ans for hn <(e x Ms oe Mad Ting 1882 mun sau, eves amen TOUR, SANTI ‘at ull To ove why this isco, we sn nl jst it eower aL he fone {alin of rate stoi th ‘The general lore presiposes souree tat provuces infinite slvings nf a=bols eye? yuh orig Sees Hows K-lieraphabel The vetuet” of the bstors play mo tie He theory, s» fo emvene fen wr suppose that hg aze he Ines 1,2, o=> « K, Denote a (shad sing pooled by the sontee ik oy ys Tp Me shen enls X fone of she integers ign 1 co KoA mtewse is plage pure Ce ses of ah jit szings in such w way chats ae eo gad the Xs ae sendom vanihiee wh meaninglly eka answer sah feuestigrs ae "Whee tha peobabig Mint Ny — 3 Ne = 1s and SMe tue ave many teimiesliee involved i spot thie Incasure, Tl they ced ak comer us ere. We are ale given a areerseal-rulued setorbwn first €1y, 41-20 wish ateee the die tention whew a tense be Fe zeeonsrt it ete Tick non consider tzanamiting te stings produce? Ty the soures by cneoding them in Uy following anger. We bree the sore sting pint loeksu' a aueresvesynbole, Sige sl Mork i composed of Soksoe symbols avd each syria ora be ore 0 K aileron integers Gienware Kleene bioeln pei. We supoowe that detion ary Js movie, hich Tris fr eoeh ose ofthese R' bles special bck Caled ite ropmeentatise Boeke ts ogee sting f-m. soaree Isto Ie produced! by Hhe sours caw ie Tooked up in che etcnacy and ‘once inn ite rperentasise booe 1f tae news of block 27ey aoc fi tho llc af the eoressvading tepresetative liek {Pon fromthe eletinary a yw dso 77> 9 tou 2 tke the quantity DY Aas, pes he stanton per bok. Wa take = average Din fo Vie level of ibtrsen aevid with the ven code Inky where the average is over! anno tru Tints now A the wine of ryyesentatie blocks i Phe dtionsry st 2 Some tole hocks tn alating the Boeke ints 2 rewesentatve hocks will yield sinter value forthe dicertios 4 than wil We eavete hy (> mse smaees¢tortion obtain by any sul, foie hans Note now Pt ee shore ate ualy 2 reoest tales bea fn ent eode books, we eal se binary digits to transit exch repe overlafiea locke nase 0 3 Aescsotin We woule wel eve disocien GU, n} and becoming ea rate B= (Lin) bile somtee sem Now fix nd write AUC) = im lun). This fnetion giver tbe smn tes distortion ebiainble fr fe itty rata Je that eam be Trad it the linit of arbitral aye code books. ‘The inverse fusion fi wai giv the amaletTinsey rage per sour Teter that will accu ern: ances 1sa8 sola given distortion sealed rhe ae atte pei, Inf to ‘heury shows lows Je ean be exes in pneple frm the =yroba distortion Finetine 8G, 1) wd tho mscatge aie tu Ue source, We donot sepa theee coral foci te aw een wirnppe this to petra tmaminins? There orc to obvious ites net of ifs the course symnbal Xi uanty of inverestin pictues coding: The method mact satin eonestanly 1 to ilercite he mezdom varie wil ovat petra, hie i pe Shee there are oalysniely many elon petres, de ro en sim has peta i eonspored 0°) Xm peter ems, ene akin fons of 2 values. We smnber ihe possible pisuzes and tee the picture umbers € the viliies of X, The estan fet 6,5), whieh ye rt now eseribe to upp the shoots, nensuns oar disatitecion having pietare y pnatieel ox pretare & Cangrptaly suche maasane iss, Bue koa Tee, An ot oi pst tfor 2") pits of ales offal ‘Ts compute a value for che me distortion fasetion, we aqulee in ‘ution a measure on the santo ss bol: ta minimty, thie Inve ssiing © peobabiilydietbcvion, bese ste elation vw oh il bbe observed in protic trswsmision, tw de == |g! Ailerent posse pias. "is tork ems ite beyond us wow, Hor fo tobinin a histogrsewmpiall in wt the esting st 0 fees et Seon, we se any 1 Feancs wr ens the cferout geile Phetues gece ro i sooruns at hate, would eke 10" ear toview thon all ate econ al, brspeey the dstibatin these retcallyrq-itos wnrrsorstadsaget te saon sas 9 have Tnetd, being abe tn acese 9 tease dstiastiny far the po sible pocturs goss a one way comes soley gba: of ofieient fading. We sasjvel thas 4 setsonshie goad espn mould ase ono bility 12¥ to one of of che pers, im ee to the west. wth sonal iced compare to 10" #18 we cut dese thie stl ‘we ml? ene eng Jog A itecan. Bat wily ave the sie Detures? Por Beteveptions series eatimezeal loops sehen Intuition eagaets thas chinsin pistuces is whieh aeavert pice leant juss alah ietscn eatin ares, seule elasided es Unlikely. Likely pitares ave, roughly epeskiny, soe op of celens af eatly capstan: hagas, "Thebvightnee set sbage rote rably frau ene region t9 eho next, I Te catch be ton sth anal 1 ms, 9° wt buck €O Sry has, re enn he bouts of fae alah ho toe wild a fat-taming Afoweres Me roomate tnber Speblitis ‘awl jrevnte a arvurats cestipien A rvoresreetable aplication of te prea Rea rans fom ws 1d un asc avezese reNSTOAL JeUHNAK, YAY He DL cing Uw snr seabol wich ¢ pletoreTement. Nox, however, the “isterton fmetion 8(j, #5) saeesiees ur eapleasure al having he jl evel of rightness for 4 pietre-clemnot rpoduze a Ce Ss level of Iihlsess, Psi i an extensively Local mari of ictere ily aad is motably spite wnat feo sh eit aged hua elses hreurantey rae Histor theory lle 2 chat to encore liens vie nat pay netention to the anoce Re” pictures ror sejencee of pstcee aud sant we wie rage he in genre By zopzuenia ve Trl whieh yield aa aeoxpable distortion, ‘he chery tells ws how fo calealae se mira. bere aoe to eebieve a given level of ‘Slop, blo cary out the valeultion se nord to hae the dito ou finelinn #1) 1) su the menaure iat gives wate desrip= Elon of the soursr. In pitts mocine we nave ab preeene very maengtr Kerowiedge comwsruing show quali Any new undenstanding of ficher wil unonstedly Teed tn ‘ngaaved praetial cot wehemcs. Xe ‘plea a rest dal of derstanding, however, to know these qusnsi= Tice well cong alow enlolatinn of arate disbion function ‘hie one man Inve rch eoniene ‘As we nse ange, we ask the ieforcacion vequinal te bring the fall fore of raielstortion tory” eae on plture eating, Neveetee Ieee, L was Ue panera appear of role €tortion theory That Tel te the encoding sehee uf out experiments, We wanted an enenting pre- feshre shal is" Rou derive fonn eavsieretions of Ikelibooe! and Sieley, but thy! wows he mranagenble in practice. Accordingly, we Tan By focusing on stmeeLione of the pitt Ttfsough re cannot charweesize edeqcacely oa eatine planes ‘hab sze hiely, perhaps we ea low for subpsetuces. Hav large must tCaestin of a TW pietwe bo before we een casero am 8 Hey sb Fieluie a” unlikely eubpictare? 1! ws loa at single pncurele trent, every salve bool” Te lo ae toe ajner.psuneele= frei aga we iis saat any pale of vanes fs key.” LE we ance uate subptnes 0 we % we pitare-clemer ts most obese {el ther form = Tiny env aleeady elksify some subpicuns om hkely batts of The Pitucephane er TY eocemble ul clots a Tse ely The dX 1 eloskerierd pattern, where uljuesn pane ewements Chetllate heen evitane vals, seene unlikely: Uke uniform <4 Supe rime hig hey ‘We cecil then Lo rock w pichse igo w 2 ox subpietares andl ta encileecch evipishue indepen’. Tf a Lege vt one, not arse omperasion poten wil be lot by neyeting the eorelation beeen