ENHANCEMENT OF MEDICAL IMAGESBY THE PAIREDTRANSFORM FatmaTArslan andArtyom M Grigoryan TheUniversity ofTexas atSanAntonio Department ofElectrical Engineering 6900North Loop1604West, SanAntonio, TX78249-0669
M Fp · 2007
Inthis paper, wediscuss theapplication ofthetwo-dimensional paired representation forprocessing medical images. Thisrepresentation leads totheeffective solution ofthediscrete aswellas continuous modelofimage reconstruction fromtheir projections, andtotheimageenhancement. Thesetwoapplications canbe combined inorder toreceive highquality images. Themethod of paired representation oftwo-dimensional (2-D) images isconsidered withrespect tothe2-Ddiscrete Fourier transform (DFT). Basisfunctions ofthepaired transformation aredefined completely byparallel projections. Atthesametime, thepaired representation describes theimageasasetofshort 1-Dreal signals (splittingsignals) whichcompletely determine the2-DDFToftheimage atdisjoint subsets offrequency-points. Theimage enhancement procedure isthuscanbereduced toprocessing splitting-signals andsuchprocess requires only afewspectral components ofthe image. Forinstance, thetraditional a-rooting method ofimage enhancement canbefulfilled through processing thesplitting-signals defined foronly 3N -2frequency-points, whentheimage hasthe size N xN,andN isapoweroftwo.Itisshown, that processing oneorafewsplitting signals leads toahighimage enhancement. Index Terms - Imageenhancement, paired representation, fast paired transform, Fourier transform.