De-Noising ENMR Spectra by Wavelet Shrinkage

Wavelet Shrinkage de-noi si ng i s appl i ed to El ect rophoret i c Nucl ear Magnet i c Resonance (ENMR) data. Both threshol d rul es for removi ng noi se, namel y sof t and hard, proposed i n Donoho's Vi suShri nk are used simul t aneousl y. Sof t t hreshol di ng i s appl i ed to ne l evel s of wavel et decomposi t i on coe ci ent s and hard threshol di ng to coarse l evel s. Thi s impl ementat i on i s coordi nat ed by vi sual i zi ng the f eatures presented i n ENMRspect ra. 1: Int r oduct i on Wavelet shrinkage (WS) has recentl y emerged as a powerful tool f or extracti ng si gnal s f romnoi sy data [1]. Whi l e tradi ti onal l i near methods of smoothi ng usual l y achi eve noi se suppressi on by broadeni ng f eatures si gni cantl y, WS i s capabl e to enti rel y suppressi ng the noi se as wel l as retai ni ng f eatures. Therefore i t makes sense to appl yWSto f eature sensi ti ve data such as hi gh-resol uti on el ectrophoreti c NMR (ENMR) data. ENMRi s a method for resol vi ng NMRspectra on the basi s of el ectrophoreti c mobi l i ti es of NMRacti ve speci es [ 2] . Several practi cal f actors such as magneti c gradi ents i nduced by currents i n sampl e, resi sti ve heati ng & convecti on, el etroosmosi s, etc. resul t i n obtai ni ng noi sy data. In thi s report, we present resul ts of de-noi si ng such ENMRdata by WS. 2: Theory 2.1: The discrete wavelet transform A di screte wavel et transformW i s a l i near operati on whi ch decomposes a si gnal f i nto a wei ghted sumof basi s functi ons ;k f(x) = X X k c ; k ; k(x) ; k 2 Z: (1) The ; k are generated f roma si ngl e mother wavel et by di l ati ons and transl ati ons ; k(x) =2 =2 (2 (x k)) (2) ere i s the di l ati on scal e i ndex and k i s the transl ati on i ndex. The empi ri cal wavel et ci ents c ; k are obtai ned by projecti ng the si gnal f onto the wavel et basi s set ; k [ 3] .