Audio De-noising Analysis Using Diagonal and Non-Diagonal Estimation Techniques

Transcription

1 Audo De-nosng Anlyss Usng Dgonl nd Non-Dgonl Estmton Technques Sugt R. Pwr 1, Vshl U. Gdero 2, nd Rhul N. Jdhv 3 1 AISSMS, IOIT, Pune, Ind Eml: sugtpwr@gml.com 2 Govt Polytechnque, Pune, Ind Eml: vshl.gdero@gml.com 3 AISSMS, IOIT, Pune, Ind Eml: jdhvrn@gml.com Abstrct Audo sgnls re often contmnted by bcground envronment nose nd buzzng or hummng nose from udo equpment. Audo denosng ms t ttenutng the nose whle retnng the underlyng sgnls. Mjor udo sgnl denosng technques re bsed on ttenuton n tme-frequency sgnl representtons. The tme-frequency udo denosng lgorthms of MMSE-LSA estmtor of Dgonl Estmton technque nd Adptve tmefrequency bloc Thresholdng of non-dgonl estmton technques re consdered. Removng nose from udo sgnls requres non-dgonl processng of tme-frequency coeffcents to vod producng muscl nose. Tme-frequency udo denosng procedures compute Short-Tme Fourer Trnsform (STFT) of the nosy sgnl nd process the resultng coeffcents to ttenute the nose. Smple tmefrequency denosng lgorthms compute ech ttenuton fctor only from the correspondng nosy coeffcents nd re thus clled dgonl estmtors. Index Terms Audo Denosng, Bloc Thresholdng, STFT Trnsform, Spectrogrm. I. INTRODUCTION The mn m s to reduce the muscl nose by performng dgonl nd non-dgonl estmton procedures n tme-frequency domn to cheve better SNR of the muscl nose sgnl by suppressng the nose nd to cheve best udo percepton of the muscl sgnl. Dgonl estmtors of the SNR re computed from the posteror SNR. The ttenuton fctor of these dgonl estmtors only depends upon correspondng nose coeffcent wth no tmefrequency regulrzton. The resultng ttenuted coeffcents thus lc of tme-frequency regulrty. It produces solted tme-frequency coeffcents whch restore solted tme-frequency structures tht re perceved s muscl nose. Ths nose s sum of loclzed tme-frequency structures correspondng to solted spectrogrm coeffcents. Ths superposton of muscl nose contmntes the denosed sound nd degrdes the udo percepton. An dptve bloc thresholdng non-dgonl estmton procedure descrbed, djusts ll prmeters dptvely to sgnl property by mnmzng Sten estmton of the rs. The dptton s performed by mnmzng Sten unbsed rs estmtor clculted from the dt. The dptve bloc thresholdng procedure gves best sgnl propertes. The bloc ttenuton elmntes the resdul nose nd provdes good pproxmton of the ttenuton. II STATE OF THE PROBLEM A. Dgonl Estmton Smple tme-frequency denosng lgorthms compute ech ttenuton fctor only from the correspondng nosy coeffcent nd re thus clled dgonl estmtors. These lgorthms hve lmted performnce nd produce muscl nose. In Dgonl Estmton the Posteror SNR s consdered. Posteror SNR s the SNR of the Audo Nosy Sgnl. Dgonl estmtors of the SNR re computed from the posteror SNR. The ttenuton fctor of these dgonl estmtors only depends upon nosy coeffcents wth no tmefrequency regulrzton. The resultng ttenuted coeffcents thus lc of tme-frequency regulrty. It produces solted tme-frequency coeffcents whch restore solted tme-frequency structures tht re perceved s muscl nose. Some of the Dgonl estmton technques re Power subtrcton (PS), Ephrm nd Mlh log-spectrogrm mpltude (LSA) nd decson drected SNR estmtor. B. Non- Dgonl Estmton To reduce muscl nose s well s the estmton rs, severl uthors hve proposed to estmte pror SNR wth tme-frequency regulrzton of the posteror SNR. Resultng ttenuton fctors thus depend upon the dt vlues n whole neghborhood of nd the resultng estmtor s sd to be non-dgonl. In non-dgonl Estmton pror SNR s consdered. Pror SNR s the SNR of orgnl udo sgnl..non-dgonl estmtors clerly outperform dgonl estmtors but depend upon regulrzton flterng prmeters. Lrge regulrzton flters reduce the nose energy but ntroduce more sgnl dstorton. It s desrble tht flter prmeters re djusted dependng upon the nture of udo sgnls. In prctce, however, they re selected emprclly. Some of the Non-Dgonl estmton technques re p-pont uncertnty model nd Bloc thresholdng (BT). III. METHODOLOG The bsc steps followed to denose the muscl nose sgnl re s shown n the followng bloc dgrm. 3

2 Dgonl estmton technque (MMSE-LSA) Orgnl Mozrt Sgnl Mozrt sgnl corrupted by whte Gussn nose Muscl nose sgnl Denosng technques Fgure 3.1: Bloc Dgrm of Denosng Muscl nose sgnl. A. Mmse-LSA Estmtor Method Non-dgonl estmton technque (BT) The mn m of the MMSE-LSA Estmtor s to mnmze the error of the log spectr s of clen sgnl nd the enhnced sgnl. There were no specfc ssumptons mde bout the dstrbuton of the spectrl components of ether of the sgnl or nose. Ths method s mnly use for the speech enhncement pplctons. In ths method the ssumptons re mde tht Sttonry ddtve Gussn nose wth nown PSD nd An estmte of the speech spectrum s vlble.spectrl components re sttstclly ndependent nd ech follows Gussn dstrbuton. The mn m of the MMSE-LSA Estmtor s to mnmze the error of the log spectr s of clen sgnl nd the enhnced sgnl. There were no specfc ssumptons mde bout the dstrbuton of the spectrl components of ether of the sgnl or nose. In ths method, the dstrbuton of the spectrl components of the udo sgnl nd the nosy sgnls re defned. Ths serves to mprove the qulty of the resultng enhnced udo sgnl. By ths method Better output SNR, less muscl nose nd less dstorton to the sgnl re cheved. The decson-drected pproch, proposed by Ephrm nd Mlh, provdes useful estmton method for the pror SNR. STFT s ppled to determne tme nd frequency coeffcents. The ttenuton fctor nd spectrl gn functons re determned by pplyng MMSE-LSE Estmtor to ttenute the nose nd to get the denosed sgnl. The estmton problem of the STSA [9] s formulted s tht of estmtng the mpltude of ech Fourer expnson coeffcent of the speech sgnl { x ( t ), 0 < t < T}, gven the nosy process { y ( t ),0 < t < T}. Speech Estmt on (LSA) G(l,) j Let, X A e, D nd j R e,...eq. (3.1) (l Segment ton & Wndo wng ST FT ( SNR Estmton l, ) ξ(l,) (l,) Ŝ(l,) ) ISTF T Overlp Add Method Ŝ(l) th Denote the Fourer expnson coeffcent of the speech sgnl, the nose process, nd the nosy observtons, respectvely, n the nlyss ntervl [0, T]. nd re nterpreted s the pror nd posteror sgnl to- nose rto (SNR), respectvely. On consderng (3.1), we get the desred mpltude estmtor = exp { }.Eq. (3.2) It s useful to consder A ˆ s beng obtned from Fgure 3.2: Bloc Dgrm of MMSE-LSA Method R, by multplctve nonlner gn functon whch depends only on the pror nd the posteror SNR nd, respectvely. Ths gn functon s defned by, Ths MMSE-LSA technque mnly conssts of two steps to be determned.they re, (, )....Eq. (3.3) Decson-Drected method estmtng the pror SNR of the sgnl spectrum. MMSE Short-Tme Spectrl Ampltude The MMSE-STLSA estmtor ws mplemented n (STSA) estmtor. the udo sgnl enhncement system, opertng The MMSE-LSA estmtor ws mplemented n the wth the decson- drected pror SNR estmtor. udo sgnl enhncement system, opertng wth The reducton n the resdul nose level obtned the decson- drected pror SNR estmtor. The used s probbly result of the lower gn, reducton n the resdul nose level s obtned. 4

3 prtculrly n regons of low nstntneous SNR vlues. B. Bloc Thresholdng Method estmte. Best bloc szes re computed by mnmzng ths estmted rs. A tme-frequency bloc thresholdng estmtor regulrzes estmton by clcultng sngle ttenuton fctor over tme-frequency blocs. The sgnl estmtor ˆf s clculted from the nosy dt y wth constnt ttenuton fctor over ech Fgure.3.3: BT Bloc Dgrm To reduce muscl nose s well s the estmton rs, severl uthors hve proposed to estmte pror SNR l, wth tme-frequency regulrzton of the posteror SNR. l,. Resultng ttenuton fctors l, thus depend upon the dt vlues l ', ' for ', ' l n whole neghborhood of nd the resultng estmtor s sd to be non-dgonl nd s gven by, [ ] = (1 ) [, ] [, ], [ ],... Eq. (3.4) Ephrm nd Mlh hve ntroduced decsondrected SNR estmtor obtned wth frst order recursve tme flterng: [, ] = [ 1, ] + (1 )( [, ] 1). Eq. (3.5) In non-dgonl Estmton we consder pror SNR. Pror SNR s the SNR of Audo sgnl. Non-dgonl estmtors clerly outperform dgonl estmtors but depend upon regulrzton flterng prmeters. A bloc thresholdng segments the tme-frequency plne n dsjont rectngulr blocs of length tme nd wdth L n W n frequency. In the followng by bloc sze we men choce of bloc shpes nd szes mong collecton of possbltes. The dptve bloc thresholdng chooses the szes by mnmzng n estmte of the rs. The rs E { ƒ-ƒ 2 } cnnot be clculted snce ƒ s unnown, but t cn be estmted wth Sten rs bloc B [n] = [, ] [, ] [ ] (, )...Eq. (3.6) To understnd how to compute ech one reltes the Sten estmton rs, r =E { ƒ- ˆf 2} to the frme energy converson nd gven by, = { { { [, ] (, ) [, ] }Eq. (3.7) Where f s the orgnl sgnl. = (, ) { [, ] [, ] } Eq. (3.9) 5 And s the sgnl estmtor clculted from the nosy dt wth constnt ttenuton fctor over ech bloc B. A s the redundnt fctor.if A=1 then tght frme s n orthogonl bss. A frme representton provdes n energy control. The redundncy mples tht sgnl f hs non-unque wy to be reconstructed from tght frme. Snce l, F l, l, one cn verfy tht the upper bound s mnmzed by choosng Eq. (3.8) A bloc thresholdng estmtor cn be nterpreted s non-dgonl estmtor derved from verged SNR estmtons over blocs. Ech ttenuton fctor s clculted from ll coeffcents n ech bloc, whch regulrzes the tme-frequency coeffcent estmton. To estmte the bloc thresholdng rs C used the sten estmtor of the rs when computng the men. Estmton to the rs { } s derved by computng n Estmtor B of the rs n ech bloc

4 Under the hypothess tht the nose vrnce remns constnt on ech bloc, the resultng Sten estmtor of the rs s gven by, = # λ # λ( # ) / ( λ ) + ( / ) + 2 #. () ( λ ) Here, # = s the fxed wve length t ech bloc sze. The prmeter λ s set dependng upon by djustng resdul nose probblty. Gven choce of bloc sze nd the resdul nose probblty level δ tht one tolertes, the thresholdng level λ.for ech bloc wdth nd length, λ s estmted usng Monte Crlo smulton.the below Tble shows the resultng λ wth δ = 0.1%. Let us remr tht for bloc wdth W > 1, blocs tht contn sme number of coeffcents, B # L W, hve close λ vlues. Sgnl & SNR MMSE -LSA BT Mozrt 2 db dB 10.60dB Mozrt 5 db dB 15.67dB Mozrt 8 db 14.85dB 18.19dB Mozrt 10 db 15.67dB 19.53dB Mozrt 15 db 17.92dB 21.98dB Mozrt 20 db 18.63dB 23.78dB Pno 5 db db db Recorded 5 db db db Tble 4.1: Performnce Comprson of MMSE-LSA nd BT methods for Mozrt, Pno nd Recorded Sgnl wth dfferent SNR vlues. From the bove comprson we cn conclude tht the resdul nose mss the muscl nose. Bloc thresholdng ntroduces less sgnl dstorton s reflected by the systemtc = 4dB SNR mprovement thn LSA method. λ vlue W= 16 W = 8 W = 4 W = 2 W = 1 L = L = L = Tble.3.1: Thresholdng level λ clculted wth dfferent bloc sze B# = L X W nd wth δ = 0.1%. The prtton of mcro blocs n to blocs of dfferent szes s s shown below: Frequency Fgure 4.1: Comprson of Orgnl, Nosy nd Denose Mozrt Sgnl Grphs of MMSE-LSA. Fgure 3.4: Prtton of mcro blocs Tme Fgure 4.2: Mozrt Sgnl Grph fter MMSE-LSA method The bove fgure shows the output sgnl grph fter IV. PERFORMANCE COMPARISON pplcton of MMSE-LSA method. The SNR vlue obtned The below tble compres the performnce of fter pplyng MMSE-LSA method for the Mozrt sgnl on Mnmum Men Squre Error Log Spectrl Ampltude Estmton lgorthm by usng Decson pplcton of 5dB whte Gussn nose s dB Drect method (MMSE-LSA-DD) nd Bloc Thresholdng (BT) lgorthm n terms of SNR. 6

5 Bloc Thresholdng out performed MMSE-LSA bsed lgorthm. Thus non-dgonl udo denosng lgorthm through dptve Tme-frequency Bloc Thresholdng produces hrdly ny muscl nose sgnl nd mproves the SNR compred to Dgonl estmton procedure of MMSE-LSA technque. Bloc thresholdng regulrzes the estmte nd s thus effectve n muscl nose reducton Numercl experments demonstrte mprovements of Tme- Frequency Bloc Thresholdng wth respect to MMSE-LSA procedure. REFERENCES Fgure.4.3: Comprson of Orgnl, Nosy nd Denosed Mozrt Sgnl Grphs of BT Method. Fgure.4.4: Mozrt Sgnl Grph fter Bloc Thresholdng The bove fgure shows the output sgnl grph fter pplcton of BT method. The SNR vlue obtned fter pplyng BT method for the Mozrt sgnl on pplcton of 5dB whte Gussn nose s 15.53dB. CONCLUSIONS An dptve bloc thresholdng non-dgonl estmton procedure s descrbed, whch djusts ll prmeters dptvely to sgnl property by mnmzng Sten unbsed rs estmtor clculted from the dt. Non-dgonl estmtors re derved from tme-frequency SNR estmton performed wth prmeterzed flters ppled to tmefrequency coeffcents. The coeffcents re grouped nto blocs to compute ttenuton fctors. Ths bloc groupng regulrzes the estmton whch removes muscl noses. The objectve evlutons hve been performed by consderng the SNR mesures of muscl nose sgnl nd denosed sgnl. The Bloc Thresholdng bsed lgorthm cheved systemtclly better SNR mprovement thn MMSE-LSA method wth n verge gn of 2dB.The numercl SNR vlues for dfferent nose levels re tbulted. These results confrm tht tht [1] C.Sten, Estmton of the men of multvrte norml dstrbuton, Ann.Sttst.,vol.9,pp ,1980. [2] G. Mtz nd F. Hlwtsch, Mnmx robust on sttonry sgnl estmton bsed on p- pont uncertnty model, J. Frnln Inst.(Specl Issue on Tme-Frequency Sgnl Anlyss nd Applctons), vol.337, no. 4, pp , Jul [3] Cohen, Optml speech enhncement under sgnl presence uncertnty usng log- spectrl mpltude estmtor, IEEE Sgnl Process. Lett., vol. 9, no. 4, pp , Apr [4] Cohen, Relxed sttstcl model for speech enhncement nd pror SNR estmton, IEEE Trns. Speech Audo Process., vol.13, no.5, pp , Sep [5] Ivn Selesnc, "Short Tme Fourer Trnsform, Connexons, August 9, [6] R. M. Gry, A. Buzo, A. H. Gry, Jr., nd. Mtsuym, Dstorton mesures for speech processng, IEEE Trns.A coust,,speech, Sgnlprocessng, vol. ASSP-28, pp , Aug [7] T. C, Adptve wvelet estmton: A bloc thresholdng nd orcle nequlty pproch, Ann. Sttst., vol. 27, pp , [8]. Ephrm nd D. Mlh, Speech enhncement usng mnmum men squre error Log- spectrl mpltude estmtor, IEEE.Trns. Acoust., Speech, Sgnl Process., vol. 32, no. 6, pp , Dec [9] Zxel Robel, Anlyss/resynthess wth the short tme Fourer trnsform Insttute of communcton scence 25th August