Adaptive Noise Estimation Based on Non-negative Matrix Factorization

Transcription

1 dvanced cience and Technology Leers Vol.3 (ICC 213), pp hp://dx.doi.org/ /asl.213 dapive Noise Esimaion ased on Non-negaive Marix Facorizaion Kwang Myung Jeon and Hong Kook Kim chool of Informaion and Communicaions Gwangju Insiue of cience and Technology (GIT) {kmjeon, bsrac. In his paper, an adapive noise esimaion echnique is proposed on he basis of non-negaive marix facorizaion (NMF). s an iniial sep of he proposed mehod, he noise basis marix of NMF is esimaed from a collecion of noise signals. Then, he proposed mehod updaes he iniially esimaed noise basis marix on he fly by using an esimae of he noise specrum from he noisy signal. I is here demonsraed ha he proposed mehod provides a beer noise esimae han a NMF-based mehod wihou using any adapaion, especially when here is a mismach in noise condiions for noise basis raining and esimaion using NMF. Keywords: Noise esimaion, non-negaive marix facorizaion (NMF), mismached noise condiion, basis adapaion 1 Inroducion In general, noise esimaion mehods based on signal-o-noise raio (NR), such as Wiener filering [1] or minimum mean squared error log-specral ampliude (MME- L) [2], work well under saionary noise condiions. However, hey may no accuraely esimae non-saionary noises ha occur in mos real environmens [3]. s an alernaive, non-negaive marix facorizaion (NMF) based noise reducion mehods have been proposed [4][5] o effecively esimae noise specrum under non-saionary noise condiions. Neverheless, he performance of he NMF-based noise esimaion mehod can be limied depending on how accuraely he noise basis marix can be used o decompose a noisy signal ino a clean and noise signals. In his paper, an adapive noise esimaion mehod is proposed in an NMF framework. s an iniial sep of he proposed mehod, he noise basis marix of NMF is esimaed from a collecion of noise signals. Then, he proposed mehod updaes he iniially esimaed noise basis marix on he fly by using an esimae of noise specrum from he noisy signal. Thus, he noise specrum is esimaed from he adaped noise basis marix in he proposed mehod, while convenional NMF-based noise esimaion mehods rely on prior knowledge of a cerain ype of noise. Therefore, i is expeced ha he proposed mehod should be able o more accuraely esimae noise specrum han he convenional mehods, especially when here is a mismach in noise condiions for noise basis raining and esimaion using NMF. IN: TL Copyrigh 213 ERC

2 dvanced cience and Technology Leers Vol.3 (ICC 213) Following his inroducion, ecion 2 proposes an NMF-based adapive noise esimaion mehod. ubsequenly, ecion 3 evaluaes he performance of he proposed noise esimaion mehod. Finally, ecion 4 concludes his paper. 2 Proposed NMF-ased dapive Noise Esimaion Mehod Le y i s i and d i be noisy speech, clean speech, and addiive noise for he i-h analysis frame, respecively, where d i is uncorrelaed wih s i. y applying a shor-ime Fourier ransform (TFT), y i can be represened as specral componens, such as i ( k) = i ( k) + i ( k) for k =,, K 1, where i, i, and i denoe he k-h specral componens of y i s i and d i respecively. The goal of he proposed noise esimaion mehod is o esimae i from i wihou prior knowledge of i and i. To his end, several analysis frames are concaenaed so ha = + is obained. Thus, all he marices,,, and, are all K N marices, where K and N are he number of frequency bins and he number of concaenaed frames, respecively. In he NMF framework, is represened as a form of =, where and are a basis marix and an acivaion marix of, respecively. Firs of all, he NMF raining [5] is applied o obain an iniial noise basis marix, ~, from he collecion of noise signals. fer ha, he noise basis adapaion is performed ieraively by he following equaions 1T ˆ = ˆ, (1) 1T 1 T 1 1 = (2) T 1 where ˆ = ~, is an ieraion index, T is he ranspose operaor, and 1 is a K N marix wih all elemens equal o uniy. Moreover, boh muliplicaion,, and division indicae elemen-wise operaors. In Eqs. (1) and (2), is a specral magniude marix of iniial noise signal wihin shor-pause region of noisy speech signal. Noe ha he duraion of he shor-pause region is se o.5 sec in his paper. Nex, ˆ and ˆ are a K a basis marix and an a N acivaion marix obained afer he -h ieraion, respecively, where a is he number of bases and i is a conrollable parameer in NMF. Noe ha all elemens for are se as random ˆ values beween and 1, and = ~. The ieraive procedure described above is 16 Copyrigh 213 ERC

3 dvanced cience and Technology Leers Vol.3 (ICC 213) erminaed if he difference of an objecive funcion according o he ieraion is less han a pre-defined hreshold. Tha is, he objecive funcion is defined as [7] ( ˆ ˆ ) ˆ obj = ˆ ( ) log (3) K N, ˆ where summaion means he addiion of all he elemens of a marix. ccordingly, if obj ( ) obj( 1) / obj( 1) < θ, hen he procedure described in Eqs. (1) and (2) is erminaed, where θ is manually se o 1 in his paper by rading off he ieraion number and he adapaion accuracy. Consequenly, = ˆ is obained if he procedure is erminaed a he -h ieraion. Nex, is esimaed, which corresponds o finding from by applying he equaions of where and are an 1T =, (4) 1T 1 T 1 1 = (5) T 1 K a basis marix and an a N acivaion marix of, respecively. Moreover, [ = ; ] and = [ ; ]. Noe ha all ele- mens of and are se as random values beween and 1. imilarly o he erminaion condiion in Eq. (3), he esimaion procedure is finished by checking log( / ) is going o be converged. Finally, if wheher [( ) ( )] K, N he procedure of Eqs. (4) and (5) is erminaed a he -h ieraion, he noise specrum,, is esimaed as ˆ. 3 Performance Evaluaion The performance of a noise esimaion mehod was evaluaed by measuring he logspecral disance (L) in d [8] beween he rue noise specrum and he esimaed one by he noise esimaion mehod. To his end, 1 speakers uered 2 senences each, resuling in 2 senences in oal. Each senence was mixed wih home TV noise a around 2 d NR. Noe here ha home TV noise was used o simulae a highly non-saionary noisy environmen in which a person was alking while waching differen genres of TV programs, such as dramas, news, spors, and movies. In addiion, in order o simulae mismached noise condiion, ~, for Eqs. (1) and (2), Copyrigh 213 ERC 161

4 dvanced cience and Technology Leers Vol.3 (ICC 213) Table 1. Performance comparison of he noise esimaion mehods in L (d). peaker Convenional Proposed L reducion C E F G H I J verage was obained from 1 minues of noise signal consising of bus sops, resaurans, and subway noises. Moreover, K, a, and N were se o 257, 4, 3, respecively. Table 1 compares he Ls beween he proposed mehod and a convenional NMF-based mehod ha did no have any adapaion scheme for he noise esimaion [5]. Tha is, he convenional mehod used = [ ; ~ ] in Eq. (4) insead of = [ ; ˆ ]. I was shown from he able ha he proposed mehod reduced average L by 1.17 d, compared o he convenional mehod. This implies ha he proposed mehod could provide a beer noise specral esimae han he convenional mehod. 4 Conclusion In his paper, an NMF-based adapive noise esimaion mehod was proposed o overcome a mismach in noise condiions for noise basis raining and esimaion using NMF. The proposed mehod firs performed he noise basis adapaion o updae he iniially esimaed noise basis marix on he fly by using an esimae of noise specrum from he noisy signal. Then, noise specrum of curren noise environmen was esimaed by NMF wih he adapive noise basis marix. I has been shown from he experimen ha he proposed mehod provided lower L han he convenional NMFbased mehod. cknowledgmens. This work was suppored in par by he IT R& program of MIP/KEIT [135252, evelopmen of dialog-based sponaneous speech inerface echnology on mobile plaform] and he Naional Research Foundaion of Korea (NRF) gran, funded by he governmen of Korea (MIP) (No ). 162 Copyrigh 213 ERC

5 dvanced cience and Technology Leers Vol.3 (ICC 213) References 1. Lim, J., Oppenheim,. V.: ll-pole modeling of degraded speech. IEEE Transacions on cousics, peech, and ignal Processing, 26(3), (1978) pp Ephraim,., Malah,.: peech enhancemen using a minimum mean-square error shorime specral ampliude esimaor. IEEE Transacions on cousics, peech, and ignal Processing, 32(6), (1984) pp Rangachari,., Loizou, P., Hu,.: noise esimaion algorihm wih rapid adapaion for highly nonsaionary environmens. In: Proceedings of ICP, (24) pp Kim,. M., Park, J. H., Kim, H. K., Lee,. J., Lee,. K.: Non-negaive marix facorizaion based noise reducion for noise robus auomaic speech recogniion. Lecure Noes in Compuer cience, 7191, (212) pp Jeon, K. M., Park, N. I., Kim, H. K., Hwang, K. I., Choi, M. K.: Non-saionary noise esimaion based on non-negaive marix facorizaion. dvanced cience and Technology Leers, 14, (212) pp Lee,.., eung, H..: Learning he pars of objecs by non-negaive marix facorizaion. Naure, 41(6755), (1999) pp Lee,.., eung, H..: lgorihms for nonnegaive marix facorizaion. dvances in Neural Informaion Processing ysems (NIP), 13, (2) pp Gray,. H., Markel, J..: isance measures for speech processing. IEEE Transacions on cousics, peech, and ignal Processing, 24(5), (1976) pp Copyrigh 213 ERC 163