Precise Psychoacoustic Correction Method Based on Calculation of JND Level

Transcription

1 Vol. 116 (2009) ACTA PHYSICA POLONICA A No. 3 Optical ad Acoustical Methods i Sciece ad Techology Precise Psychoacoustic Correctio Method Based o Calculatio of JND Level Z. Piotrowski Faculty of Electroics, Military Uiversity of Techology, ge. S. Kaliskiego 2, Warsaw, Polad This paper costitutes a proposal of a method of spectral shapig of the watermark sigal without adjustig the iterceptio poit based directly o psychoacoustics of the huma auditory system ad the proposed calculatio formula. The proposed calculatio formula eables correctio of watermark sigal both as regards its spectrum shape ad adjustmet of watermark sigal to the host s JND. PACS umbers: x, y, c, d 1. Itroductio Iformatio hidig is oe of the techiques used i digital sigal processig. Digital watermarkig [1] is the iformatio hidig techique used to hide additioal digital cotet withi origial cotet (digital music, image, movie), for example to esure idetifiability of a acoustic sigal amog may other idetical sigals. I such a evet the watermark sigal (WS) iserted ito the origial host sigal (HS) must be ot oly be resistat to itetioal ad uitetioal degradatio factors, but also perceptually trasparet. I case of acoustic sigals trasparecy of WS is esured by meas of the so- -called psychoacoustic models, which are based o the huma auditory system (HAS) ad used i iformatio hidig techique to compute the just oticeable differece (JND) level. I psychoacoustics the JND level is defied as the level of distortio that ca be perceived i 50% of experimetal trials. Of course, as calculatio of the JND level is based o average ad subjective perceptio of listeers with ormal hearig ad o loss of hearig is idicated by the audiogram i case of listeers with ormal hearig, listeers with a exceptioally sesitive auditory system who are ofte referred to as golde ears are i most cases still able to perceive a differece betwee the origial ad the sigal degraded to JND level. I the subjective fidelity audio test coducted i accordace with BS-1116 recommedatio the listeer is asked to assess which of the two preseted similar audio stimuli has bee degraded acoustically. Therefore the purpose of psychoacoustic models is to provide the basis for mathematical computatio of a respose to the acoustic stimulus perceived by the listeer. The watermarked (WM) sigal equals HS with embedded WS corrected to the JND level. Zbigiew.Piotrowski@wel.wat.edu.pl Preseted below is the mathematical formula for calculatio of the spectral correctio coefficiet, which costitutes the basis of correctio of WS to JND level. WS correctio to JND level is calculated through icorporatio of the huma auditory system ito the Mpeg Layer 1 lossy compressio algorithm, which is commoly referred to as the mp3 format. The proposed spectrum correctio coefficiet differs from the stadard method for calculatio of the isertio poit, by which the WS spectrum is corrected [2 4]. 2. Huma auditory system psychoacoustic model The objective of the acoustic perceptio model is to estimate the miimum maskig threshold for each critical sub-bad () withi Bark scale, defied i [5 7] as: LT mi () = mi[lt g (i)] [db], where LT g (i) global maskig threshold computed for each spectral lie (i), critical sub-bad (Bark) specified as i [8, 9]: z(f) = 13 arcta( f) [ ( ) ] 2 f +3.5 arcta [Bark]. (1) 7600 Bark critical bads ca be preseted as a fuctio of a Bark scale umber ad the correspodig liear frequecy [Hz], as i Fig. 1. The miimum maskig threshold (LT mi ) costitutes the basis for calculatio of the sigal-to-mask ratio (SMR), as i Fig. 2. SMR is the differece betwee the masker ad the miimum value of the maskig threshold withi bad measured i the Bark scale ad SMR is expressed with the followig formula: SMR sb () = L sb () LT mi () [db], (2) where L sb () soud pressure level i [db] for each crit- (375)

2 376 Z. Piotrowski SF() = ( ) ( ) 2. (4) The miimum maskig threshold for the sigal uder cosideratio is preseted i Fig. 4. Fig. 1. Critical bads i the Bark scale (x-axis [Barks], y-label frequecy [Hz]). Fig. 4. Miimum maskig threshold level (horizotal lie) vs. host sigal SPL curve (decreasig). Fig. 2. SMR ratio ad miimum maskig threshold i the audio perceptual model, y-axis soud pressure level (SPL), x-axis Bark scale. ical bad (Bark), as agaist referece level pp = 20 µpa ad expressed with the followig formula: SPL() = 20 log 10(p/pp). (3) The miimum maskig threshold is computed o the basis of the frequecy maskig effect. This meas that, based o the so-called spreadig fuctio, it is possible to estimate both the frequecy areas ad the correspodig sigal levels below which the sigal will be iaudible, as the give frequecy rage is domiated by aother sigal that is stroger tha the remaiig sigals, as i Fig. 3. Fig. 3. Frequecy maskig pheomea the masker ad maskig threshold computed based o spreadig fuctio. The shape of the spreadig fuctios depeds o the Bark critical bad () ad it ca be expressed with the followig formula: 3. Watermark psychoacoustic correctio procedures Determiatio of the miimum maskig threshold is useful i determiatio of the spectral shape ad efficiecy of the watermark. Whe WS is corrected just below the miimum maskig threshold, the JND level is reached, which costitutes a guaratee that the corrected watermark embedded ito HS will be iaudible for most listeers with ormal hearig. This is possible due to the fact that ay eergy just below LT mi is iaudible to HAS. Aother well-kow watermark correctio method [2, 7, 9] is based o determiatio of the miimum maskig threshold for HS. The watermark sigal WS is geerated i accordace with a well-kow pseudo-radom oise sequece ad represeted by white oise. The first stage of WS formatio cosists i spectral shapig of white oise to LT mi shape by frequecy filterig. White oise udergoes fast Fourier trasformatio (FF) ad the is combied with LT mi values for each subbad. The secod stage cosists i correctio of WS agaist the LT mi curve iterceptio poit. This stage is completed by computatio of the miimum differece (of the correctio coefficiet) betwee LT mi curve ad shaped oise (coloured oise) i the logarithmic scale of the sigal s amplitude. Upo applicatio of iversio fast Fourier trasformatio (IFFT) coloured oise is corrected by meas of the correctio coefficiet. The resultig oise is iaudible i the presece of the origial sigal. The stages of watermark correctio are preseted i Fig. 5. The corrected watermark sigal is the embedded ito HS. As a result the output shaped oise (WS) after the two-stage correctio procedure is iaudible at HS presece. To sum up, the method proposed i [2] requires the followig:

3 Precise Psychoacoustic Correctio Method Based The result of ormalizatio for power desity fuctio for oe HS frame is preseted i Fig. 6. The obtaied value Delta H equals i this example db. Fig. 5. Watermark sigal two-stage correctio procedure: (A) white oise (WM) ad LT mi (dotted lie), (B) stage 1: oise filterig (colored oise), (C) stage 2: oise scalig usig iterceptio poit, just below LT mi curve. I stage 1: oe FFT operatio ad oe multiplicatio of the mask with a complex sigal (FFT for WS, multiplicatio of LT mi mask vector with WS spectrum). I stage 2: computatio of the miimum differece betwee corrected WS (coloured oise) ad LT g global maskig threshold (LT mi set for all Bark subbads), computatio of IFFT for corrected WS ad multiplicatio of corrected WS by the correctio coefficiet. The method proposed i this paper cosists of oe stage ad is based o the followig formula for computatio of oly oe correctio coefficiet o the basis of the psychoacoustic model: coef WM = SPL WM + (Delta H Delta WM ) LT mi + C, (5) where coef WM correctio coefficiet values [db] for WS, SPL WM soud pressure level [db] for WS, Delta H ormalizatio coefficiet for HS, Delta WM ormalizatio coefficiet for WS i referece to 96 db SPL (for 16 bit A/C coverter), C (optioally) costat value added i order to determie SMR [db]. Before WS is thoroughly processed i accordace with MPEG 1 Layer 1 psychoacoustic model [5] HS must be divided ito frames ad trasformed ito frequecy domai by meas of FFT. The the power spectrum desity of WS is computed o the basis of the followig formula: X = max (20 log 10 (abs (fft(xw)) /512) 200), (6) X power spectrum desity, x iput sigal vector, w widowig fuctio, 512 symmetric FFT poits [-], 200 miimum sigal power [db]. The widowig fuctio, defied as ormalizatio to 96 db SPL referece level, is carried out i stadard [5] i accordace with the followig formula: 8 w = haig(512). (7) 3 Normalizatio to the referece level 96 db SPL is carried out i stadard [5] usig the followig formula: Delta = 96 max(x), (8) X = X + Delta. (9) Fig. 6. Normalizatio of the power spectrum desity to the referece soud pressure level of 96 db. Sigal spectrum (A) before ormalizatio (maximum value: db); (B) after ormalizatio (maximum value: 96 db). Correctio of WS i accordace with the proposed procedure requires performace of two FFT operatios ad oe multiplicatio of the complex vector by correctio coefficiet coef WM (FFT is required for determiatio of ormalized power spectrum desity fuctio, multiplicatio of WS spectrum vector by correctio coefficiet coef WM ad IFFT i order to obtai the corrected WS vector i time). Figure 7 presets the results of oe-stage correctio. Fig. 7. Watermark sigal oe-stage correctio procedure usig proposed formula. Upper curve sigal spectrum before correctio, bottom oe after correctio procedure. 4. Compariso of computatioal effectiveess of the two proposed watermark sigal correctio procedures The computatioal requiremets for the method proposed i [2], accordig to the two-stages sigal processig, are as follows: Stage 1 is dedicated to frequecy domai filterig ad requires performace of the followig procedures: oe FFT of the white oise, oe multiplicatio of the mask vector with the oise spectrum. Successful completio of

4 378 Z. Piotrowski stage 1 results i the so-called coloured oise with spectral shape that resembles the curve of miimum maskig threshold (JND level). Stage 2 cosists i ormalizatio of the sigature to sigal level ad requires calculatio of the miimum differece betwee WS (coloured oise) ad the calculated LT mi level, as well as performace of oe IFFT ad oe multiplicatio of WS i time domai with the correctio coefficiet. The procedure proposed i this paper requires oly oe stage of processig of watermark sigal cosistig i oe FFT, oe multiplicatio of complex watermark sigal by the correctio coefficiet coef WM, ad oe IFFT to get filtered WS i time domai. 5. Experimetal results The basic metrics of the watermarked sigal, usig proposed WS correctio method based o (5) formula, were calculated. The computed metrics are described by the followig formulae: SNR = / A 2 (A A ) 2 sigal-to-oise ratio, (10) MSE = 1 A A N mea square error, (11) NMSE = / (A A ) 2 A 2 ormalized mea square error, (12) / PSNR = N max A2 (A A ) 2 peak sigal to oise ratio, (13) AF = 1 / (A A ) 2 A 2 audio fidelity. (14) I Table the metrics computed for corrected WS embedded ito HS are preseted. TABLE Basic metrics calculatio for HS, WS after the correctio procedure usig formula (5), WM for audio *.wav format tracks. PHS PWS PWM SMR MSE NMSE PSNR AF Track Track Track Track Track Track Track Track Track Track Track Track Track Track Track Track Track Track Track Track Track Track mea mi max std

5 Precise Psychoacoustic Correctio Method Based Coclusio The proposed method of psychoacoustic correctio of watermark sigal proves to be efficiet as agaist existig methods. I real-time processig mode the actual cost of computatio costitutes the key elemet as regards implemetatio of the digital sigal trasformatio algorithm. The proposed method of correctio of the sigal to JND level was implemeted i real-time watermarkig system i order to hide additioal iformatio i a acoustic sigal. The method discussed above may be implemeted i state-of-the-art applicatios used for watermarkig acoustic cotet i order to fulfil the eeds of, amog others, Digital Rights Maagemet Systems. Refereces [1] Z. Piotrowski, I. Zagoździński, P. Gajewski, L. Nowosielski, i: Proc. Europea DSP Educatio & Research Symp. EDERS 2008, Texas Istrumets, Tel Aviv 2008, p [2] Y. Casuto, M. Lustig, S. Mizrachy, Real-Time Digital Watermarkig System for Audio Sigals Usig Perceptual Maskig, Sigal ad Image Processig Lab, Techio IIT, Haifa [3] Z. Piotrowski, Polish Patet Office, P , Wydawictwo Urzędu Patetowego, Warsaw [4] Z. Damija, J. Wiciak, Mol. Quat. Acoust. 28, 66 (2007). [5] ISO CD , Codig of movig pictures ad associated audio for digital storage media at up to about 1.5 Mbit/s Part 3 Audio. [6] K. Pohlma, Priciples of Digital Audio, McGraw- -Hill, New York [7] J.G. Beereds, Audio Quality Determiatio Based o Perceptual Measuremet Techiques, Kluwer Academic Press, Bosto 1998, p. 1. [8] T. Powalowski, Z. Trawiski, J. Wojcik, Mol. Quat. Acoust. 28, 279 (2007). [9] E. Zwicker, H. Fastl, Psychoacoustics Facts ad Models, Spriger-Verlag, Berli Heidelberg 1990.