Lecture 14. Design of audio WM Model of digital audio CO ( WAV-format): - dependent samples with frequency 44,1кHz, - amplitude of samples is

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1 Lecture 14. Desig of audio WM Model of digital audio CO WAV-format: - depedet samples wit frequecy 44,1кHz, - amplitude of samples is quatized o 2 16 =65536 levels 16 bits Remark 1. Tere exists a lossy compressio of WAV to mp3-format. Remark 2. Aoter model of audio CO is commercial speec sigals. All metods of WM embeddig ad extractio cosidered before ca be applied to audio CO owever a desig of audio WM systems as some peculiarities : - CO music first of all lose teir value eve after small corruptios Gaussia oise, filterig, pulse oise ctr. - I desig of audio WM it is ecessary to take ito accout so called HAS Huma Auditory System [20] Remark 3. For video WM it is also ecessary to take ito accout so called HVS Huma Visual System [20], but its impact o suc desig is ot so large because audio sigal as large frequecy rage. 1

2 Some properties of HAS 1. HAS is modeled usually by bak of filter overlappig o frequecy wit bad widt of about 200Hz for cetral frequecies lower 500Hz ad wit bad widt of about 5000 Hz for cetral frequecies witi te rage Hz. 2. Sesitivity of HAS to additive Gaussia oise is very large it ca be eard eve wit level 70dB lower ta te level of some oter soud 3. HAS as maskig property o frequecy. 4. HAS as maskig property i time. 5. HAS is tolerable to pase spectrum of audio sigal 6. HAS perceives additio of some eco sigals as a cagig of acoustic eviromet. Cosider some properties more detail. 2

3 3. Frequecy maskig Sigal wit small amplitude o te frequecy f m is ot eard masked i te presece of aoter sigal wit larger amplitude o te frequecy f о, tat is close to te first frequecy. Here maskig frequecy is 1кHz Tresold quiet-is suc level of audio sigal depedig o its frequecy tat tis sigal is ot eard wit lower amplitude. Maskig tresold is te level of masked sigal depedig o te frequecies of bot masked ad maskig sigals tat sigal is ot eard wit amplitude below tis tresold. Coclusio: Audio sigal ca be masked eve if its amplitude is larger ta tresold quiet, moreover te sigals o ig frequecies are masked better ta o lower frequecies. 3

4 4. Time maskig Additioal sigal aead or delayed wit respect to te mai sigal is ot eard if tese differeces i time are ot so large. Coclusio: Delayed sigal is masked worse ta aead sigal. 4

5 Te mai embeddig metods for audio WM: 1. Embeddig i LSB. 2. Modified embeddig i LSB. 3. Embeddig i pase domai. 4. Embeddig wit te use of eco sigals. 5. Te use of SS i frequecy or i time domai. 6. Te use of ISS i frequecy or i time domai. 7. Te use of QPD i frequecy or i time domai. 8. Embeddig based o a modulatio of some caracteristics of audio sigal. Cosider furter some of tese metods. 5

6 1. Embeddig i LSB: Te samples wit LSB embeddig are cose by stegokey. Uder te attack tese samples are ukow but a radomizatio of all samples ca result i large distortios of CO Remark 1: Trade off betwee embeddig rate, quality of CO ad efficiecy of attack are commoly for tis metod. Remark 2: It is commoly for audio CO to embed messages ot i oe least sigificat bit of samples but i several least sigificat bits. 2. Modified embeddig i LSB: Te idea is : cage LSB i additioal samples wic ave bee ot cose by stegokey if it results i reducig of CO distortios. Let us deote : C te amplitude of CO sample before embeddig, C w te amplitude of CO sample after embeddig of k LSB C w te amplitude of CO sample after embeddig of k+1 LSB. C w fial amplitude after embeddig of k LSB e = C- C w -te error uder embeddig i k LSB e = C- C w -te error uder embeddig i k+1 LSB Embeddig: C w C' w C'', if e' w, if e' e'' e'' 6

7 3. Embeddig i pase of CO Justificatio: HAS is tolerable to pase sift of audio sigal. а WM embeddig: 1. Samples of audio sigal are splited o te blocks of fixed legt. 2. To eac of blocks is applied DFT. 3. WM embeddig is provided by pase siftig of DFT. 4. It is provided «a smootig» of trasitios betwee blocks of DFT because tere may ave jumps of pases just after WM embeddig. 5. It is performed IDFT i order to form te WM-ed sigal fially. 7

8 b WM extractio: 1. Samples of audio stegosigal are divided o te blocks of fixed legt, moreover te bouds of tese blocks ave to coicide exactly wit te bouds of blocks uder embeddig. 2. DFT is applied to eac of blocks. 3. WM is extracted by digital pase detector. Embeddig rate: 8-32 bits/s uder a good quality of CO after embeddig. Improved metod: Divide sigal ito frequecy domais ad embed i DCT pases for eac of tese domais separately.experimet sows tat date embeddig rate ca be icreased te up to 1200 bit/s. Our experimets sow tat embeddig i pase domai ca ot take for grated agaist WM removal attack. be 8

9 4. Eco watermarkig Justificatio: Additio of «eco» origial sigal sifted i time to te mai CO is cosidered by HAS ot as additive oise but like to appearace of additioal resoaces similar to cagig of acoustic eviromet uder creatio of audio sigal. Te idea of eco-based WM embeddig: А А 1 А 0 δ 1 δ 0 tмсек A amplitude of origial audio sigal, A 1 amplitude of eco sigal correspodig to embeddig of te bit «1». A 0 amplitude of eco sigal correspodig to embeddig of te bit «0». δ 1 delay of eco correspodig to te bit «1». δ 0 delay of eco correspodig to te bit «0». Te parameters wic affect o te CO quality after embddig: 1 A1, A 0 A0, A 1, 0. 9

10 a WM embeddig: 1. Split samples of audio sigal ito blocks of te fixed legt. 2. Embed WM o eac of block usig eco sigals. 3. Smoot trasitio areas as a cosequece of eco sigal embeddig betwee blocks. b WM extractio : 1. Split samples of audio sigal ito blocks of fixed legt for wic te bouds ave to be coicide wit te bouds of blocks after embeddig. 2. Calculate autocorrelatio fuctioacf for eac of blocks. 3. Compare te side peaks of ACF wit some tresold.take decisio about embeddig of te correspodig bit depedig o a dispositio of peaks exceedig to te tresold. 10

11 WM embeddig based o eco idig S 0 0 x S b 1 1 x S were S - iput audio sigal b - filter pulse respose correspodig to, embeddig bit b = 0,1 *- covolutio b, 1,2...N, 1

12 Complex cepstrum Complex cepstrum S of sigal S, 0,1,..., N-1 is determied as follows : S 1 N N k 1 0 [log S k N 1 2 jk Sk k] e were N S k S e, - sigal amplitude 0 j 2 jk N 2 k - sigal pase

13 Correlatio receiver based o cepstrum 1,2,..., S x b b b x x 0, Uder te coditio D F p Te followig relatio olds for gaussia model: were dt e x F S Var D x t ,,

14 Correlatio receiver o subitervals L k k L k b b k x x were xk - Cepstrum of WM-ed sigal computed o te k-t subiterval, L te umber of subitervals o bit iterval N. Te we get te followig formula for te probability of error : L F p 8 9

15 Experimetal results Sigal Complex cepstrum GN PR Cov.

16 Waveform of music ad its cepstrum

17 Weter equality give below olds?? S x b b S S x 2 2 Let us deote by

18 N N N - Te legt of Gaussia oise appeded to zeros

19 p Te probability of errors p versus eco amplitude A A

20 Te umber of subitervals Rectagular widow Te probability of errors computed by simulatio Expoetial widow Hammig widow Haa widow Remark. Te legt of oe-bit iterval is 4000 samples

21 Coclusio o WM systems for audio sigals based o eco idig Qualitatively, te results of simulatio coicide wit te teory, but quatitatively tere are sigificat differeces wic ca be explai by te fact tat Te additive property of cepstrum for covolutio, does ot old correctly o limited itervals. Receivig o subitervals results i a sigificat decreasig of te probability of errors. Cagig of Gaussia sigal to real audio musical sigals results i sever degradatio tat ca be explaied by te existece of strog correlatio peaks i audio cepstrum. Error free extractio metod based o te use of wet paper codeswpc

22 Examples of filter pulse resposes correspodig to reverberatio.[49] Filter 1. Filter 2. 22

23 Amplitude of reverberatio Te umber of subitervals Total umber of embedded bits Errors , , , , , , , ,

24 Coclusio o WM systems for audio sigals based o reverberatio [49]. 1.Te use of o-trivial widow allows to decrease te amplitude of pulse respose give te probability of errors ad a cosequece to improve te origial sigal quality after embeddig.. Te best results gives Haa Widow 2.Te use of multi-iterval receiver decreases te probability of errors. 3.Te coice of filter pulse resposes simulatig reverberatio sould satisfy to te umber of coditios : - small ruiig of te origial souds music, -impossibility of pulse respose guessig like stego-key, -small correlatio of pulse respose cepstrum ad audio sigal cepstrums, -resistace to de-reverberatio attack, -acceptable time of sigal processig i embeddig procedure, -acceptable message embeddig rate. 4.Desig of audio WM based o reverberatio requires furter ivestigatios. 24

25 6. SS-based WM Oe ca use all metods of embeddig ad extractio cosidered before i Lecture 9 but takig ito accout HAS : а WM embeddig: C b C w HAS aalysis i time domai HAS aalysis i fr. domai a stegokey PRS geerator π WM {b} a и b amplificatio coefficiets, tat ave to be obtaied wit te use of time ad frequecy aalysis i lie wit HAS. 25

26 b WM extractio: C w LF filter Decisio sceme {b} stegokey PRS geerator PRS filter Low frequecy filter is used i order to reduce iterferece from CO. PRS filter results i suc PRS tat occurs te same as after filterig of WM-ed sigal. Remark 1. It is commoly to use blid decoder for audio WM. Remark 2. I order to icrease te embeddig date rate ca be used ortogoal PRS or error correctio codes wit soft decodig algoritm. 26

27 Improvemet of WM sceme for audio sigals [37]. 1. Adaptive embeddig based o possible attack aalysis for eac block of samples attack caracterizatio. 2. Te use of «WM sigal diversity» similar to tose metods wic are used i commuicatio tecique takig ito accout tat mp3 trasform ca be cosidered as selective fadig of WM carrier. 3. Te use of adaptive ISS or QPD i lie wit HAS ad possible attacks. 4.Te use of error correctig codes wit soft decodig algoritm turbo codes, LPDC-codes. 27

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29 It is easy to see tat suc embeddig procedure results i error free extractio. Te sacrifice witi tis approac is a decreasig of embeddig rate because some N-blocks are removed from te embeddig process. Te embeddig process wit te use of WPC

30 Simulatio results for tis approac give differet music files are sow i Table below: I tis table are used te followig otatios: - T - te total umber of te embedded bits wic were embedded i give musical file, - t is te potetial umber of embedded bits, - d is te umber of cageable bits i audio file.