Ph.D. thesis defense

1. Digital watermarking methods applied to non-additive channels Ph.D. candidate: M. Scagliola Tutor: P. Guccione Research Doctorate Course in Information Engineering

4. Definition: watermarking is a mechanism to create a communication channel that is multiplexed into original content By adopting a communication point of view: Watermark signal Watermarked signal Attacked signal Estimated message Host signal Error probability Michele Scagliola, DEE – Politecnico di Bari Torino, February 25 2010 Watermarking as communications Message

5. According to a communication approach: MSE-based metrics Data to Watermark Ratio: Watermark to Noise Ratio: being Michele Scagliola, DEE – Politecnico di Bari Torino, February 25 2010 Distortion measures

10. It can be considered somewhat solved in literature by various approaches, such as Rational Dither Modulation (RDM) RDM uses a variable quantization step-size which scales according to the gain on the channel. Michele Scagliola, DEE – Politecnico di Bari Torino, February 25 2010 Fixed gain attack and RDM

11. RDM asymptotically approaches the BER of DM but being also invariant to constant gain scaling Michele Scagliola, DEE – Politecnico di Bari Torino, February 25 2010 Fixed gain attack and RDM

12. The power-law attack consists of a constant exponentiation and a constant gain scaling of the amplitudes of the watermarked signal: Open problem: Coping with nonlinear distortions The power-law attack models common processings such as gamma compression Michele Scagliola, DEE – Politecnico di Bari Torino, February 25 2010 Power-law attack

14. k-th host sample Function computed on the previous watermarked samples The k-th sample in the hyperbolic angle representation results Michele Scagliola, DEE – Politecnico di Bari Torino, February 25 2010 Hyperbolic RDM: hyperbolic mapping The function h belongs to the set : The geometric mean belongs to this set:

15. Inverse mapping: Host signal Watermaked signal Transformed domain h RDM encoder Michele Scagliola, DEE – Politecnico di Bari Torino, February 25 2010 Hyperbolic RDM: embedding

16. The information bits are retrieved applying the RDM decoder to the estimated marked samples in the hyperbolic angle domain: The decoder output results intrinsically invariant to the power-law attack: RDM decoder h Michele Scagliola, DEE – Politecnico di Bari Torino, February 25 2010 Hyperbolic RDM: decoding

17. For large memory vectors, the Data to Watermark Ratio has been analytically evaluated: Michele Scagliola, DEE – Politecnico di Bari Torino, February 25 2010 Performance analysis: DWR

18. Under the hypothesis of Gaussian host, high DWRs and memory vectors going to infinity, the error probability has been analytically evaluated Additive noise in hyperbolic domain results in having pdf the error probability has been computed from Michele Scagliola, DEE – Politecnico di Bari Torino, February 25 2010 Performance analysis: bit-error rate

21. Quantization-based data hiding schemes are not designed to cope with desynchronization channels, such as filtering LTI filtering attack: Linear time invariant (LTI) filtering adds to the watermarked signal a host-dependent noise that increases with the host power Michele Scagliola, DEE – Politecnico di Bari Torino, February 25 2010 LTI filtering attack Discrete Fourier Transform – Rational Dither Modulation (DFT-RDM) was designed to cope with LTI filtering attack Attack filter is totally unknown at both the embedder and the decoder

23. An RDM-like channel is constructed on each DFT channel: Michele Scagliola, DEE – Politecnico di Bari Torino, February 25 2010 DFT-RDM

24. DFT-RDM exhibits low per-channel error probabilities for white Gaussian host But it is also shown that high error probability occurs for non-white, non-Gaussian and non-stationary hosts (audio signals are used as case study) Michele Scagliola, DEE – Politecnico di Bari Torino, February 25 2010 Performance analysis of DFT-RDM

25. We consider non-white Gaussian host signal X modeled by an AR process: Michele Scagliola, DEE – Politecnico di Bari Torino, February 25 2010 DFT-RDM for non-white hosts Per-channel host signal power Per-channel host watermark power, from the properties of RDM, is

26. Michele Scagliola, DEE – Politecnico di Bari Torino, February 25 2010 DFT-RDM for non-white hosts A larger watermark signal is produced on those DFT channels having stronger spectral content Different RDM-like channel have different robustness against additive noise Per-channel host signal power Per-channel host watermark power, from the properties of RDM, is

27. Received signal: Per-channel multiplication error power Michele Scagliola, DEE – Politecnico di Bari Torino, February 25 2010 DFT-RDM for non-white hosts Depends on the host psd: multiplication error is a self-noise term Depends on the attack filter

28. The knowledge of the per-channel host power and of the per-channel multiplication error power allow to analytically predict the per-channel error probability Per-channel BER with N=256 and DWR =25 dB Low-pass attack filter with Michele Scagliola, DEE – Politecnico di Bari Torino, February 25 2010 DFT-RDM for non-white hosts

32. Then we tested W-DFT-RDM with audio clips in order to verify the performance improvement w.r.t. DFT-RDM The whitening filter resembles the psd of an average audio signal Overall error probabilities for band-pass filter The BERs for W-DFT-RDM are always lower than those for DFT-RDM Michele Scagliola, DEE – Politecnico di Bari Torino, February 25 2010 Experimental results for audio signals

33. Then we tested W-DFT-RDM and DFT-RDM with a ten-band audio equalizer as attack filter Overall error probabilities for audio equalizer The improvement given by W-DFT-RDM is increased and acceptable BERs are achieved Michele Scagliola, DEE – Politecnico di Bari Torino, February 25 2010 Experimental results for audio signals