Note estimation by contaminated normal distribution for audio watermarking method using non-negative matrix factorization

In general, the sound of a stego signal after embedding of watermarks should not deteriorate in digital audio watermarking methods. In this work, high sound quality means that the sound of the stego signal is maintained as music even if sounds not involved in the host signal is perceived. According to this definition, we focus on non-nonnegative matrix factorization (NMF). NMF is applied to the host signal and the amplitude spectrogram of the host signal is factorized to two non-nonnegative matrices that represent the spectral pattern and its activation. In previous work, we estimated notes from the activation coefficients, and we embedded the watermarks by operating the estimated activation coefficients of each note. However, the watermarks could not be extracted correctly because of the difference of the note estimation results between the embedding and extraction processes. This is caused by the change of signals due to various attacks including MP3 compression. To address this problem, we propose a note estimation method that uses contaminated normal distribution to implement robust note estimation even if the stego signal is modified by various attacks.