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• W92816013 abstract "Audio signals are represented via the sinusoidal model as a summation of a small number of sinusoids. This approach introduces sparsity to the audio signals in the frequency domain, which is exploited in this paper by applying Compressed Sensing (CS) to this sparse representation. CS allows sampling of signals at a much lower rate than the Nyquist rate if they are sparse in some basis. In this manner, a novel sinusoidal audio coding approach is proposed, which differs in philosophy from current state-of-the-art methods which encode the sinusoidal parameters (amplitude, frequency, phase) directly. It is shown here that encouraging results can be obtained by this approach, although inferior at this point compared to state-of-the-art. Several practical implementation issues are discussed, such as quantization of the CS samples, frequency resolution vs. coding gain, error checking, etc., and directions for future research in this framework are proposed. I. I NTRODUCTION The growing demand for audio content far outpaces the corre- sponding growth in users' storage space or bandwidth. Thus t here is a constant incentive to further improve the compression of audio signals. This can be accomplished either by applying compression algorithms to the actual samples of a digital audio signal, o r initially using a signal model and then encoding the model parameters as a second step. In this paper, we explore a novel method for encoding the parameters of the sinusoidal model (1). The sinusoidal model represents an audio signal using a small number of time-varying sinusoids. The remainder error signal— often termed the residual signal—can also be modelled to further improve the resulting subjective quality of the sinusoidal model (2). The sinusoidal model allows for a compact representation of the original signal and for efficient encoding and quantization . State- of-the-art methods of encoding and compressing the parameters of the sinusoidal model (amplitudes, frequencies, phases) are based on directly encoding these parameters (3)-(6). In this paper, we propose using the emerging compressed sensing (CS) (7), (8) methodology to encode and compress the sinusoidally-modelled audio signals. Compressed sensing seeks to represent a signal using a number of linear, non-adaptive measurements. Usually the number of measure- ments is much lower than the number of samples needed if the signal is sampled at the Nyquist rate. CS requires that the signal is very sparse in some basis—in the sense that it is a linear combination of a small number of basis functions—in order to correctly reconstruct the original signal. Clearly, the sinusoidally-modelled p art of an audio signal is a sparse signal, and it is thus natural to wonder how CS might be used to encode such a signal. Our method encodes the time-domain signal instead of the sinu- soidal model parameters as state-of-art methods propose (3)-(6). The advantage is that the encoding operation is simplified into r andomly sampling the time-domain sinusoidal signal, which is obtained after applying a psychoacoustic sinusoidal model to a monophonic audio signal. The random samples can be further encoded (here scalar quantization is suggested, but other methods could be used to im- prove performance). Additional advantages are that CS has inherent encryption and robustness to channel errors, and scales well to multi- channel cases. An issue that arises here is that as the encodi ng is performed in the time-domain—rather than the Fourier domain—the quantization error is not localized in frequency, and it is t herefore more complicated to predict the audio quality of the reconstructed signal. At this point, it is noted that the paper deals only wi th encoding the sinusoidal part of the model. This is to our knowledge the first attempt to exploit the sparse representation of the sinusoidal model for audio signals using compressed sensing, and it is shown here that several interesting questions arise in this conte xt." @default.
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• W92816013 date "2009-04-06" @default.
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• W92816013 title "Exploiting the Sparsity of the Sinusoidal Model Using Compressed Sensing for Audio Coding" @default.
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