A Unified Framework for Sparse Non-Negative Least Squares using Multiplicative Updates and the Non-Negative Matrix Factorization Problem

We study the sparse non-negative least squares (S-NNLS) problem. S-NNLS occurs naturally in a wide variety of applications where an unknown, non-negative quantity must be recovered from linear measurements. We present a unified framework for S-NNLS based on a rectified power exponential scale mixture prior on the sparse codes. We show that the proposed framework encompasses a large class of S-NNLS algorithms and provide a computationally efficient inference procedure based on multiplicative update rules. Such update rules are convenient for solving large sets of S-NNLS problems simultaneously, which is required in contexts like sparse non-negative matrix factorization (S-NMF). We provide theoretical justification for the proposed approach by showing that the local minima of the objective function being optimized are sparse and the S-NNLS algorithms presented are guaranteed to converge to a set of stationary points of the objective function. We then extend our framework to S-NMF, showing that our framework leads to many well known S-NMF algorithms under specific choices of prior and providing a guarantee that a popular subclass of the proposed algorithms converges to a set of stationary points of the objective function. Finally, we study the performance of the proposed approaches on synthetic and real-world data.Comment: To appear in Signal Processin

Temporal Masking for Bit-rate Reduction in Audio Codec Based on Frequency Domain Linear Prediction

Audio coding based on Frequency Domain Linear Prediction (FDLP) uses auto-regressive model to approximate Hilbert envelopes in frequency sub-bands for relatively long temporal segments. Although the basic technique achieves good quality of the reconstructed signal, there is a need for improving the coding efficiency. In this paper, we present a novel method for the application of temporal masking to reduce the bit-rate in a FDLP based codec. Temporal masking refers to the hearing phenomenon, where the exposure to a sound reduces response to following sounds for a certain period of time (up to $200$ ms). In the proposed version of the codec, a first order forward masking model of the human ear is implemented and informal listening experiments using additive white noise are performed to obtain the exact noise masking thresholds. Subsequently, this masking model is employed in encoding the sub-band FDLP carrier signal. Application of the temporal masking in the FDLP codec results in a bit-rate reduction of about $10$\% without degrading the quality. Performance evaluation is done with Perceptual Evaluation of Audio Quality (PEAQ) scores and with subjective listening tests

Scalable Wide-band Audio Codec based on Frequency Domain Linear Prediction

This paper proposes a technique for wide-band audio applications based on the predictability of the temporal evolution of Quadrature Mirror Filter (QMF) sub-band signals. An input audio signal is first decomposed into 64 frequency sub-band signals using QMF decomposition. The temporal envelopes in critically sampled QMF sub-bands are approximated using frequency domain linear prediction applied over relatively long time segments (e.g. $1000$ ms). Line Spectral Frequency parameters related to autoregressive models are computed and quantized in each frequency sub-band. The sub-band residual signals are quantized in the frequency domain using a split Vector Quantization (VQ) technique. In the decoder, the sub-band signal is reconstructed using the quantized residual and the corresponding quantized envelope. Finally, application of inverse QMF reconstructs the audio signal. Even with simple quantization techniques and without any psychoacoustic model, the proposed audio coder provides encouraging results on objective quality tests

Speech Coding based on Spectral Dynamics

In this paper we present first experimental results with a novel audio coding technique based on approximating Hilbert envelopes of relatively long segments of audio signal in critical-band-sized sub-bands by autoregressive model. We exploit the generalized autocorrelation linear predictive technique that allows for a better control of fitting the peaks and troughs of the envelope in the sub-band. Despite introducing longer algorithmic delay, improved coding efficiency is achieved. Since the described technique does not directly model short-term spectral envelopes of the signal, it is suitable not only for coding speech but also for coding of other audio signals

Spectral Noise Shaping: Improvements in Speech/Audio Codec Based on Linear Prediction in Spectral Domain

Audio coding based on Frequency Domain Linear Prediction (FDLP) uses auto-regressive models to approximate Hilbert envelopes in frequency sub-bands. Although the basic technique achieves good coding efficiency, there is a need to improve the reconstructed signal quality for tonal signals with impulsive spectral content. For such signals, the quantization noise in the FDLP codec appears as frequency components not present in the input signal. In this paper, we propose a technique of Spectral Noise Shaping (SNS) for improving the quality of tonal signals by applying a Time Domain Linear Prediction (TDLP) filter prior to the FDLP processing. The inverse TDLP filter at the decoder shapes the quantization noise to reduce the artifacts. Application of the SNS technique to the FDLP codec improves the quality of the tonal signals without affecting the bit-rate. Performance evaluation is done with Perceptual Evaluation of Audio Quality (PEAQ) scores and with subjective listening tests

Autoregressive Modelling of Hilbert Envelopes for Wide-band Audio Coding

Frequency Domain Linear Prediction (FDLP) represents the technique for approximating temporal envelopes of a signal using autoregressive models. In this paper, we propose a wide-band audio coding system exploiting FDLP. Specifically, FDLP is applied on critically sampled sub-bands to model the Hilbert envelopes. The residual of the linear prediction forms the Hilbert carrier, which is transmitted along with the envelope parameters. This process is reversed at the decoder to reconstruct the signal. In the objective and subjective quality evaluations, the FDLP based audio codec at $66$ kbps provides competitive results compared to the state-of-art codecs at similar bit-rates

Frequency Domain Linear Prediction for QMF Sub-bands and Applications to Audio Coding

This paper proposes an analysis technique for wide-band audio applications based on the predictability of the temporal evolution of Quadrature Mirror Filter (QMF) sub-band signals. The input audio signal is first decomposed into 64 sub-band signals using QMF decomposition. The temporal envelopes in critically sampled QMF sub-bands are approximated using frequency domain linear prediction applied over relatively long time segments (e.g. 1000 ms). Line Spectral Frequency parameters related to autoregressive models are computed and quantized in each frequency sub-band. The sub-band residuals are quantized in the frequency domain using a combination of split Vector Quantization (VQ) (for magnitudes) and uniform scalar quantization (for phases). In the decoder, the sub-band signal is reconstructed using the quantized residual and the corresponding quantized envelope. Finally, application of inverse QMF reconstructs the audio signal. Even with simple quantization techniques and without any sophisticated modules, the proposed audio coder provides encouraging results in objective quality tests. Also, the proposed coder is easily scalable across a wide range of bit-rates

Audio Coding Based on Long Temporal Contexts

We describe novel audio coding technique designed to be utilized at medium bit-rates. Unlike classical state-of-the-art audio coders that are based on short-term spectra, our approach uses relatively long temporal segments of audio signal in critical-band-sized sub-bands. We apply auto-regressive model to approximate Hilbert envelopes in frequency sub-bands. Residual signals (Hilbert carriers) are demodulated and thresholding functions are applied in spectral domain. The Hilbert envelopes and carriers are quantized and transmitted to the decoder. Our experiments focused on designing audio coder to provide broadcast radio-like quality audio around $10-20$kbps. Objective quality measures indicate comparable performance with the 3GPP-AMR speech codec standard for both speech and non-speech signals

Speech Coding based on Spectral Dynamics

In this paper we present first experimental results with a novel audio coding technique based on approximating Hilbert envelopes of relatively long segments of audio signal in critical-band-sized sub-bands by autoregressive model. We exploit the generalized autocorrelation linear predictive technique that allows for a better control of fitting the peaks and troughs of the envelope in the sub-band. Despite introducing longer algorithmic delay, improved coding efficiency is achieved. Since the described technique does not directly model short-term spectral envelopes of the signal, it is suitable not only for coding speech but also for coding of other audio signals

Non-uniform QMF Decomposition for Wide-band Audio Coding based on Frequency Domain Linear Prediction

This paper presents a new technique for perfect reconstruction non-uniform QMF decomposition developed to increase efficiency of a generic wide-band audio coding system based on Frequency Domain Linear Prediction (FDLP). The base line FDLP codec, operating at high bit-rates (~136 kbps), exploits an uniform QMF decomposition into 64 sub-bands followed by sub-band processing based on FDLP. Here, we propose a non-uniform QMF decomposition into 32 frequency sub-bands obtained by merging 64 uniform QMF bands. The merging operation is performed in such a way that bandwidths of the resulting critically sampled sub-bands emulate the characteristics of the critical band filters in the human auditory system. Such frequency decomposition, when employed in the FDLP audio codec, results in a bit-rate reduction of 40% over the base line. We also describe the complete audio codec, which provides high-fidelity audio compression at ~66 kbps. In subjective listening tests, the FDLP codec outperforms MPEG-1 Layer 3 (MP3) and achieves similar qualities as MPEG-4 AAC+ standard