Atomic Decomposition by Basis Pursuit
SIAM Journal on Scientific Computing
Computational Auditory Scene Analysis: Principles, Algorithms, and Applications
Computational Auditory Scene Analysis: Principles, Algorithms, and Applications
Large-scale content-based audio retrieval from text queries
MIR '08 Proceedings of the 1st ACM international conference on Multimedia information retrieval
A Sparse Decomposition Method for Periodic Signal Mixtures
IEICE Transactions on Fundamentals of Electronics, Communications and Computer Sciences
Sparse decomposition of mixed audio signals by basis pursuit with autoregressive models
ICASSP '09 Proceedings of the 2009 IEEE International Conference on Acoustics, Speech and Signal Processing
Fused Lasso and rotation invariant autoregressive models for texture classification
Pattern Recognition Letters
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In this paper, we explore an application of basis pursuit to audio scene analysis. The goal of our work is to detect when certain sounds are present in a mixed audio signal. We focus on the regime where out of a large number of possible sources, a small but unknown number combine and overlap to yield the observed signal. To infer which sounds are present, we decompose the observed signal as a linear combination of a small number of active sources. We cast the inference as a regularized form of linear regression whose sparse solutions yield decompositions with few active sources. We characterize the acoustic variability of individual sources by autoregressive models of their time domain waveforms. When we do not have prior knowledge of the individual sources, the coefficients of these autoregressive models must be learned from audio examples. We analyze the dynamical stability of these models and show how to estimate stable models by substituting a simple convex optimization for a difficult eigenvalue problem. We demonstrate our approach by learning dictionaries of musical notes and using these dictionaries to analyze polyphonic recordings of piano, cello, and violin.