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Removing Noise from Music Using Local Trigonometric Bases and Wavelet Packets
A detailed description of the application of a denoising algorithm for removing noise from music is presented. The work is closely based on the work of R. Coifman and M. V. Wickerhauser on entropy-based denoising algorithms and on the work of R. Coifman and F.Majid. An algorithm used in that work, and which is also used here, consists in broadline of choosing an "optimal" basis for a given signal from a library of local trigonometric and wavelet packet bases. Optimality is defined in terms of a cost function. The signal is then split into clean and noisy parts, and the procedure is iterated on the noisy component. The clean components from each iteration are added together. The library of orthonormal bases used is described as well as the method of choosing the optimal basis for the signal and the process of separating the signal into coherent and noisy parts. Then several methods are outlined of breaking a large music signal into windows and combining these windows in order to diminish the audible effects of the windows' edges. Different denoising approaches used within a window are discussed including the consideration of subjective perceptual criteria and frequency-band denoising with different thresholds.
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