This page maintained by Igor Popovic (firstname.lastname@example.org), FMA&H Audio Development
New! A free version of D/Noise 1.0d is available for the Apple Power Macintosh (Windows95 follows soon).
View a screenshot or download software and sample file.
Our current audio denoising efforts started with the challenge to try to recover as much as possible from a totally corrupted wax-cylinder, capturing Johannes Brahms playing one of his Hungarian Dances. The original recording was made in 1889 by an agent of Thomas Edison, in Brahms's appartement in Vienna. In a first attempt, we have managed to recover sufficient information to carry out the MIDI reconstruction of a passage, in which Brahms departs significantly from his score in free improvisation (sound examples). Subsequently, we have refined our technique for application in more realistic situations.
Our basic denoising procedure consists in separating a noisy audio file into coherent and noisy components. The decision what to consider as noise is carried out automatically by an adapted local trigonometric transform, ALTT, with entropy-driven basis selection (see References). Applying our procedure to a noisy recording of Enrico Caruso, dated 1904, yields these intermediate results on a first pass:
The top window shows the original recording (AIFF, .WAV, .snd), at the point of the singer's entrance. The middle window shows the coherent component, extracted through a single-pass procedure (AIFF, .WAV, .snd), and the bottom window shows the residual noisy component (AIFF, .WAV, .snd). As you can hear, a fair amount of music still remains embedded in the residual noise. Although that amount can be controlled--within limits--by tweaking the various parameters of the denoising algorithm, multi-pass procedures yield better results. First, we can reapply the denoising algorithm iteratively to the noisy file, and its components, thus pealing away layer after layer of noise. The resulting coherent files are then added together. Second, we can use the noise file as a model and reapply a slightly modified denoising algorithm, seeking maximal decorrelation between the noise model and the original file (AIFF, .WAV, .snd). Other techniques are currently under development. In addition, lower-grade versions of the techniques are being optimized for non-audiophile real-time applications, using speedier wavelet packet analysis-synthesis, WPA, instead of the computationally somewhat costly ALTT.
A free demo version of our software for the Apple Macintosh(tm) and the Apple PowerMacintosh(tm) is being readied. In addition, we will soon release a demo versio of our new audio signal processing framework TF-Lab (Time-Frequency Lab) for interactive audio signal processing with local trigonometric transforms and wavelet packets (screenshot). Watch this page, or e-mail us, if you wish to be notified of the software's availability.
R. R. Coifman, V. M. Wickerhauser, "Wavelets and Adapted Waveform Analysis. A Toolkit for Signal Processing and Numerical Analysis", Proceedings of Symposia in Applied Mathematics, Vol. 47, 1993, pp. 119-153.
J. Berger, R. Coifman, M. Goldberg: "A Method of Removing Noise from Old Recordings", Proceedings of the 1994 International Computer Music Conference.
J. Berger, R. Coifman, M. Goldberg: "Removing Noise from Music Using Local Trigonometric Bases and Wavelet Packets", J. Audio Eng. Soc., Vol. 42, No. 10, 1994 October, pp. 808-818.
R. R. Coifman, N. Saito: "Constructions of local orthonormal bases for classification and regression", C. R. Acad. Sci. Paris, t. 319, Série I, 1994, pp. 191-196.
N. Saito, Local Feature Extraction and Its Applications Using a Library of Bases, Ph.D. dissertation, Department of Mathematics, Yale University, 1994.
J. Berger, R. Coifman, I. Popovic: "Aspects of Pitch-Tracking and Timbre Separation: Feature Detection in Digital Audio Using Adapted Local Trigonometric Bases and Wavelet Packets", Proceedings of the 1995 International Computer Music Conference in Banff, Canada, pp. 280-283.
Original (AIFF, .WAV, .snd), denoised segment (AIFF, .WAV, .snd), and denoised segment with super-imposed MIDI (AIFF, .WAV, .snd).