Digital Audio Restoration: A Statistical Model Based Approach

Introduction.- Fundamentals.- Removal of Clicks.- Hiss Reduction.- A Bayesian Approach to Click Removal.- Bayesian Sequential Click Removal.- Implementation and Experimental Results for Bayesian Detection.- Removal of Low Frequency Noise Pulses.- Restoration of pitch variation defects.- Conclusions and further research Appendices.

[1]  Edmund Taylor Whittaker.  On a New Method of Graduation , 1922, Proceedings of the Edinburgh Mathematical Society.

[2]  L. M. M.-T..  Theory of Probability , 1929, Nature.

[3]  U.R. Furst.  Periodic Variations of Pitch in Sound Reproduction by Phonographs , 1946, Proceedings of the IRE.

[4]  P. E. Axon,et al.  A study of frequency fluctuations in sound recording and reproducing systems , 1949 .

[5]  Norbert Wiener,et al.  Extrapolation, Interpolation, and Smoothing of Stationary Time Series, with Engineering Applications , 1949 .

[6]  J. Doob.  Stochastic processes , 1953 .

[7]  N. Metropolis,et al.  Equation of State Calculations by Fast Computing Machines , 1953, Resonance.

[8]  J. P. Hartog.  Mechanical vibration / J.P. Den Hartog , 1956 .

[9]  Edward Molloy,et al.  High fidelity sound reproduction , 1958 .

[10]  J. Durbin.  EFFICIENT ESTIMATION OF PARAMETERS IN MOVING-AVERAGE MODELS , 1959 .

[11]  J. Davenport.  Editor , 1960 .

[12]  E. Gilbert.  Capacity of a burst-noise channel , 1960 .

[13]  David L. Phillips,et al.  A Technique for the Numerical Solution of Certain Integral Equations of the First Kind , 1962, JACM.

[14]  Norbert Wiener,et al.  Extrapolation, Interpolation, and Smoothing of Stationary Time Series , 1964 .

[15]  Andrew J. Viterbi,et al.  Error bounds for convolutional codes and an asymptotically optimum decoding algorithm , 1967, IEEE Trans. Inf. Theory.

[16]  Ray Dolby,et al.  An Audio Noise Reduction System , 1967 .

[17]  G. C. Tiao,et al.  A bayesian approach to some outlier problems. , 1968, Biometrika.

[18]  J. Loewenthal.  DECISION , 1969, Definitions.

[19]  W. K. Hastings,et al.  Monte Carlo Sampling Methods Using Markov Chains and Their Applications , 1970 .

[20]  Gwilym M. Jenkins,et al.  Time series analysis, forecasting and control , 1972 .

[21]  P. R. Fisk,et al.  Distributions in Statistics: Continuous Multivariate Distributions , 1971 .

[22]  Daniel W. Gravereaux,et al.  Automatic Detection of Impulse Noise , 1971 .

[23]  Milton C. Chew.  Distributions in Statistics: Continuous Univariate Distributions-1 and 2 , 1971 .

[24]  G. C. Tiao,et al.  Bayesian inference in statistical analysis , 1973 .

[25]  Richard O. Duda,et al.  Pattern classification and scene analysis , 1974, A Wiley-Interscience publication.

[26]  I. Guttman.  Care and Handling of Univariate or Multivariate Outliners in Detecting Spuriosity—a Bayesian Approach , 1973 .

[27]  W. R. Buckland,et al.  Distributions in Statistics: Continuous Multivariate Distributions , 1973 .

[28]  Jr. G. Forney,et al.  The viterbi algorithm , 1973 .

[29]  D. F. Andrews,et al.  Scale Mixtures of Normal Distributions , 1974 .

[30]  J. Makhoul,et al.  Linear prediction: A tutorial review , 1975, Proceedings of the IEEE.

[31]  T. M. Cannon,et al.  Blind deconvolution through digital signal processing , 1975, Proceedings of the IEEE.

[32]  E. Owens.  Introduction to the Psychology of Hearing , 1977 .

[33]  John W. Tukey,et al.  Exploratory Data Analysis. , 1979 .

[34]  Frederick Mosteller,et al.  Data Analysis and Regression , 1978 .

[35]  Jont B. Allen,et al.  Short term spectral analysis, synthesis, and modification by discrete Fourier transform , 1977 .

[36]  D. Rubin,et al.  Maximum likelihood from incomplete data via the EM - algorithm plus discussions on the paper , 1977 .

[37]  Alan V. Oppenheim,et al.  All-pole modeling of degraded speech , 1978 .

[38]  Bovas Abraham,et al.  Linear Models and Spurious Observations , 1978 .

[39]  Vic Barnett,et al.  Outliers in Statistical Data , 1980 .

[40]  S. Boll,et al.  Suppression of acoustic noise in speech using spectral subtraction , 1979 .

[41]  A.V. Oppenheim,et al.  Enhancement and bandwidth compression of noisy speech , 1979, Proceedings of the IEEE.

[42]  Robert D. Preuss.  A frequency domain noise cancelling preprocessor for narrowband speech communications systems , 1979, ICASSP.

[43]  G. Box,et al.  Bayesian analysis of some outlier problems in time series , 1979 .

[44]  Richard M. Schwartz,et al.  Enhancement of speech corrupted by acoustic noise , 1979, ICASSP.

[45]  Bruno O. Shubert,et al.  Random variables and stochastic processes , 1979 .

[46]  D. Thomson,et al.  Robust Estimation of Power Spectra , 1979 .

[47]  M. J. Carey,et al.  A system for reducing impulsive noise on gramophone reproduction equipment , 1980 .

[48]  Stephen A. Billings,et al.  Identi cation of nonlinear systems-A survey , 1980 .

[49]  R. McAulay,et al.  Speech enhancement using a soft-decision noise suppression filter , 1980 .

[50]  Lawrence R. Rabiner,et al.  Digital Techniques for Changing the Sampling Rate of a Signal , 1982 .

[51]  D. B. Preston.  Spectral Analysis and Time Series , 1983 .

[52]  David Malah,et al.  Speech enhancement using optimal non-linear spectral amplitude estimation , 1983, ICASSP.

[53]  Paul Bratley,et al.  A guide to simulation , 1983 .

[54]  Roger Lagadec,et al.  Signal Enhancement via Digital Signal Processing , 1983 .

[55]  Gene H. Golub,et al.  Matrix computations , 1983 .

[56]  John B. Anderson,et al.  Sequential Coding Algorithms: A Survey and Cost Analysis , 1984, IEEE Trans. Commun..

[57]  Donald Geman,et al.  Stochastic Relaxation, Gibbs Distributions, and the Bayesian Restoration of Images , 1984, IEEE Transactions on Pattern Analysis and Machine Intelligence.

[58]  M. West.  Outlier Models and Prior Distributions in Bayesian Linear Regression , 1984 .

[59]  S. Biyiksiz,et al.  Multirate digital signal processing , 1985, Proceedings of the IEEE.

[60]  David Malah,et al.  Speech enhancement using a minimum mean-square error log-spectral amplitude estimator , 1984, IEEE Trans. Acoust. Speech Signal Process..

[61]  Hans-Joachim Platte,et al.  A Burst Error Concealment Method for Digital Audio Tape Application , 1985 .

[62]  Editors , 1986, Brain Research Bulletin.

[63]  Jonathan D. Cryer,et al.  Time Series Analysis , 1986 .

[64]  James A. Moorer,et al.  Linear-Phase Bandsplitting: Theory and Applications , 1986 .

[65]  S. Haykin,et al.  Adaptive Filter Theory , 1986 .

[66]  L. Devroye.  Non-Uniform Random Variate Generation , 1986 .

[67]  Raymond N. J. Veldhuis,et al.  Adaptive interpolation of discrete-time signals that can be modeled as autoregressive processes , 1986, IEEE Trans. Acoust. Speech Signal Process..

[68]  Kaoru Arakawa,et al.  Separation of a Nonstationary Component from the EEG by a Nonlinear Digital Filter , 1986, IEEE Transactions on Biomedical Engineering.

[69]  Thomas F. Quatieri,et al.  Speech analysis/Synthesis based on a sinusoidal representation , 1986, IEEE Trans. Acoust. Speech Signal Process..

[70]  Robert M. Gray,et al.  Random processes : a mathematical approach for engineers , 1986 .

[71]  Lennart Ljung,et al.  System Identification: Theory for the User , 1987 .

[72]  Kuldip K. Paliwal,et al.  A speech enhancement method based on Kalman filtering , 1987, ICASSP '87. IEEE International Conference on Acoustics, Speech, and Signal Processing.

[73]  Pjw Rayner,et al.  A new application of adaptive filters for restoration of archived gramophone recordings , 1988, ICASSP-88., International Conference on Acoustics, Speech, and Signal Processing.

[74]  John G. Proakis,et al.  Introduction to Digital Signal Processing , 1988 .

[75]  Xavier Serra,et al.  A system for sound analysis/transformation/synthesis based on a deterministic plus stochastic decomposition , 1989 .

[76]  L. Cohen,et al.  Time-frequency distributions-a review , 1989, Proc. IEEE.

[77]  S. D. Gray,et al.  Filtering of colored noise for speech enhancement and coding , 1989, International Conference on Acoustics, Speech, and Signal Processing,.

[78]  A. Dale Magoun,et al.  Decision, estimation and classification , 1989 .

[79]  Ehud Weinstein,et al.  Maximum likelihood noise cancellation using the EM algorithm , 1989, IEEE Trans. Acoust. Speech Signal Process..

[80]  J. Valiere,et al.  DÉTECTION ET SUPPRESSION DE BRUITS IMPULSIONNELS APPLIQUÉS À LA RESTAURATION D'ENREGISTREMENTS ANCIENS , 1990 .

[81]  Andrew Harvey,et al.  Forecasting, Structural Time Series Models and the Kalman Filter , 1990 .

[82]  Ioannis Pitas,et al.  Nonlinear Digital Filters - Principles and Applications , 1990, The Springer International Series in Engineering and Computer Science.

[83]  Adrian F. M. Smith,et al.  Sampling-Based Approaches to Calculating Marginal Densities , 1990 .

[84]  R. Marks.  Introduction to Shannon Sampling and Interpolation Theory , 1990 .

[85]  Howell Tong,et al.  Non-Linear Time Series , 1990 .

[86]  S. Vaseghi.  Detection and suppression of impulsive noise in speech communication systems , 1990 .

[87]  George Carayannis,et al.  Speech enhancement from noise: A regenerative approach , 1991, Speech Commun..

[88]  J. Valiere.  La restauration des enregistrements anciens par traitement numerique : contribution a l'etude de quelques techniques recentes , 1991 .

[89]  P.J.W. Rayner,et al.  The Detection and Correction of Artefacts in Degraded Gramophone Recordings , 1991, Final Program and Paper Summaries 1991 IEEE ASSP Workshop on Applications of Signal Processing to Audio and Acoustics.

[90]  P.J.W. Rayner,et al.  A Single-Input Hearing Aid Based on the Auditory Perceptual Features to Improve Speech Intelligibility in Noise , 1991, Final Program and Paper Summaries 1991 IEEE ASSP Workshop on Applications of Signal Processing to Audio and Acoustics.

[91]  S. Park,et al.  A novel structure for real-time digital sample-rate converters with finite precision error analysis , 1991, [Proceedings] ICASSP 91: 1991 International Conference on Acoustics, Speech, and Signal Processing.

[92]  Charles W. Therrien,et al.  Discrete Random Signals and Statistical Signal Processing , 1992 .

[93]  Raymond N. J. Veldhuis.  Restoration of lost samples in digital signals , 1992 .

[94]  Nicholas G. Polson,et al.  A Monte Carlo Approach to Nonnormal and Nonlinear State-Space Modeling , 1992 .

[95]  Stéphane Mallat,et al.  Singularity detection and processing with wavelets , 1992, IEEE Trans. Inf. Theory.

[96]  Mark J. T. Smith,et al.  Analysis-by-Synthesis/Overlap-Add Sinusoidal Modeling Applied to the Analysis and Synthesis of Musical Tones , 1992 .

[97]  Simon J. Godsill,et al.  A Bayesian approach to the detection and correction of error bursts in audio signals , 1992, [Proceedings] ICASSP-92: 1992 IEEE International Conference on Acoustics, Speech, and Signal Processing.

[98]  D. Mackay,et al.  Bayesian methods for adaptive models , 1992 .

[99]  A. J. Efron,et al.  Pre-whitening for detection in correlated plus impulsive noise , 1992, [Proceedings] ICASSP-92: 1992 IEEE International Conference on Acoustics, Speech, and Signal Processing.

[100]  S. V. Vaseghi,et al.  Restoration of Old Gramophone Recordings , 1992 .

[101]  Simon J. Godsill,et al.  The restoration of pitch variation defects in gramophone recordings , 1993, Proceedings of IEEE Workshop on Applications of Signal Processing to Audio and Acoustics.

[102]  Simon J. Godsill,et al.  The restoration of degraded audio signals , 1993 .

[103]  Stephen A. Dyer,et al.  Digital signal processing , 2018, 8th International Multitopic Conference, 2004. Proceedings of INMIC 2004..

[104]  Xavier Rodet,et al.  Tracking of partials for additive sound synthesis using hidden Markov models , 1993, 1993 IEEE International Conference on Acoustics, Speech, and Signal Processing.

[105]  Martin Abba Tanner,et al.  Tools for Statistical Inference: Observed Data and Data Augmentation Methods , 1993 .

[106]  John H. L. Hansen,et al.  Discrete-Time Processing of Speech Signals , 1993 .

[107]  Takis Kasparis,et al.  Adaptive scratch noise filtering , 1993 .

[108]  Simon J. Godsill,et al.  Frequency-domain interpolation of sampled signals , 1993 .

[109]  E. George,et al.  Journal of the American Statistical Association is currently published by American Statistical Association. , 2007 .

[110]  John Mourjopoulos,et al.  Speech enhancement using psychoacoustic criteria , 1993, 1993 IEEE International Conference on Acoustics, Speech, and Signal Processing.

[111]  Olivier Cappé.  Techniques de reduction de bruit pour la restauration d'enregistrements musicaux , 1993 .

[112]  Olivier Cappe.  ENHANCEMENT OF MUSICAL SIGNALS OF THE SHORT-TERM SPECTRAL COMPONENTS , 1993 .

[113]  Wj Fitzgerald,et al.  The restoration of digital audio recordings using the Gibbs sampler , 1993 .

[114]  R. McCulloch,et al.  Bayesian Inference and Prediction for Mean and Variance Shifts in Autoregressive Time Series , 1993 .

[115]  George S. Moschytz,et al.  Noise reduction by noise-adaptive spectral magnitude expansion , 1994 .

[116]  N. Shephard.  Partial non-Gaussian state space , 1994 .

[117]  Ehud Weinstein,et al.  Iterative and sequential algorithms for multisensor signal enhancement , 1994, IEEE Trans. Signal Process..

[118]  Jun S. Liu,et al.  Covariance structure of the Gibbs sampler with applications to the comparisons of estimators and augmentation schemes , 1994 .

[119]  Simon J. Godsill.  Recursive restoration of pitch variation defects in musical recordings , 1994, Proceedings of ICASSP '94. IEEE International Conference on Acoustics, Speech and Signal Processing.

[120]  Maxim J. Goldberg,et al.  Removing noise from music using local trigonometric bases and wavelet packets , 1994 .

[121]  R. Kohn,et al.  On Gibbs sampling for state space models , 1994 .

[122]  R. McCulloch,et al.  BAYESIAN ANALYSIS OF AUTOREGRESSIVE TIME SERIES VIA THE GIBBS SAMPLER , 1994 .

[123]  Olivier Cappé,et al.  Elimination of the musical noise phenomenon with the Ephraim and Malah noise suppressor , 1994, IEEE Trans. Speech Audio Process..

[124]  L. Tierney.  Markov Chains for Exploring Posterior Distributions , 1994 .

[125]  S. Frühwirth-Schnatter.  Data Augmentation and Dynamic Linear Models , 1994 .

[126]  Bradley P. Carlin,et al.  Markov Chain Monte Carlo conver-gence diagnostics: a comparative review , 1996 .

[127]  Robert C. Maher,et al.  A Method for Extrapolation of Missing Digital Audio Data , 1994 .

[128]  Wj Fitzgerald,et al.  Interpolation of missing samples for audio restoration , 1994 .

[129]  Jean Laroche,et al.  Evaluation of short-time spectral attenuation techniques for the restoration of musical recordings , 1995, IEEE Trans. Speech Audio Process..

[130]  C. L. Nikias,et al.  Signal processing with alpha-stable distributions and applications , 1995 .

[131]  N. Shephard,et al.  The simulation smoother for time series models , 1995 .

[132]  Simon J. Godsill,et al.  A Bayesian approach to the restoration of degraded audio signals , 1995, IEEE Trans. Speech Audio Process..

[133]  Simon J. Godsill,et al.  Robust noise modelling with application to audio restoration , 1995, Proceedings of 1995 Workshop on Applications of Signal Processing to Audio and Accoustics.

[134]  Sylvia Richardson,et al.  Markov chain concepts related to sampling algorithms , 1995 .

[135]  Petros G. Voulgaris,et al.  On optimal ℓ∞ to ℓ∞ filtering , 1995, Autom..

[136]  Yariv Ephraim,et al.  A signal subspace approach for speech enhancement , 1995, IEEE Trans. Speech Audio Process..

[137]  T. Moon.  The expectation-maximization algorithm , 1996, IEEE Signal Process. Mag..

[138]  Anil C. Kokaram,et al.  A System for Reconstruction of Missing Data in Image Sequences Using Sampled 3D AR Models and MRF Motion Priors , 1996, ECCV.

[139]  Maciej Niedzwiecki,et al.  Adaptive scheme for elimination of broadband noise and impulsive disturbances from AR and ARMA signals , 1996, IEEE Trans. Signal Process..

[140]  Thomas L. Harman,et al.  Advanced Engineering Mathematics Using Matlab V.4 , 1996 .

[141]  Simon J. Godsill,et al.  Robust noise reduction for speech and audio signals , 1996, 1996 IEEE International Conference on Acoustics, Speech, and Signal Processing Conference Proceedings.

[142]  R. Kohn,et al.  Markov chain Monte Carlo in conditionally Gaussian state space models , 1996 .

[143]  Simon J. Godsill,et al.  Robust treatment of impulsive noise in speech and audio signals , 1996 .

[144]  K. Riedel.  Numerical Bayesian Methods Applied to Signal Processing , 1996 .

[145]  Anil C. Kokaram,et al.  Joint interpolation, motion and parameter estimation for image sequences with missing data , 1996, 1996 8th European Signal Processing Conference (EUSIPCO 1996).

[146]  Patrick Duvaut,et al.  Fully Bayesian analysis of Hidden Markov models , 1996, 1996 8th European Signal Processing Conference (EUSIPCO 1996).

[147]  Saeed Vaseghi.  Advanced Signal Processing and Digital Noise Reduction , 1996 .

[148]  G. Kitagawa.  Smoothness priors analysis of time series , 1996 .

[149]  S. Godsill,et al.  Restoration of Image Sequences using a Causal Spatio-Temporal Model , 1997 .

[150]  Geoffrey P. Hull,et al.  Since Records Began: Emi : The First 100 Years , 1997 .

[151]  Joint detection, interpolation, motion and parameter estimation for image sequences with missing data , 1997, Proceedings of International Conference on Image Processing.

[152]  J. J. Rajan,et al.  Bayesian approach to parameter estimation and interpolation of time-varying autoregressive processes using the Gibbs sampler , 1997 .

[153]  G. Roberts,et al.  Updating Schemes, Correlation Structure, Blocking and Parameterization for the Gibbs Sampler , 1997 .

[154]  Simon J. Godsill,et al.  Bayesian Enhancement of Speech and Audio Signals which can be Modelled as ARMA Processes , 1997 .

[155]  Simon J. Godsill,et al.  Bayesian model selection for time series using Markov chain Monte Carlo , 1997, 1997 IEEE International Conference on Acoustics, Speech, and Signal Processing.

[156]  Simon J. Godsill,et al.  Removal of low frequency transient noise from old recordings using model-based signal separation techniques , 1997, Proceedings of 1997 Workshop on Applications of Signal Processing to Audio and Acoustics.

[157]  A. Doucet,et al.  Bayesian estimation of filtered point processes using Markov chain Monte Carlo methods , 1997, Conference Record of the Thirty-First Asilomar Conference on Signals, Systems and Computers (Cat. No.97CB36136).

[158]  Simon J. Godsill,et al.  Robust modelling of noisy ARMA signals , 1997, 1997 IEEE International Conference on Acoustics, Speech, and Signal Processing.

[159]  Xavier Rodet.  Musical Sound Signal Analysis/Synthesis: Sinusoidal+Residual and Elementary Waveform Models , 1997 .

[160]  M. Lorber,et al.  A combined approach for broadband noise reduction , 1997, Proceedings of 1997 Workshop on Applications of Signal Processing to Audio and Acoustics.

[161]  Patrick Duvaut,et al.  Bayesian estimation of state-space models applied to deconvolution of Bernoulli - Gaussian processes , 1997, Signal Process..

[162]  Simon J. Godsill,et al.  Digital audio restoration , 1998 .

[163]  Simon J. Godsill,et al.  Multidimensional optimisation of harmonic signals , 1998, 9th European Signal Processing Conference (EUSIPCO 1998).

[164]  Simon J. Godsill,et al.  Bayesian model selection for linear and non-linear time series using the Gibbs sampler , 1998 .

[165]  Simon J. Godsill,et al.  Statistical reconstruction and analysis of autoregressive signals in impulsive noise using the Gibbs sampler , 1998, IEEE Trans. Speech Audio Process..

[166]  Simon J. Godsill,et al.  A reversible jump sampler for autoregressive time series , 1997, Proceedings of the 1998 IEEE International Conference on Acoustics, Speech and Signal Processing, ICASSP '98 (Cat. No.98CH36181).

[167]  Simon J. Godsill,et al.  Restoration of Nonlinearly Distorted Audio Using Markov Chain Monte Carlo Methods , 1998 .

[168]  Simon J. Godsill,et al.  MCMC methods for restoration of nonlinearly distorted autoregressive signals , 1998, 9th European Signal Processing Conference (EUSIPCO 1998).

[169]  Ephraim.  Speech enhancement using a minimum mean square error short-time spectral amplitude estimator , 1984 .