Missing feature theory Statistical estimation of unreliable features for robust speech recognition 2) Missing feature theory and probabilistic estimation of clean speech components for robust speech recognition 3) State based imputation of missing data for robust speech recognition and speech enhancement 4) Missing data theory,spectral subtraction and signal-to-noise estimation for robust ASR: an integrated study

Parameters used in speech recognition can be Introduction Parameters used in speech recognition can be divided in two subsets 1) reliable or present parameters 2) unreliable or missing parameters

Introduction There are 2 problems in the application of missing data in robust ASR 1) identification of the reliable regions 2) recognition techniques that can deal with incomplete data

Detection of unreliable feature Method: (1) negative energy criterion (2) SNR criterion or

Detection of unreliable feature (3) statistical approach : noise is considered as normally distributed

Noise estimation method in [4] simple estimation weighted average estimation C) second order method D) Histogram method

Accuracy for the three detection methods

Recognition with incomplete data Method (1) Marginalization : unreliable data are ignored for a single state model ,the probability to emit vector is

Marginalization

Marginalization =1 bounded marginalization

Marginalization In Philippe’s another paper [2] ,the clean parameters are represented as pdfs and missing parameters are considered as being uniformly if 0<x<|Y(w)| otherwise

Recognition with incomplete data Method (2) GMM based Imputation : unreliable data are estimated advantages of the approach are that can be followed by conventional techniques like cepstral,RASTA In the estimation process,the GMM means are used to replace the unreliable features the means and variances of GMM are compensated with the additive noise,as in PMC

Imputation using inverse log-normal approximation

Imputation transformed into log-spectral domain :

Imputation using the noisy GMM,the weighting factor associated with each distribution is computed as follows:

Imputation Finally,the reliable data are enhanced using a spectral subtraction and the unreliable data are replaced by a weighted sum of the GMM means

features spetra

Discussion Why using GMM in this paper? A HMM based data imputation has been proposed in [3], when using time-dependent statistical models,if an error in the decoding sequence occurs,it can influence the recognition in the second feature domain therefore , GMM instead of HMM,but sufficient and computationally efficient for data imputation

Experiments results

Experiments results

Experiments results

Experiments results

Experiments results

Experiments results

Experiments results

Experiments results