Denoising Based on Multivariate Stochastic Volatility Modeling of Multiwavelet Coefficients

In this paper, signal denoising using multiwavelet based on multivariate GARCH model is presented where the multivariate GARCH modeling captures in addition to the correlations among the multiwavelet streams, the dependencies among the multiwavelet coefficients after time decimation at each level of multiwavelet decomposition. Then, a maximum a posteriori (MAP) estimator based on multivariate GARCH model is proposed for the purpose of the multiwavelet coefficients. This MAP estimator separates a heteroscedastic signal from a non-heteroscedastic noise, then, in order to demonstrate that heteroscadisticity assumption for real signals is plausible we show analytically that existence of errors in time-varying coefficients of the time-varying autoregression(TVAR) for natural signal modeling causes conditional heteroscedasticity. A statistical validation estimations at each step of this new denoising approach is provided via bootstrapping. In experimental results, synthetic and real signals are used for comparison of denoising methods.