Performance of multiscale model-based denoising

The performance and properties of multiscale Bayesian rectification are compared with those of other methods in the following examples. The examples compare the performance for rectification of Gaussian errors with steady-state and dynamic linear models for stochastic and deterministic underlying signals. 

Three independent material balance equations can be written for the flowsheet shown in Fig. 10 as [24] 

The performance of various rectification methods is compared for the noise-free underlying signal represented as a uniform distribution, non-stationary stochastic process, and data with deterministic features. 

Uniform distribution. The data used for this illustration are similar to those used by Johnston and Kramer [24]. The noise-free measurements for the flowrates, F and F4, are uniformly distributed in the intervals [1,5,15,40], respectively. The flowrates F through F5 are contaminated by independent 

Gaussian errors with standard deviations 1, 4, 4, 3, and 1, respectively. The performance of maximum likelihood, single-scale Bayesian, and multiscale Bayesian rectification are compared by Monte-Carlo simulation with 500 realizations of 2048 measurements for each variable. The prior probability distribution is assumed to be Gaussian for the single-scale and multiscale Bayesian methods. The normalized mean-square error of approximation is computed as, 

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