Single-scale model-based denoising

Data rectification involves solving the following optimization problem minimize 0(Y,Y) (3) 

The process model is represented by f, the equality constraints by h, and the inequality constraints by g. 

A common representation of the objective function in Eq. (3) minimizes the mean-square error of approximation as 

This approach is equivalent to maximum likelihood rectification for data contaminated by Gaussian errors. The likelihood function is proportional to the probability of realizing the measured data, yj, given the noise-free data, yi. 

In most rectification problems, information about the nature of the underlying noise-free variables is available, or can be determined from historical data. The Bayesian approach uses such prior information in the form of a probability distribution to improve the smoothness and accuracy of the 

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