A multiscale approach to data rectification is proposed for data containing features with different time and frequency localization. Noisy data are decomposed into contributions at multiple scales and a Bayesian optimization problem is solved to rectify the wavelet coefficients at each scale. A linear dynamic model is used to constrain the optimization problem, which facilitates an error-in-variables (EIV) formulation and reconciles all measured variables. Time-scale recursive algorithms are obtained by propagating the prior with temporal and scale models. The multiscale Kalman filter is a special case of the proposed Bayesian EIV approach.