Generalized Multiresolution Decomposition Frameworks for the Analysis of Industrial Data with Uncertainty and Missing Values

In this paper, we address the problem of extending the multiscale decomposition framework based upon the wavelet transform to situations where datasets contain any type of missing data patterns (e.g., random, multirate). Furthermore, the proposed approaches explicitly integrate data uncertainty information into their algorithms, to explore all knowledge available about data during the decomposition stage, as well as to enable its posterior use in subsequent data-analysis tasks. Beside their role in the multiscale decomposition of complex datasets, these frameworks, called generalized multiresolution decomposition frameworks (GMRD), also lead to new developments in data-analysis tools based upon the information they provide, namely, in the selection of relevant scales for data analysis and in the improvement of signal-denoising procedures. Guidelines are presented regarding their adequate use and how they can be combined into an integrated multiscale data analysis framework. The pertinence of the proposed GMRD frameworks is illustrated through several examples involving simulated, laboratory, and industrial datasets.