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Background  Recent research has found that abnormal functioning of Microtubules (MTs) could be linked to fatal diseases such as Alzheimer’s. Hence, there is an imminent need to understand the implications of MTs for disease- diagnosis. However, studies of cellular processes like MTs are often constrained by physical limitations of their data acquisition systems such as optical microscopes and are vulnerable to either destruction of the specimen or the probe. In addition, study of MTs is challenged with non-uniform sampling of the MT dynamic instability phenomenon relative to its time-lapse observation of the cellular processes. Thus, the above caveats limit the overall period of time that the MT data can be collected, thereby causing limited data availability scenario.    Results  In this work, two novel superresolution frameworks based on Expectation Maximization (EM) based Maximum Likelihood (ML) estimation using Kalman filters (MLK) technique are proposed to address the issues of non-uniform sampling and limited data availability of MT signals. The proposed MLK methods optimizes prediction of missing observations in the MT signal through information extraction using correlation-based patch processing and principal component analysis -based mutual information. Experimental results prove that the proposed MLK-based superresolution methods outperformed nonlinear interpolation and compressed sensing methods.    Conclusions  This work aims to address limited data availability and data/observation loss incurred due to non-uniform sampling of biological signals such as MTs. For this purpose, statistical modelling of stochastic MT signals using EM based ML driven Kalman estimation (MLK) is considered as a fundamental framework for prediction of missing MT observations. It was experimentally validated that the proposed superresolution methods provided superior overall performance, better MT signal estimation using fewer samples, high SNR, low errors, and better MT parameter estimation than other methods.

Novel EM based ML Kalman estimation framework for superresolution of stochastic three-states microtubule signal