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

Abstract

BackgroundRecent 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.ResultsIn 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.ConclusionsThis 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.

Multifractality nature of microtubule dynamic instability process

“…The maximum likelihood technique has been applied to estimate parameters for a linear dynamic system from the observed data. Many wavelet-based hidden Markov processes have been also involved to capture real-world non-Gaussian signals [14].…”

The long-run analysis of COVID-19 dynamic using random evolution, peak detection and time series

“…We have also performed a short-term time series analysis for a complete analysis of each phase of the pandemic (Menon et al. 2018 ), the short-term time series analysis although doesn’t add novelty by itself, but we use the existing literature and reproduce it to be able to compare it with the long-run analysis.…”

“…Similar to ( 3.1 ), the probabilities and switching frequencies can be defined as follows (Menon et al. 2018 ).

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“…There is a huge literature on the mathematical foundation (Bena 2006 ; Pinsky 1991 ; Pinsky and Karlin 2010 ; Kolesnik et al. 2011 ; Pinsky 1975 ) and the applications of the random evolution in science, engineering, biology and environmental phenomena (Bicout 1997 ; Menon and Yarahmadian 2008 ; Harandi et al. 2014 ; Menon and Yarahmadian 2019 , 2018 ).…”

Adaptive Cubature Kalman Filter Based on the Expectation-Maximization Algorithm

“…Fortunately, the expectationmaximization (EM) algorithm is a suitable method [24], [25]. By utilizing the EM algorithm to calculate unknown parameters, the derivation is simple, and the calculation is convenient [26]- [29]. However, we found that there is very limited research that employs the ML criterion and EM algorithm with the CKF to estimate unknown noise.…”