Superresolution and EM based ML Kalman Estimation of the Stochastic Microtubule Signal Modeled as Three States Random Evolution

Data collection of cellular processes (such as Microtubules (MTs) Dynamic Instability) using optical microscopes, are often threatened by either destruction of the specimen or the probe; thereby limiting the extensive period of time that the data can be collected. This leads to scarcity of data. Due to this, we encounter non-uniform sampling of the MT dynamic instability phenomenon relative to the time-lapse observation of the cellular processes. In this paper, we present a novel super-resolution technique to address both non-uniform sampling and limited data availability of MT signals. We use Expectation Maximization (EM) based Maximum Likelihood (ML) estimation using Kalman filters on the interpolated (from non-uniformly sampled) MT signals to optimize prediction of the missing observations in the data. This is followed by correlation-patch based post processing to further refine our predictions. The three-state dynamic instability MT parameters are estimated using wavelet-based peak detection. Experimental results show that our prediction method had superior performance, high SNR and low errors compared to interpolation-only and compressed sensing methods.