Studies of biological processes such as Microtubules (MTs), often suffer from limited data availability due to physical constraints of the data acquisition process. Typically, the periodic collection of biological data using optical microscopes is prone to the dangers of overexposure and destruction of either specimen or probe, thereby limiting the data collected over a period of time. In addition, the data collected is often a sampled and approximated observation of the analog physical phenomena. Hence, to emulate the non-uniform sampling process that occurs during the physical data acquisition process, compressed sensing (CS) based sampling is used in an effort to reconstruct the MT signal from fewer samples than the Nyquist rate. We also introduce a novel wavelet estimation based N-states random evolution model to study the MT dynamic instability phenomenon. Experimental results demonstrate that our proposed method yielded superior overall performance, effective reconstruction and estimation of MT signal from fewer samples with low error rates. Even at lower sampling rates, the estimated MT transition parameters are shown to closely approximate the original MT signal.
