On using Compressed Sensing and peak detection method for the Dynamic Instability parameters estimation for Microtubules modeled in three states

Recent studies has revealed that Microtubules (MTs) exhibit three transition states of growth, shrinkage and pause states. In this paper, we use Trichotomous Markov Noise (TMN) as a framework for studying MTs dynamics in its three transition states. We then apply Compressed Sensing (CS) to the experimental data of MT length and apply peak detection in the wavelet domain to efficiently detect the three transition states of MTs. One of the novelties of our method is in detecting the peaks and encoding them simultaneously in the wavelet domain without having the need to do further processing after decoding stage. Experimental results show that using CS in conjunction with wavelets provides better compression and reconstruction performance comparing to the traditional sampling schemes. Dynamic Instability parameters of MTs are estimated and are shown to closely approximate original MT data for lower sampling rates.