The conformational changes that biological macro-molecules undergo play a crucial role in functionality. These changes are measurable at the single molecular level using a technique known as single molecule Förster resonance energy transfer (smFRET). By measuring conformational changes at the single molecule (SM) level, distributions of physical properties, such as dwell times of the stepping motion observed in molecular motors, can be statistically modelled and monitored over time. However, there are several sources of error that are introduced when recording smFRET data. The recorded data typically have a low signal-to-noise ratio (SNR) and the number of conformations and transitional rates need to be estimated from this noisy data. Common software packages are available to analyze smFRET data, estimating these parameters and have some success in applications to data where the power of the noise is much less than that of the underlying signal. As the SNR is lowered, these packages naturally produce less accurate parameter estimations. In this thesis, we investigate the denoising ability of the K-SVD algorithm, which computes the singular value decomposition (SVD) of transform coefficients to improve the reconstructive abilities of the atoms in a transform dictionary. A dictionary is learned through varying training data parameters until an optimal dictionary is produced. Simulated data is then approximated and analyzed after projecting the data to a sparse subspace determined by the learned dictionary. The approximations from the K-SVD allow accurate estimation of the number of conformations in the data and the respective smFRET efficiencies. The kinetic rate estimates are less reliable due to approximation errors.
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