Improved resolution of complex single-molecule FRET systems via wavelet shrinkage

The resolution of complex interactions found in single-molecule fluorescence resonance energy transfer (smFRET) experiments is hindered by noise. Wavelet shrinkage is proven to reduce noise, but traditional methods introduce artifacts when acting on discontinuous signals, such as those acquired in smFRET experiments. Modifications to the basic method that are specific to smFRET are developed and tested on simulated systems. Use of the Haar wavelet basis produces the most optimally denoised estimates. We also assess various thresholding methods, develop a time-localized noise estimator, and implement a translation-invariant wavelet transformation to reduce artifacts associated with discontinuities and inadequate distinction of noise. The time-local estimator enhances noise reduction by 5-20%, and translation-invariant transformation nearly eliminates the aforementioned artifacts. Kinetic parameters extracted from denoised estimates are accurate to within 5% of the simulated values. Overall, the improved resolution results in the complete and accurate characterization of both simple and complex smFRET systems.