Digital deconvolution filter derived from linear discriminant analysis and application for multiphoton fluorescence microscopy.

A digital filter derived from linear discriminant analysis (LDA) is developed for recovering impulse responses in photon counting from a high speed photodetector (rise time of ~1 ns) and applied to remove ringing distortions from impedance mismatch in multiphoton fluorescence microscopy. Training of the digital filter was achieved by defining temporally coincident and noncoincident transients and identifying the projection within filter-space that best separated the two classes. Once trained, data analysis by digital filtering can be performed quickly. Assessment of the reliability of the approach was performed through comparisons of simulated voltage transients, in which the ground truth results were known a priori. The LDA filter was also found to recover deconvolved impulses for single photon counting from highly distorted ringing waveforms from an impedance mismatched photomultiplier tube. The LDA filter was successful in removing these ringing distortions from two-photon excited fluorescence micrographs and through data simulations was found to extend the dynamic range of photon counting by approximately 3 orders of magnitude through minimization of detector paralysis.