Optimal Acquisition and Analysis of Images for PALM and STORM

Abstract

Superresolution microscopy techniques like PALM and STORM enable fluorescence imaging subwavelength resolution. Fluorophores are switched on and off, with a sparse subset of the fluorophores emitting light at any given time. Consequently, the fluorophores form non-overlapping blurs in the image plane, enabling localization of molecules with subwavelength resolution limited only by noise in photon detection. We used a combination of theoretical, statistical, and computational techniques to determine the fundamental limits of performance. Using a kinetic model of fluorophore activation and bleaching, we are able to prove the existence of an optimal image acquisition scheme, that maximizes the number of single-molecule (i.e. no over-lapping blurs) within a given time constraint. In this scheme, the error rate (defined as the ratio of the number of multi-molecule overlap images to the number of images of single molecules) is constant. Interestingly, at fast acquisition speeds, the scheme is actually very robust: Deviations from the optimal scheme decrease the number of good images, but decrease the number of bad images (overlaps) to partially compensate. We also developed a formalism for benchmarking algorithms that correct errors by removing overlap images. Surprisingly, only a handful of performance parameters matter for image quality, opening up the possibility of designing fast error correction algorithms based on simple principles. Finally, to optimize the localization procedure, we have developed a rapid approximation to the Gaussian Mask technique for least squares fits. Our algorithm uses a simple expansion to significantly reduce the number of function evaluations used in fitting. The results are similar to those obtained when the Gaussian Mask algorithm is applied to an image that has undergone noise filtering. This suggests the possibility of doing very fast molecule localization on images represented in a basis where they are sparse.