Generalized recovery algorithm for 3D super-resolution microscopy using rotating point spread functions

Abstract

Super-resolution microscopy with phase masks is a promising technique for 3D imaging and tracking. Due to the complexity of the resultant point spread functions, generalized recovery algorithms are still missing. We introduce a 3D super-resolution recovery algorithm that works for a variety of phase masks generating 3D point spread functions. A fast deconvolution process generates initial guesses, which are further refined by least squares fitting. Overfitting is suppressed using a machine learning determined threshold. Preliminary results on experimental data show that our algorithm can be used to super-localize 3D adsorption events within a porous polymer film and is useful for evaluating potential phase masks. Finally, we demonstrate that parallel computation on graphics processing units can reduce the processing time required for 3D recovery. Simulations reveal that, through desktop parallelization, the ultimate limit of real-time processing is possible. Our program is the first open source recovery program for generalized 3D recovery using rotating point spread functions.

Breaking the Axial Diffraction Limit: A Guide to Axial Super‐Resolution Fluorescence Microscopy

“…Although the imaging performance of these localization‐based axial SRFM methods is affected by many experimental factors, such as the marker labeling density, detector noise, optical system aberrations, refractive index mismatch, photon efficiency, and field‐dependent aberrations, it is possible to design the optimal PSF with few localization errors by considering the PSF as individual designing parameter, and analyzing and balancing the interactions among the pupil function, ambiguity function, Fisher information, CRLB, and the relevant experimental parameters mentioned above . Benefiting from the development of 3D localization‐based super‐resolution reconstruction algorithms, these PSF engineering techniques have become a powerful research tool for many challenging topics, being used for velocity measurement, dipole orientation analysis, spectral traits tracking, etc. More recently, Gustavsson et al.…”

3D super-resolution imaging using a generalized and scalable progressive refinement method on sparse recovery (PRIS)

“…For example: Assuming an input image patch of 64-by-64 pixels, with a cubic volume of 6.4×6.4×1 m 3 represented by close-packed voxels of size 16 3 nm 3 , the RAM requirement for the sensing matrix A with single float precision is approximately 152.6 Gigabytes. We note here that setting up the problem with Fourier transforms [7] can significantly reduce the RAM requirement, but relies on the convolution assumption that we explicitly would like to avoid as discussed in the previous section.…”

“…Junghong et al introduced sparse recovery followed by refinement of localizations (FALCON 3D ) and demonstrated its utility for an astigmatic/biplane imaging system [6]. Shuang et al developed a similar approach with open source software package that was validated on various 3D PSFs [7]. *xiyu.yi@gmail.com; + sweiss@chem.ucla.edu…”

“…However, such integrations are challenging in 3D under high-density conditions using the existing framework of open source implementation [7]. This is because the algorithm solves a sub-problem in the Fourier space, which indeed significantly reduces the computation cost, but causes the method to rely on the convolution assumption that requires the PSF to be translational invariant, therefore, without the ability to account for optical aberrations.…”

“…The high spatial resolution relies on the adequate accumulation of precise localizations of bright fluorophores, which requires the bright fluorophores to possess a relatively low spatial density. Several methods have demonstrated localization at higher densities in both two dimensions (2D) [3,4] and three dimensions (3D) [5][6][7]. Additionally, with further advancements, such as functional super-resolution [8,9] and point spread function (PSF) engineering with [8][9][10][11] or without [12] multi-channel observations, extra information (spectra, dipole orientation) can be encoded and recovered at the single molecule level.…”