Modified K-factor image decomposition for three-dimensional super resolution microscopy

The ability to track single fluorescent particles within a three dimensional (3D) cellular environment can provide valuable insights into cellular processes. In this paper, we present a modified nonlinear image decomposition technique called K-factor that reshapes the 3D point spread function (PSF) of an XYZ image stack into a narrow Gaussian profile. The method increases localization accuracy by ~60% with compare to regular Gaussian fitting, and improves minimal resolvable distance between overlapping PSFs by ~50%. The algorithm was tested both on simulated data and experimentally. This work presets a novel use of the nonlinear image decomposition technique called K-factor that reshapes the three dimensional (3D) point spread function (PSF) of an XYZ image stack into a narrow Gaussian profile. The experimentally obtained PSF of a Z-stack raw data that is acquired by a widefield microscope has a more elaborate shape that is given by the Gibson and Lanni model. This shape increases the computational complexity associated with the localization routine, when used in localization microscopy techniques. Furthermore, due to its nature, this PSF spreads over a larger volume, making the problem of overlapping emitters detection more pronounced. The ability to use Gaussian fitting with high accuracy on 3D data can facilitate the computational complexity, hence reduce the processing time required for the generation of the 3D superresolved image. In addition it allows the detection of overlapping PSFs and reduces the effects of the penetration of out of focus PSFs into in focused PSFs, therefore enables the increase in the activated fluorophore density by ~50%. The algorithm was tested both on simulated data and experimentally, where it yielded an increase in the localization accuracy by ~60% with compare to regular Gaussian fitting, and improved the minimal resolvable distance between overlapping PSFs by ~50%, making it extremely applicable to the field of 3D biomedical imaging,

[1]  S. Gibson,et al.  Experimental test of an analytical model of aberration in an oil-immersion objective lens used in three-dimensional light microscopy. , 1992, Journal of the Optical Society of America. A, Optics and image science.

[2]  J. Zerubia,et al.  Gaussian approximations of fluorescence microscope point-spread function models. , 2007, Applied optics.

[3]  X. Zhuang,et al.  Statistical deconvolution for superresolution fluorescence microscopy. , 2012, Biophysical journal.

[4]  Zeev Zalevsky,et al.  Improved Localization Accuracy in Stochastic Super-resolution Fluorescence Microscopy by K- Factor Image Deshadowing References and Links , 2022 .

[5]  Jerry Chao,et al.  Quantitative study of single molecule location estimation techniques. , 2009, Optics express.

[6]  Jaime R. Taylor,et al.  K-factor image factorization , 1999, Defense, Security, and Sensing.

[7]  J. Lippincott-Schwartz,et al.  Imaging Intracellular Fluorescent Proteins at Nanometer Resolution , 2006, Science.

[8]  S. Ram,et al.  Localization accuracy in single-molecule microscopy. , 2004, Biophysical journal.

[9]  Jerry Chao,et al.  A 3D resolution measure for optical microscopy , 2009, 2009 IEEE International Symposium on Biomedical Imaging: From Nano to Macro.

[10]  R. Sec..  XV. On the theory of optical images, with special reference to the microscope , 2009 .

[11]  Michael J Rust,et al.  Sub-diffraction-limit imaging by stochastic optical reconstruction microscopy (STORM) , 2006, Nature Methods.

[12]  P. Stokseth.  Properties of a Defocused Optical System , 1969 .

[13]  Jaime R. Taylor,et al.  Image factorization: a new hierarchical decomposition technique , 1999 .

[14]  Wilfrid Taylor Dempster,et al.  Principles of Microscope Illumination and the Problem of Glare , 1944 .

[15]  Keith A. Lidke,et al.  Simultaneous multiple-emitter fitting for single molecule super-resolution imaging , 2011, Biomedical optics express.

[16]  Mark Bates,et al.  Three-Dimensional Super-Resolution Imaging by Stochastic Optical Reconstruction Microscopy , 2008, Science.

[17]  Beiträge zur Theorie des Mikroskops und der mikroskopischen Wahrnehmung , 1873 .

[18]  N. Bobroff.  Position measurement with a resolution and noise‐limited instrument , 1986 .

[19]  L. Shepp,et al.  Maximum Likelihood Reconstruction for Emission Tomography , 1983, IEEE Transactions on Medical Imaging.

[20]  Michael D. Mason,et al.  Ultra-high resolution imaging by fluorescence photoactivation localization microscopy. , 2006, Biophysical journal.

[21]  Ricardo Henriques,et al.  PALM and STORM: Unlocking live‐cell super‐resolution , 2011, Biopolymers.

[22]  R. Juškaitis.  Measuring the Real Point Spread Function of High Numerical Aperture Microscope Objective Lenses , 2006 .

[23]  J. Lippincott-Schwartz,et al.  Interferometric fluorescent super-resolution microscopy resolves 3D cellular ultrastructure , 2009, Proceedings of the National Academy of Sciences.

[24]  J. Lichtman,et al.  Optical sectioning microscopy , 2005, Nature Methods.

[25]  S. Hess,et al.  Three-dimensional sub–100 nm resolution fluorescence microscopy of thick samples , 2008, Nature Methods.

[26]  S. Ram,et al.  Simultaneous imaging of different focal planes in fluorescence microscopy for the study of cellular dynamics in three dimensions , 2004, IEEE Transactions on NanoBioscience.

[27]  M Unser,et al.  3‐D PSF fitting for fluorescence microscopy: implementation and localization application , 2013, Journal of microscopy.