Abstract

Multiple signal classification algorithm (MUSICAL) exploits temporal fluctuations in fluorescence intensity to perform super-resolution microscopy by computing the value of a super-resolving indicator function across a fine sample grid. A key step in the algorithm is the separation of the measurements into signal and noise subspaces, based on a single user-specified parameter called the threshold. The resulting image is strongly sensitive to this parameter and the subjectivity arising from multiple practical factors makes it difficult to determine the right rule of selection. We address this issue by proposing soft thresholding schemes derived from a new generalized framework for indicator function design. We show that the new schemes significantly alleviate the subjectivity and sensitivity of hard thresholding while retaining the super-resolution ability. We also evaluate the trade-off between resolution and contrast and the out-of-focus light rejection using the various indicator functions. Through this, we create significant new insights into the use and further optimization of MUSICAL for a wide range of practical scenarios.

Highlights

  • Conventional optical microscopy is limited in resolution due to diffraction of light

  • A stack of images taken of such sample from a diffraction-limited system over T time-steps is expressed in a matrix form as A = [a(1) . . . a(T)], where each column vector a(t) contains the intensity measured by a set of sensing elements at time step t

  • Sn(t) is the number of photons produced by the nth emitter during the time step t, which is a random variable resulting from the photokinetics of the fluorophore

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Summary

Introduction

Conventional optical microscopy is limited in resolution due to diffraction of light. The need to overcome this limit has given rise to super-resolution microscopy techniques, called optical nanoscopy Among these techniques, structured illumination microscopy (SIM) [1] allows a lateral resolution enhancement by a factor of 2 over the optical resolution limit, stimulated emission depletion (STED) microscopy [2] and single molecule localization (SML) [3,4,5] can achieve resolutions close to 20 nm, and MINFLUX [6] which combines concepts of SML and STED to achieve even 2 nm resolution. Every single image is a linear combination of the columns of G, weighted by the photon emissions of emitters

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