COL0RME: Super-resolution microscopy based on sparse blinking/fluctuating fluorophore localization and intensity estimation

Abstract

To overcome the physical barriers caused by light diffraction, super-resolution techniques are often applied in fluorescence microscopy. State-of-the-art approaches require specific and often demanding acquisition conditions to achieve adequate levels of both spatial and temporal resolution. Analyzing the stochastic fluctuations of the fluorescent molecules provides a solution to the aforementioned limitations, as sufficiently high spatio-temporal resolution for live-cell imaging can be achieved by using common microscopes and conventional fluorescent dyes. Based on this idea, we present COL0RME, a method for COvariance-based ℓ 0 super-Resolution Microscopy with intensity Estimation, which achieves good spatio-temporal resolution by solving a sparse optimization problem in the covariance domain and discuss automatic parameter selection strategies. The method is composed of two steps: the former where both the emitters' independence and the sparse distribution of the fluorescent molecules are exploited to provide an accurate localization; the latter where real intensity values are estimated given the computed support. The paper is furnished with several numerical results both on synthetic and real fluorescence microscopy images and several comparisons with state-of-the art approaches are provided. Our results show that COL0RME outperforms competing methods exploiting analogously temporal fluctuations; in particular, it achieves better localization, reduces background artifacts and avoids fine parameter tuning.

Fluorescence image deconvolution microscopy via generative adversarial learning (FluoGAN)

“…It is therefore not likely to contain high-frequency details, hence a smooth regularisation term, i.e. R 2 (b) = λ 2 2 ∇b 2 2 , λ 2 > 0 can be considered, see [30] for analogous choices.…”

Fluctuation-based deconvolution in fluorescence microscopy using plug-and-play denoisers

“…In this work, we leverage the framework of PnP approaches with convergence guarantees [3,13,14] to show good empirical performance on the inverse problem of fluctuation-based image deconvolution presented, e.g., in [25,27,29]. In Section 2, we review the recent advances in the field of PnP approaches for inverse problems, pointing out the convergent scheme we employ.…”

“…We consider the following image formation model considered, e.g., in [25,29,27] to describe, for t = 1, . .…”

“…We look for a deconvolved image x ∈ R n 2 , defined as x = 1 T T t=1 x t . In [25,27], a reformulation of the model (4) was done in the covariance domain in order to exploit temporal information. In the following, we proceed similarly but consider a simplified modeling where only auto-covariance vectors are taken into account, thus neglecting cross-terms.…”

“…Some of these approaches are: the Super-resolution Optical Fluctuation Imaging (SOFI) approach [5] where the lack of correlation between distinct emitters is exploited by analyzing high-order statistics, the Super-Resolution Radial Fluctuations (SRRF) [11] microscopy, where super-resolution is achieved by calculating at each frame the degree of local symmetry and, finally, the Sparsity-based Super-resolution Correlation Microscopy (SPARCOM) [25] which models the sparse distribution of the fluorescent molecules via the use of a convex 1 regularisation applied on the emitters' covariance matrix. To improve the performance of SPARCOM, the Covariancebased 0 super-resolution microscopy with intensity estimation (COL0RME) method [27,29] has been proposed to estimate both molecule positions and intensities, which is a valuable piece of information in several applications, such as, e.g., 3D imaging [28], by means of a two-step procedure relying on hand-crafted sparsity promoting regularisers. The approach further estimates noise statistics and background terms (containing out-of-focus molecules).…”