Multi-target localization algorithm for super-resolution microscopy

Abstract

Super resolution microscopy has been developed to image biological samples at the nanometer scale. In order to overcome the conventional spatial resolution limit, which is fundamentally restricted by light diffraction, super-resolution techniques rely on several mechanisms of non-linear optical phenomena. For example, localization based approach such as STORM and (F)PALM, which is one of the well-known super resolution microscopy techniques, can achieve super resolution by controlling the activation events of fluorescent probes. Specifically, the fluorescent probes are intermittently activated, so that their emissions are separated in time and space. Accordingly, the individual positions of the probes can be precisely localized. By repeating this localization process, a super resolution image can be generated. This conventional imaging scheme, however, requires a long data acquisition time, resulting in slow temporal resolution. Therefore, these super-resolution techniques are limited when it comes to investigating live-cell dynamics. This problem can be resolved by using a high density imaging scheme, which literally acquires data at an increased level of molecule activation. As a result, the same number of localizations can be processed from fewer measurements, allowing faster super-resolution imaging. In practice, in this high-density scenario, an advanced localization algorithm is needed which can resolve closely spaced molecules. Moreover, a high-density imaging scheme raises several additional issues, such as point spread function (PSF) estimation, background estimation and 3-dimensional (3D) imaging. In this thesis, I address these high-density imaging problems in two different spaces, using an image domain based approach, and a Fourier domain based approach. First, in the image based framework, I present a new continuous localization formulation by using a sparsity-promoting prior with Taylor series approximation of the PSF. The new localization formulation is computationally efficient, and allows multiple source localizations on a continuous domain. Furthermore, I extend this algorithm to 3D live cell imaging by employing a new hybrid imaging system. The hybrid system is implemented by combining astigmatic and biplane imaging, resulting in better conditions for multiple-source localization. On the other branch, with the Fourier-domain based localization, I propose a truly grid-free localization algorithm with data-driven PSF estimation. Specifically, based on the observation that the sparsity in the spatial domain implies low-ranking in the Fourier domain, the proposed method converts the PSF estimation as well as the source localization problems to Fourier domain signal processing problems, so that a truly grid-free localization is possible, with a spatially adaptive PSF estimation.