Grid-Free Localization Algorithm Using Low-rank Hankel Matrix for Super-Resolution Microscopy.

Area of Science:

• Biophysics
• Optical Microscopy
• Computational Biology

Background:

• Super-resolution microscopy techniques like STORM/PALM achieve nanometer resolution by localizing fluorescence molecules.
• Improving temporal resolution necessitates localizing densely activated molecules, posing challenges for existing algorithms.
• Current sparsity-driven methods often require fine sampling grids or approximations, leading to localization bias and requiring prior point-spread function (PSF) knowledge.

Purpose of the Study:

• To develop a true grid-free localization algorithm for super-resolution microscopy.
• To overcome the limitations of existing sparsity-driven methods, including localization bias and the need for prior PSF information.
• To enhance the accuracy and efficiency of localizing closely spaced molecules in high-density imaging.

Main Methods:

• A novel grid-free localization algorithm is proposed, leveraging the relationship between spatial sparsity and Fourier-domain low rank.
• The method transforms the source localization problem into Fourier-domain signal processing.
• Adaptive estimation of the point-spread function (PSF) is incorporated into the algorithm.

Main Results:

• The proposed algorithm enables truly grid-free localization, eliminating grid-induced bias.
• Adaptive PSF estimation is achieved without requiring prior knowledge.
• Numerical simulations and live-cell imaging experiments demonstrate the method's effectiveness.

Conclusions:

• The developed grid-free localization algorithm offers a significant advancement for super-resolution microscopy.
• This approach enhances the ability to resolve closely spaced molecules, crucial for high-density imaging.
• The method provides a more accurate and robust alternative to existing localization techniques.