Novel Computational Methods for Three-dimensional Point Source Localization Based on Point Spread Function Analytics
- Hon Fu Raymond CHAN (Principal Investigator / Project Coordinator)Department of Mathematics
- Robert PLEMMONS (Co-Investigator)
- Sudhakar PRASAD (Co-Investigator)
- Chao WANG (Co-Investigator)
DescriptionSingle-molecule localization microscopy (SMLM) was awarded the 2014 Nobel Prize in Chemistry for bypassing the optical resolution limit of traditional microscopy. The main idea is to use laser to turn the fluorescence of individual molecules on and off. Then one can take the images of the same area multiple times with just a few interspersed molecules glowing each time. Superimposing these images, usually thousands of them, yields a dense super-resolution image resolved at the nanolevel. Many point source localization algorithms have since been developed for localizing the positions of the fluorescing molecules.A major difficulty of traditional microscopes is that they cannot determine the depth position of a point source because its image is roughly the same above or below the focal plane. Therefore, the traditional imaging techniques to obtain 3D information is to take 2D images slice by slice in the depth direction. For 3D SMLM, we will have to take thousands of images in each depth level and composing them all into a 3D image of the object of interest by image reconstruction techniques.One of the newer optical techniques to obtain 3D positions of points simultaneously is by using specially designed optical elements, e.g. rotating point spread function (rPSFs). These rPSFs encode the depth information of the point sources into one single 2D snapshot. The amount of rotation of the PSF in the snapshot gives the depth of the point source. The depth can then be recovered by image processing techniques. However, the inverse process of going from the 2D snapshot to the 3D positions of the point sources is a large scale and highly ill-posed problem. This project is to develop novel and efficient algorithms for getting the locations and the intensity of the point sources accurately. We will design optimization methods based on the sparsity information of the solution and also methods from deep neutral networks.The successful implementation of our algorithms will be profitable to a broad spectrum in science where 3D SMLM is used, such as cell imaging in biology, spectral diffusion in chemistry, and quantum optics in physics. We will also consider its application in locating and classifying debris in outer space. On the theoretical side, new techniques for image processing, optimization, convex analysis, and machine learning will arise through the study of our algorithms and their convergence analysis. A better understanding of these techniques will be beneficial to all fields concerned.
|Effective start/end date||1/01/21 → …|