42 research outputs found
Iterative Discretization of Optimization Problems Related to Superresolution
International audienceWe study an iterative discretization algorithm for solving optimization problems regularized by the total variation norm over the space M(Ω) of Radon measures on a bounded subset Ω of R d. Our main motivation to study this problem is the recovery of sparse atomic measures from linear measurements. Under reasonable regularity conditions, we arrive at a linear convergence rate guarantee
DeepSTORM3D: dense three dimensional localization microscopy and point spread function design by deep learning
Localization microscopy is an imaging technique in which the positions of
individual nanoscale point emitters (e.g. fluorescent molecules) are determined
at high precision from their images. This is the key ingredient in
single/multiple-particle-tracking and several super-resolution microscopy
approaches. Localization in three-dimensions (3D) can be performed by modifying
the image that a point-source creates on the camera, namely, the point-spread
function (PSF). The PSF is engineered using additional optical elements to vary
distinctively with the depth of the point-source. However, localizing multiple
adjacent emitters in 3D poses a significant algorithmic challenge, due to the
lateral overlap of their PSFs. Here, we train a neural network to receive an
image containing densely overlapping PSFs of multiple emitters over a large
axial range and output a list of their 3D positions. Furthermore, we then use
the network to design the optimal PSF for the multi-emitter case. We
demonstrate our approach numerically as well as experimentally by 3D STORM
imaging of mitochondria, and volumetric imaging of dozens of
fluorescently-labeled telomeres occupying a mammalian nucleus in a single
snapshot.Comment: main text: 9 pages, 5 figures, supplementary information: 29 pages,
20 figure
Atomic super-resolution tomography
We consider the problem of reconstructing a nanocrystal at atomic resolution from electron microscopy images taken at a few tilt angles. A popular reconstruction approach called discrete tomography confines the atom locations to a coarse spatial grid, which is inspired by the physical a priori knowledge that atoms in a crystalline solid tend to form regular lattices. Although this constraint has proven to be powerful for solving this very under-determined inverse problem in many cases, its key limitation is that, in practice, defects may occur that cause atoms to deviate from regular lattice positions. Here we propose a grid-free discrete tomography algorithm that allows for continuous deviations of the atom locations similar to super-resolution approaches for microscopy. The new formulation allows us to define atomic interaction potentials explicitly, which results in a both meaningful and powerful incorporation of the available physical a priori knowledge about the crystal's properties. In computational experiments, we compare the proposed grid-free method to established grid-based approaches and show that our approach can indeed recover the atom positions more accurately for common lattice defects