Phase retrieval from low-rate samples

The paper considers the phase retrieval problem in N-dimensional complex vector spaces. It provides two sets of deterministic measurement vectors which guarantee signal recovery for all signals, excluding only a specific subspace and a union of subspaces, respectively. A stable analytic reconstruction procedure of low complexity is given. Additionally it is proven that signal recovery from these measurements can be solved exactly via a semidefinite program. A practical implementation with 4 deterministic diffraction patterns is provided and some numerical experiments with noisy measurements complement the analytic approach.Comment: Preprint accepted for publication in Sampling Theory in Signal and Image Processing -- Special issue on SampTa 201

Visualization of Endothelial Actin Cytoskeleton in the Mouse Retina

Angiogenesis requires coordinated changes in cell shape of endothelial cells (ECs), orchestrated by the actin cytoskeleton. The mechanisms that regulate this rearrangement in vivo are poorly understood - largely because of the difficulty to visualize filamentous actin (F-actin) structures with sufficient resolution. Here, we use transgenic mice expressing Lifeact-EGFP to visualize F-actin in ECs. We show that in the retina, Lifeact-EGFP expression is largely restricted to ECs allowing detailed visualization of F-actin in ECs in situ. Lifeact-EGFP labels actin associated with cell-cell junctions, apical and basal membranes and highlights actin-based structures such as filopodia and stress fiber-like cytoplasmic bundles. We also show that in the skin and the skeletal muscle, Lifeact-EGFP is highly expressed in vascular mural cells (vMCs), enabling vMC imaging. In summary, our results indicate that the Lifeact-EGFP transgenic mouse in combination with the postnatal retinal angiogenic model constitutes an excellent system for vascular cell biology research. Our approach is ideally suited to address structural and mechanistic details of angiogenic processes, such as endothelial tip cell migration and fusion, EC polarization or lumen formation