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For the information content of microscopy images to be appropriately interpreted, reproduced, and meet FAIR (Findable Accessible Interoperable and Reusable) principles, they should be accompanied by detailed descriptions of microscope hardware, image acquisition settings, image pixel and dimensional structure, and instrument performance. Nonetheless, the thorough documentation of imaging experiments is significantly impaired by the lack of community-sanctioned easy-to-use software tools to facilitate the extraction and collection of relevant microscopy metadata. Here we presentMicro-Meta App, an intuitive open-source software designed to tackle these issues that was developed in the context of nascent global bioimaging community organizations, includingBioImagingNorthAmerica (BINA) andQUAlity Assessment andREProducibility inLightMicroscopy (QUAREP-LiMi), whose goal is to improve reproducibility, data quality and sharing value for imaging experiments. The App provides a user-friendly interface for building comprehensive descriptions of the conditions utilized to produce individual microscopy datasets as specified by the recently proposed 4DN-BINA-OME tiered-system of Microscopy Metadata model. To achieve this goal the App provides a visual guide for a microscope-user to: 1) interactively build diagrammatic representations of hardware configurations of given microscopes that can be easily reused and shared with colleagues needing to document similar instruments. 2) Automatically extracts relevant metadata from image files and facilitates the collection of missing image acquisition settings and calibration metrics associated with a given experiment. 3) Output all collected Microscopy Metadata to interoperable files that can be used for documenting imaging experiments and shared with the community. In addition to significantly lowering the burden of quality assurance, the visual nature of Micro-Meta App makes it particularly suited for training users that have limited knowledge of the intricacies of light microscopy experiments. To ensure wide-adoption by microscope-users with different needs Micro-Meta App closely interoperates withMethodsJ2andOMERO.mde, two complementary tools described in parallel manuscripts.

Prony's method is a prototypical eigenvalue analysis based method for the reconstruction of a finitely supported complex measure on the unit circle from its moments up to a certain degree. In this note, we give a generalization of this method to the multivariate case and prove simple conditions under which the problem admits a unique solution. Provided the order of the moments is bounded from below by the number of points on which the measure is supported as well as by a small constant divided by the separation distance of these points, stable reconstruction is guaranteed. In its simplest form, the reconstruction method consists of setting up a certain multilevel Toeplitz matrix of the moments, compute a basis of its kernel, and compute by some method of choice the set of common roots of the multivariate polynomials whose coefficients are given in the second step. All theoretical results are illustrated by numerical experiments.

A straightforward discretisation of high-dimensional problems often leads to a curse of dimensions and thus the use of sparsity has become a popular tool. Efficient algorithms like the fast Fourier transform (FFT) have to be customised to these thinner discretisations and we focus on two major topics regarding the Fourier analysis of high-dimensional functions: We present stable and effective algorithms for the fast evaluation and reconstruction of multivariate trigonometric polynomials with frequencies supported on an index set.I&sub