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Single molecule localization microscopy (SMLM) techniques enable imaging biological samples well beyond the diffraction limit of light, but they vary significantly in their spatial and temporal resolutions. High-order statistical analysis…
We present a systematic investigation of particle number fluctuations in the crossover region near the critical endpoint of a first-order phase transition using molecular dynamics simulations of the classical Lennard-Jones fluid. We extend…
In the recent years, multi-core processor designs have found their way into many computing devices. To exploit the capabilities of such devices in the best possible way, signal processing algorithms have to be adapted to an operation in…
By switching fluorophores on and off in either a deterministic or a stochastic manner, superresolution microscopy has enabled the imaging of biological structures at resolutions well beyond the diffraction limit. Superresolution optical…
Spatially resolving two incoherent point sources whose separation is well below the diffraction limit dictated by classical optics has recently been shown possible using techniques that decompose the incoming radiation into orthogonal…
Fluorescence microscopy is indispensable in nanoscience and biological sciences. The versatility of labeling target structures with fluorescent dyes permits to visualize structure and function at a subcellular resolution with a wide field…
We address the problem of clustering a set of points in $\mathbb{R}^d$ with axis-parallel clusters. Previous exact approaches to this problem are mostly based on integer programming formulations and can only solve to optimality instances of…
Spatial-mode projective measurements could achieve super-resolution in remote sensing and imaging, yet their performance is usually sensitive to the parameters of the target scenes. We propose and demonstrate a robust classifier of close-by…
I present two new methods for exactly summing a set of floating-point numbers, and then correctly rounding to the nearest floating-point number. Higher accuracy than simple summation (rounding after each addition) is important in many…
We consider the numerical optimization of performance for a computational extension of a confocal microscope. Using a system where the pinhole detector is replaced with a detector array, we seek to exploit this additional information for…
Monolayer semiconductors hold great potential for nanoscale electronics, optoelectronics, and photonics. Excitons dominate their optical properties. As their electric fields extend outside the monolayer, they are sensitive to their…
This paper focuses on regularisation methods using models up to the third order to search for up to second-order critical points of a finite-sum minimisation problem. The variant presented belongs to the framework of [3]: it employs random…
While sensing in high temporal resolution is necessary for wide range of application, it is still limited nowadays due to cameras sampling rate. In this work we try to increase the temporal resolution beyond the Nyquist frequency, which is…
The Floater--Hormann family of rational interpolants do not have spurious poles or unattainable points, are efficient to calculate, and have arbitrarily high approximation orders. One concern when using them is that the amplification of…
We propose a criterion to classify and compare sources of single photons: the $p$-norm of their $k$th-order photon correlations. While ideally one should use the uniform norm with $p\rightarrow\infty$, in practice, the 3-norm already allows…
Corrector estimates constitute a key ingredient in the derivation of optimal convergence rates via two-scale expansion techniques in homogenization theory of random uniformly elliptic equations. The present work follows up - in terms of…
This paper considers the problem of lossy compression for the computation of a function of two correlated sources, both of which are observed at the encoder. Due to presence of observation costs, the encoder is allowed to observe only…
In this article, we provide an alternative up-sampling and PSF deconvolution method for the iterative multi-exposure coaddition. Different from the previous works, the new method has a ratio-correction term, which allows the iterations to…
In a lens-assisted imaging scheme with speckle illumination, the spatial resolution can surpass the Rayleigh resolution limit by a factor of $\sqrt{2}$ with second-order auto-correlation of light intensity. In this work, integrated with the…
We consider simultaneously identifying the membership and locations of point sources that are convolved with different low-pass point spread functions, from the observation of their superpositions. This problem arises in three-dimensional…