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— Many sources of information are of analog or continuous-time nature. However, digital signal processing applications rely on discrete data. We consider the problem of approximating L2 inner products, i.e., representation coefficients of a continuous-time signal, from its generalized samples. Taking a robust approach, we process these generalized samples… (More)

This paper is devoted to the characterization of an extended family of CARMA (continuous-time autoregressive moving average) processes that are solutions of stochastic differential equations driven by white Lévy innovations. These are completely specified by: (1) a set of poles and zeros that fixes their correlation structure, and (2) a canonical… (More)

A Sobolev reproducing-kernel Hilbert space approach to image interpolation is introduced. The underlying kernels are exponential functions and are related to stochastic autoregressive image modeling. The corresponding image interpolants can be implemented effectively using compactly-supported exponential B-splines. A tight l(2) upper-bound on the… (More)

—The problem of estimating continuous-domain au-toregressive moving-average processes from sampled data is considered. The proposed approach incorporates the sampling process into the problem formulation while introducing exponential models for both the continuous and the sampled processes. We derive an exact evaluation of the discrete-domain power-spectrum… (More)

— This paper is devoted to the characterization of an extended family of continuous-time autoregressive moving average (CARMA) processes that are solutions of stochastic differential equations driven by white Lévy innovations. These are completely specified by: 1) a set of poles and zeros that fixes their correlation structure and 2) a canonical infinitely… (More)

- Daniel Sage, Hagai Kirshner, Thomas Pengo, Nico Stuurman, Junhong Min, Suliana Manley +1 other
- Nature methods
- 2015

The quality of super-resolution images obtained by single-molecule localization microscopy (SMLM) depends largely on the software used to detect and accurately localize point sources. In this work, we focus on the computational aspects of super-resolution microscopy and present a comprehensive evaluation of localization software packages. Our philosophy is… (More)

—We consider the problem of sampling continuous time auto-regressive processes on a uniform grid. We investigate whether a given sampled process originates from a single continuous-time model, and address this uniqueness problem by introducing an alternative description of poles in the complex plane. We then utilize Kronecker's approximation theorem and… (More)

We introduce an ImageJ application that allows one to generate various 3D PSF models. Keeping the biological practitioner in mind, few input parameters are required only (Figure 1). Our application can generate z-stacks at any size and at any lateral and axial resolution. Our implementation utilizes a multi-thread design that allows for parallel and fast… (More)

- Junhong Min, Cédric Vonesch, Hagai Kirshner, Lina Carlini, Nicolas Olivier, Seamus Holden +3 others
- Scientific reports
- 2014

Super resolution microscopy such as STORM and (F)PALM is now a well known method for biological studies at the nanometer scale. However, conventional imaging schemes based on sparse activation of photo-switchable fluorescent probes have inherently slow temporal resolution which is a serious limitation when investigating live-cell dynamics. Here, we present… (More)