arXiv subjects

Robert Dahl Jacobsen

Publications and source records attributed to Robert Dahl Jacobsen.

3 recordsLinked to original sources

arXiv2017

Investigations of the effects of random sampling patterns on the stability of generalized sampling

We investigate how the choice of spatial point process for generating random sampling patterns affects the numerical stability of non-uniform generalized sampling between Fourier bases and Daubechies scaling functions. Specifically, we consider binomial, Poisson and determinantal point processes and demonstrate that the more regular point patterns from the determinantal point process are superior.

stat.AP↗

arXiv2017

Frequentist and Bayesian inference for Gaussian-log-Gaussian wavelet trees, and statistical signal processing applications

We introduce new estimation methods for a sub-class of the Gaussian scale mixture models for wavelet trees by Wainwright, Simoncelli & Willsky that rely on modern results for composite likelihoods and approximate Bayesian inference. Our methodology is illustrated for denoising and edge detection problems in two-dimensional images.

math.ST↗

arXiv2016

Generalized Sampling in Julia

Generalized sampling is a numerically stable framework for obtaining reconstructions of signals in different bases and frames from their samples. In this paper, we will introduce a carefully documented toolbox for performing generalized sampling in Julia. Julia is a new language for technical computing with focus on performance, which is ideally suited to handle the large size problems often encountered in generalized sampling. The toolbox provides specialized solutions for the setup of Fourier bases and wavelets. The performance of the toolbox is compared to existing implementations of generalized sampling in MATLAB.

cs.MS↗