We propose a new solver for the sparse spikes deconvolution problem over the space of Radon measures. A common approach to off-the-grid deconvolution considers semidefinite (SDP) relaxations of the total variation (the total mass of the absolute value of the measure) minimization problem. The direct resolution of this SDP is however intractable for large scale settings, since the problem size g...

Uniform confidence bands for densities f via nonparametric kernel estimates were first constructed by Bickel and Rosenblatt [Ann. Statist. 1, 1071–1095]. In this paper this is extended to confidence bands in the deconvolution problem g = f ∗ ψ for an ordinary smooth error density ψ. Under certain regularity conditions, we obtain asymptotic uniform confidence bands based on the asymptotic distri...

Whenever we use devices to take measurements, calibration is indispensable. While the purpose of calibration is to reduce bias and uncertainty in the measurements, it can be quite difficult, expensive and sometimes even impossible to implement. We study a challenging problem called self-calibration, i.e., the task of designing an algorithm for devices so that the algorithm is able to perform ca...

BACKGROUND Quantitative assessment of myocardial blood flow (MBF) from cardiovascular magnetic resonance (CMR) perfusion images appears to offer advantages over qualitative assessment. Currently however, clinical translation is lacking, at least in part due to considerable disparity in quantification methodology. The aim of this study was to evaluate the effect of common methodological differen...

Methods of three-dimensional deconvolution with a point-spread function as frequently employed in optical microscopy to reconstruct true three-dimensional distribution of objects are extended to holographic reconstructions. Two such schemes have been developed and are discussed: an instant deconvolution using the Wiener filter as well as an iterative deconvolution routine. The instant 3d-deconv...

We derive the asymptotic distribution of the supremum distance of the deconvolution kernel density estimator to its expectation for certain supersmooth deconvolution problems. It turns out that the asymptotics are essentially different from the corresponding results for ordinary smooth deconvolution.

Introduction: Prior studies comparing Hemodynamic Response Function (HRF) in the young and elderly adults based on fMRI data have reported inconsistent findings for brain vision and motor regions in healthy aging. It is shown that the averaging method employed in all previous works has caused this inconsistency. The averaging is so sensitive to outliers and noise. However, fMRI data are o...

where A is a matrix and x, b are vectors and n is the realization of random noise. We analyze the solution x̂ = A−1b which is completely dominated by noise. A useful solution can only be obtained by using additional information about the true solution x∗. The resulting solution x̂ is called the regularized solution of the inverse problem. Two popular regularization techniques, Tikhonovand total v...

The desire to recover the unknown density when data are contaminated with errors leads to nonparametric deconvolution problems. Optimal global rates of convergence are found under the weighted Lp-loss (1 $ p $ 00). It appears that the optimal rates of convergence are extremely slow for supersmooth error distributions. To overcome the difficulty, we examine how large the noise level can be for d...