795 citations · 1.3k across the 32 of their papers we have counts for
8 papers · 1 filter
On the absence of the RIP in real-world applications of compressed sensing and the RIP in levels
Alexander Bastounis, Anders C. Hansen
The purpose of this paper is twofold. The first is to point out that the Restricted Isometry Property (RIP) does not hold in many applications where compressed sensing is successfu…
Density theorems for nonuniform sampling of bandlimited functions using derivatives or bunched measurements
Ben Adcock, Milana Gataric, Anders C. Hansen
We provide sufficient density condition for a set of nonuniform samples to give rise to a set of sampling for multivariate bandlimited functions when the measurements consist of po…
Recovering piecewise smooth functions from nonuniform Fourier measurements
Ben Adcock, Milana Gataric, Anders C. Hansen
In this paper, we consider the problem of reconstructing piecewise smooth functions to high accuracy from nonuniform samples of their Fourier transform. We use the framework of non…
On asymptotic structure in compressed sensing
Bogdan Roman, Anders Hansen, Ben Adcock
This paper demonstrates how new principles of compressed sensing, namely asymptotic incoherence, asymptotic sparsity and multilevel sampling, can be utilised to better understand u…
Weighted frames of exponentials and stable recovery of multidimensional functions from nonuniform Fourier samples
Ben Adcock, Milana Gataric, Anders C. Hansen
In this paper, we consider the problem of recovering a compactly supported multivariate function from a collection of pointwise samples of its Fourier transform taken nonuniformly.…
The quest for optimal sampling: Computationally efficient, structure-exploiting measurements for compressed sensing
Ben Adcock, Anders C. Hansen, Bogdan Roman
An intriguing phenomenon in many instances of compressed sensing is that the reconstruction quality is governed not just by the overall sparsity of the signal, but also on its stru…
Linear Stable Sampling Rate: Optimality of 2D Wavelet Reconstructions from Fourier Measurements
Ben Adcock, Anders C. Hansen, Gitta Kutyniok +1
In this paper we analyze two-dimensional wavelet reconstructions from Fourier samples within the framework of generalized sampling. For this, we consider both separable compactly-s…
A note on compressed sensing of structured sparse wavelet coefficients from subsampled Fourier measurements
Ben Adcock, Anders C. Hansen, Bogdan Roman
This note complements the paper "The quest for optimal sampling: Computationally efficient, structure-exploiting measurements for compressed sensing" [2]. Its purpose is to present…