795 citations · 1.3k across the 32 of their papers we have counts for
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Compressed Sensing MRI With Variable Density Averaging (CS-VDA) Outperforms Full Sampling At Low SNR
Jasper Schoormans, Gustav J. Strijkers, Anders C. Hansen +2
We investigated whether a combination of k-space undersampling and variable density averaging enhances image quality for low-SNR MRI acquisitions. We implemented 3D Cartesian k-spa…
Non-uniform recovery guarantees for binary measurements and infinite-dimensional compressed sensing
Laura Thesing, Anders Christian Hansen
Due to the many applications in Magnetic Resonance Imaging (MRI), Nuclear Magnetic Resonance (NMR), radio interferometry, helium atom scattering etc., the theory of compressed sens…
The foundations of spectral computations via the Solvability Complexity Index hierarchy
Matthew J. Colbrook, Anders C. Hansen
The problem of computing spectra of operators is arguably one of the most investigated areas of computational mathematics. However, the problem of computing spectra of general boun…
On the stable sampling rate for binary measurements and wavelet reconstruction
Anders Christian Hansen, Laura Thesing
This paper is concerned with the problem of reconstructing an infinite-dimensional signal from a limited number of linear measurements. In particular, we show that for binary measu…
Linear reconstructions and the analysis of the stable sampling rate
Laura Thesing, Anders Christian Hansen
The theory of sampling and the reconstruction of data has a wide range of applications and a rich collection of techniques. For many methods a core problem is the estimation of the…
What do AI algorithms actually learn? - On false structures in deep learning
Laura Thesing, Vegard Antun, Anders C. Hansen
There are two big unsolved mathematical questions in artificial intelligence (AI): (1) Why is deep learning so successful in classification problems and (2) why are neural nets bas…
Uniform recovery in infinite-dimensional compressed sensing and applications to structured binary sampling
Ben Adcock, Vegard Antun, Anders C. Hansen
Infinite-dimensional compressed sensing deals with the recovery of analog signals (functions) from linear measurements, often in the form of integral transforms such as the Fourier…
On instabilities of deep learning in image reconstruction - Does AI come at a cost?
Vegard Antun, Francesco Renna, Clarice Poon +2
Deep learning, due to its unprecedented success in tasks such as image classification, has emerged as a new tool in image reconstruction with potential to change the field. In this…