Anders C. Hansen

Publication Activity (10 Years)

Years Active: 2010-2023
Publications (10 Years): 17

Top Topics

Compressed Sensing

Fourier Coefficients

Computationally Efficient

Top Venues

SIAM J. Imaging Sci.

IEEE Trans. Inf. Theory

IEEE Signal Process. Lett.

Publications

Alexander Bastounis, Felipe Cucker, Anders C. Hansen
When can you trust feature selection? - I: A condition-based analysis of LASSO and generalised hardness of approximation. CoRR (2023)
Johan S. Wind, Vegard Antun, Anders C. Hansen
Implicit regularization in AI meets generalized hardness of approximation in optimization - Sharp results for diagonal linear networks. CoRR (2023)
Alexander Bastounis, Alexander N. Gorban, Anders C. Hansen, Desmond J. Higham, Danil V. Prokhorov, Oliver J. Sutton, Ivan Yu. Tyukin, Qinghua Zhou
The Boundaries of Verifiable Accuracy, Robustness, and Generalisation in Deep Learning. CoRR (2023)
Theresa Loss, Matthew J. Colbrook, Anders C. Hansen
Stratified Sampling Based Compressed Sensing for Structured Signals. IEEE Trans. Signal Process. 70 (2022)
Vegard Antun, Matthew J. Colbrook, Anders C. Hansen
Can stable and accurate neural networks be computed? - On the barriers of deep learning and Smale's 18th problem. CoRR (2021)
Alexander Bastounis, Anders C. Hansen, Verner Vlacic
The mathematics of adversarial attacks in AI - Why deep learning is unstable despite the existence of stable neural networks. CoRR (2021)
Matthew J. Colbrook, Anders C. Hansen
On the infinite-dimensional QR algorithm. CoRR (2020)
Nina M. Gottschling, Vegard Antun, Ben Adcock, Anders C. Hansen
The troublesome kernel: why deep learning for inverse problems is typically unstable. CoRR (2020)
Laura Thesing, Vegard Antun, Anders C. Hansen
What do AI algorithms actually learn? - On false structures in deep learning. CoRR (2019)
Matthew J. Colbrook, Anders C. Hansen
On the infinite-dimensional QR algorithm. Numerische Mathematik 143 (1) (2019)
Ben Adcock, Vegard Antun, Anders C. Hansen
Uniform recovery in infinite-dimensional compressed sensing and applications to structured binary sampling. CoRR (2019)
Vegard Antun, Francesco Renna, Clarice Poon, Ben Adcock, Anders C. Hansen
On instabilities of deep learning in image reconstruction - Does AI come at a cost? CoRR (2019)
Alexander Bastounis, Anders C. Hansen
On the Absence of Uniform Recovery in Many Real-World Applications of Compressed Sensing and the Restricted Isometry Property and Nullspace Property in Levels. SIAM J. Imaging Sci. 10 (1) (2017)
Alexander Daniel Jones, Ben Adcock, Anders C. Hansen
On Asymptotic Incoherence and Its Implications for Compressed Sensing of Inverse Problems. IEEE Trans. Inf. Theory 62 (2) (2016)
Alexander Daniel Jones, Ben Adcock, Anders C. Hansen
Analyzing the structure of multidimensional compressed sensing problems through coherence. CoRR (2016)
Ben Adcock, Anders C. Hansen, Bogdan Roman
A Note on Compressed Sensing of Structured Sparse Wavelet Coefficients From Subsampled Fourier Measurements. IEEE Signal Process. Lett. 23 (5) (2016)
Ben Adcock, Anders C. Hansen
Generalized Sampling and Infinite-Dimensional Compressed Sensing. Found. Comput. Math. 16 (5) (2016)
Ben Adcock, Anders C. Hansen, Gitta Kutyniok, Jackie Ma
Linear Stable Sampling Rate: Optimality of 2D Wavelet Reconstructions from Fourier Measurements. SIAM J. Math. Anal. 47 (2) (2015)
Ben Adcock, Anders C. Hansen
Generalized sampling and the stable and accurate reconstruction of piecewise analytic functions from their Fourier coefficients. Math. Comput. 84 (291) (2015)
Jonathan Ben-Artzi, Anders C. Hansen, Olavi Nevanlinna, Markus Seidel
Can everything be computed? - On the Solvability Complexity Index and Towers of Algorithms. CoRR (2015)
Ben Adcock, Milana Gataric, Anders C. Hansen
On Stable Reconstructions from Nonuniform Fourier Measurements. SIAM J. Imaging Sci. 7 (3) (2014)
Alexander Daniel Jones, Ben Adcock, Anders C. Hansen
On Asymptotic Incoherence and its Implications for Compressed Sensing of Inverse Problems. CoRR (2014)
Alexander Bastounis, Anders C. Hansen
On the absence of the RIP in real-world applications of compressed sensing and the RIP in levels. CoRR (2014)
Bogdan Roman, Anders C. Hansen, Ben Adcock
On asymptotic structure in compressed sensing. CoRR (2014)
Ben Adcock, Anders C. Hansen, Bogdan Roman
The quest for optimal sampling: Computationally efficient, structure-exploiting measurements for compressed sensing. CoRR (2014)
Ben Adcock, Anders C. Hansen, Alexei Shadrin
A Stability Barrier for Reconstructions from Fourier Samples. SIAM J. Numer. Anal. 52 (1) (2014)
Ben Adcock, Anders C. Hansen, Bogdan Roman, Gerd Teschke
Generalized sampling: stable reconstructions, inverse problems and compressed sensing over the continuum. CoRR (2013)
Ben Adcock, Anders C. Hansen, Clarice Poon
Beyond Consistent Reconstructions: Optimality and Sharp Bounds for Generalized Sampling, and Application to the Uniform Resampling Problem. SIAM J. Math. Anal. 45 (5) (2013)
Ben Adcock, Anders C. Hansen, Clarice Poon
Beyond consistent reconstructions: optimality and sharp bounds for generalized sampling, and application to the uniform resampling problem CoRR (2013)
Ben Adcock, Anders C. Hansen, Clarice Poon, Bogdan Roman
Breaking the coherence barrier: asymptotic incoherence and asymptotic sparsity in compressed sensing CoRR (2013)
Ben Adcock, Anders C. Hansen, Clarice Poon
On optimal wavelet reconstructions from Fourier samples: linearity and universality of the stable sampling rate CoRR (2012)
Ben Adcock, Anders C. Hansen
A Generalized Sampling Theorem for Reconstructions in Arbitrary Bases CoRR (2010)