A Generalized Sampling Theorem for Reconstructions in Arbitrary Bases - Ben Adcock; Anders C. Hansen (CoRR, 2010)

On optimal wavelet reconstructions from Fourier samples: linearity and universality of the stable sampling rate - Ben Adcock; Anders C. Hansen; Clarice Poon (CoRR, 2012)

Generalized sampling: stable reconstructions, inverse problems and compressed sensing over the continuum. - Ben Adcock; Anders C. Hansen; Bogdan Roman; Gerd Teschke (CoRR, 2013)

Breaking the coherence barrier: asymptotic incoherence and asymptotic sparsity in compressed sensing - Ben Adcock; Anders C. Hansen; Clarice Poon; Bogdan Roman (CoRR, 2013)

Beyond Consistent Reconstructions: Optimality and Sharp Bounds for Generalized Sampling, and Application to the Uniform Resampling Problem. - Ben Adcock; Anders C. Hansen; Clarice Poon (SIAM J. Math. Anal., 2013)

The quest for optimal sampling: Computationally efficient, structure-exploiting measurements for compressed sensing. - Ben Adcock; Anders C. Hansen; Bogdan Roman (CoRR, 2014)

On the absence of the RIP in real-world applications of compressed sensing and the RIP in levels. - Alexander Bastounis; Anders C. Hansen (CoRR, 2014)

On asymptotic structure in compressed sensing. - Bogdan Roman; Anders C. Hansen; Ben Adcock (CoRR, 2014)

On Stable Reconstructions from Nonuniform Fourier Measurements. - Ben Adcock; Milana Gataric; Anders C. Hansen (SIAM J. Imaging Sci., 2014)

A Stability Barrier for Reconstructions from Fourier Samples. - Ben Adcock; Anders C. Hansen; Alexei Shadrin (SIAM J. Numer. Anal., 2014)

Can everything be computed? - On the Solvability Complexity Index and Towers of Algorithms. - Jonathan Ben-Artzi; Anders C. Hansen; Olavi Nevanlinna; Markus Seidel (CoRR, 2015)

Generalized sampling and the stable and accurate reconstruction of piecewise analytic functions from their Fourier coefficients. - Ben Adcock; Anders C. Hansen (Math. Comput., 2015)

Linear Stable Sampling Rate: Optimality of 2D Wavelet Reconstructions from Fourier Measurements. - Ben Adcock; Anders C. Hansen; Gitta Kutyniok; Jackie Ma (SIAM J. Math. Anal., 2015)

Analyzing the structure of multidimensional compressed sensing problems through coherence. - Alexander Daniel Jones; Ben Adcock; Anders C. Hansen (CoRR, 2016)

Generalized Sampling and Infinite-Dimensional Compressed Sensing. - Ben Adcock; Anders C. Hansen (Found. Comput. Math., 2016)

A Note on Compressed Sensing of Structured Sparse Wavelet Coefficients From Subsampled Fourier Measurements. - Ben Adcock; Anders C. Hansen; Bogdan Roman (IEEE Signal Process. Lett., 2016)

On Asymptotic Incoherence and Its Implications for Compressed Sensing of Inverse Problems. - Alexander Daniel Jones; Ben Adcock; Anders C. Hansen (IEEE Trans. Inf. Theory, 2016)

On the Absence of Uniform Recovery in Many Real-World Applications of Compressed Sensing and the Restricted Isometry Property and Nullspace Property in Levels. - Alexander Bastounis; Anders C. Hansen (SIAM J. Imaging Sci., 2017)

On instabilities of deep learning in image reconstruction - Does AI come at a cost? - Vegard Antun; Francesco Renna; Clarice Poon; Ben Adcock; Anders C. Hansen (CoRR, 2019)

Uniform recovery in infinite-dimensional compressed sensing and applications to structured binary sampling. - Ben Adcock; Vegard Antun; Anders C. Hansen (CoRR, 2019)

What do AI algorithms actually learn? - On false structures in deep learning. - Laura Thesing; Vegard Antun; Anders C. Hansen (CoRR, 2019)

Linear reconstructions and the analysis of the stable sampling rate. - Laura Thesing; Anders Christian Hansen (CoRR, 2019)

On the stable sampling rate for binary measurements and wavelet reconstruction. - Anders Christian Hansen; Laura Thesing (CoRR, 2019)

Non-uniform recovery guarantees for binary measurements and infinite-dimensional compressed sensing. - Laura Thesing; Anders Christian Hansen (CoRR, 2019)

On the infinite-dimensional QR algorithm. - Matthew J. Colbrook; Anders C. Hansen (Numerische Mathematik, 2019)

The troublesome kernel: why deep learning for inverse problems is typically unstable. - Nina Maria Gottschling; Vegard Antun; Ben Adcock; Anders C. Hansen (CoRR, 2020)

Can stable and accurate neural networks be computed? - On the barriers of deep learning and Smale's 18th problem. - Vegard Antun; Matthew J. Colbrook; Anders C. Hansen (CoRR, 2021)

The mathematics of adversarial attacks in AI - Why deep learning is unstable despite the existence of stable neural networks. - Alexander Bastounis; Anders C. Hansen; Verner Vlacic (CoRR, 2021)

Stratified Sampling Based Compressed Sensing for Structured Signals. - Theresa Loss; Matthew J. Colbrook; Anders C. Hansen (IEEE Trans. Signal Process., 2022)

The Boundaries of Verifiable Accuracy, Robustness, and Generalisation in Deep Learning. - Alexander Bastounis; Alexander N. Gorban; Anders C. Hansen; Desmond J. Higham; Danil V. Prokhorov; Oliver J. Sutton; Ivan Yu. Tyukin; Qinghua Zhou (ICANN (1), 2023)

Implicit regularization in AI meets generalized hardness of approximation in optimization - Sharp results for diagonal linear networks. - Johan S. Wind; Vegard Antun; Anders C. Hansen (CoRR, 2023)

When can you trust feature selection? - I: A condition-based analysis of LASSO and generalised hardness of approximation. - Alexander Bastounis; Felipe Cucker; Anders C. Hansen (CoRR, 2023)

Do stable neural networks exist for classification problems? - A new view on stability in AI. - Zhen Ning David Liu; Anders C. Hansen (CoRR, 2024)

On the consistent reasoning paradox of intelligence and optimal trust in AI: The power of 'I don't know'. - Alexander Bastounis; Paolo Campodonico; Mihaela van der Schaar; Ben Adcock; Anders C. Hansen (CoRR, 2024)

The Troublesome Kernel: On Hallucinations, No Free Lunches, and the Accuracy-Stability Tradeoff in Inverse Problems. - Nina Maria Gottschling; Vegard Antun; Anders C. Hansen; Ben Adcock (SIAM Rev., 2025)