Publications

My Google Scholar profile can be found here.

Books

2. B. Adcock, S. Brugiapaglia and C. G. Webster
Sparse Polynomial Approximation of High-Dimensional Functions
SIAM, 2022
www.sparse-hd-book.com
https://doi.org/10.1137/1.9781611976885

1. B. Adcock and A. C. Hansen
Compressive Imaging: Structure, Sampling, Learning
Cambridge University Press, 2021
www.compressiveimagingbook.com
https://doi.org/10.1017/9781108377447

Submitted Papers

61. B. Adcock and S. Brugiapaglia
Is Monte Carlo a bad sampling strategy for learning smooth functions in high dimensions?
Preprint: arXiv:2208.09045

60. B. Adcock, S. Brugiapaglia, N. Dexter and S. Moraga
On efficient algorithms for computing near-best polynomial approximations to high-dimensional, Hilbert-valued functions from limited samples
Preprint: arXiv:2203.13908

59. B. Adcock, J. M. Cardenas and N. Dexter
CAS4DL: Christoffel Adaptive Sampling for function approximation via Deep Learning
Preprint: arXiv:2208.12190

58. B. Adcock and M. Neyra-Nesterenko
Stable, accurate and efficient deep neural networks for inverse problems with analysis-sparse models
Preprint: arXiv:2203.00804

57. B. Adcock, J. M. Cardenas and N. Dexter
An adaptive sampling and domain learning strategy for multivariate function approximation on unknown domains
Preprint: arXiv:2202.00144

Journal Papers

2022

56. B. Adcock and A. Shadrin
Fast and stable approximation of analytic functions from equispaced samples via polynomial frames
Constr. Approx. (to appear)
Preprint: arXiv:2110.03755

55. B. Adcock, S. Brugiapaglia and M. King-Roskamp
Do log factors matter? On optimal wavelet approximation and the foundations of compressed sensing
Found. Comput. Math. 22(1):99-159
https://doi.org/10.1137/20M131309X
Preprint: arXiv:1905.10028

2021

54. B. Adcock, S. Brugiapaglia, N. Dexter and S. Moraga
Deep neural networks are effective at learning high-dimensional Hilbert-valued functions from limited data
Proceedings of Machine Learning Research 145:1-36
https://proceedings.mlr.press/v145/adcock22a.html
Preprint: arXiv:2012.06081

53. B. Adcock, S. Brugiapaglia and M. King-Roskamp
The benefits of acting locally: reconstruction algorithms for sparse in levels signals with stable and robust recovery guarantees
IEEE Trans. Signal Process. 69:3160-3175
https://doi.org/10.1109/TSP.2021.3080458
Preprint: arXiv:2006.13389

52. B. Adcock, N. Dexter and Q. Xu
Improved recovery guarantees and sampling strategies for TV minimization in compressive imaging
SIAM J. Imaging Sci. 13(3):1149-1183
https://doi.org/10.1137/20M136788X
Preprint: arXiv:2009.08555

51. B. Adcock, V. Antun and A. C. Hansen
Uniform recovery in infinite-dimensional compressed sensing and applications to structured binary sampling
Appl. Comput. Harmon. Anal. 55:1-40
https://doi.org/10.1016/j.acha.2021.04.001
Preprint: arXiv:1905.00126

50. B. Adcock and N. Dexter
The gap between theory and practice in function approximation with deep neural networks
SIAM J. Math. Data Sci. 3(2):624-655
https://doi.org/10.1137/20M131309X
Preprint: arXiv:2001.07523

49. B. Adcock, C. Boyer and S. Brugiapaglia
On oracle-type local recovery guarantees in compressed sensing
Inf. Inference 10(1):1-49
https://doi.org/10.1093/imaiai/iaaa007
Preprint: arXiv:1806.03789

48. B. Adcock and M. Seifi
Frame approximation with bounded coefficients
Adv. Comput. Math. 47(1):4
https://doi.org/10.1137/20M131309X
Preprint: arXiv:2001.00983

2020

47. B. Adcock and D. Huybrechs
Frames and numerical approximation II: generalized sampling
J. Fourier Anal. Appl. 26(6):87
https://doi.org/10.1007/s00041-020-09796-w
Preprint: arXiv:1802.01950

46. V. Antun, F. Renna, C. Poon, B. Adcock and A. C. Hansen
On instabilities of deep learning in image reconstruction and the potential costs of AI
Proc. Natl. Acad. Sci. USA 117(48):30088-30095
https://doi.org/10.1073/pnas.1907377117
Preprint: arXiv:1902.05300

45. B. Adcock and Juan M. Cardenas
Near-optimal sampling strategies for multivariate function approximation on general domains
SIAM J. Math. Data Sci. 2(3):607-630
https://doi.org/10.1137/19M1279459
Preprint: arXiv:1908.01249

44. B. Adcock and D. Huybrechs
Approximating smooth, multivariate functions on irregular domains
Forum Math. Sigma 8:e27
https://doi.org/10.1017/fms.2020.23
Preprint: arXiv:1802.00602

43. I. Y. Chun and B. Adcock
Uniform recovery from subgaussian multi-sensor measurements
Appl. Comput. Harmon. Anal. 48(2):731-765
https://doi.org/10.1016/j.acha.2018.09.003
Preprint: arXiv:1610.05758

2019

42. B. Adcock and D. Huybrechs
Frames and numerical approximation
SIAM Rev. 61(3):443-473
https://doi.org/10.1137/17M1114697
Preprint: arXiv:1612.04464
Supplementary materials: TW-675

41. B. Adcock, R. Platte and A. Shadrin
Optimal sampling rates for approximating analytic functions from pointwise samples
IMA J. Numer. Anal. 39(3):1360-1390
https://doi.org/10.1093/imanum/dry024
Preprint: arXiv:1610.04769

40. I. Y. Chun, D. Hong, B. Adcock and J. A. Fessler
Convolutional analysis operator learning: dependence on training data
IEEE Signal Process. Lett. 26(8):1137-1141
https://doi.org/10.1109/LSP.2019.2921446
Preprint: arXiv:1902.08267

39. B. Adcock and Y. Sui
Compressive Hermite interpolation: sparse, high-dimensional approximation from gradient-augmented measurements
Constr. Approx. 50(1):167-207
https://doi.org/10.1007/s00365-019-09467-0
Preprint: arXiv:1712.06645

38. B. Adcock, A. Bao and S. Brugiapaglia
Correcting for unknown errors in sparse high-dimensional function approximation
Numer. Math. 142(3):667-711
https://doi.org/10.1007/s00211-019-01051-9
Preprint: arXiv:1711.07622

37. C. Li and B. Adcock
Compressed sensing with local structure: uniform recovery guarantees for the sparsity in levels class
Appl. Comput. Harmon. Anal. 46(3):453-477
https://doi.org/10.1016/j.acha.2017.05.006
Preprint: arXiv:1601.01988

36. B. Adcock, A. Gelb, G. Song and Y. Sui
Joint sparse recovery based on variances.
SIAM J. Sci. Comput. 41(1):A246-268
https://doi.org/10.1137/17M1155983

35. B. Adcock, M. Gataric and J. L. Romero
Computing reconstructions from nonuniform Fourier samples: Universality of stability barriers and stable sampling rates
Appl. Comput. Harmon. Anal. 46(2):226-249
https://doi.org/10.1016/j.acha.2017.05.004
Preprint: arXiv:1606.07698

2018

34. B. Adcock, A. Bao, U. Author and A. Narayan
Compressed sensing with sparse corruptions: Fault-tolerant sparse collocation approximations
SIAM/ASA J. Uncertain. Quantif. 6(4):1424-1453
https://doi.org/10.1137/17M112590X
Preprint: arXiv:1703.00135

33. S. Brugiapaglia and B. Adcock
Robustness to unknown error in sparse regularization
IEEE Trans. Inform. Theory 64(10):6638-6661
https://doi.org/10.1109/TIT.2017.2788445
Preprint: arXiv:1705.10299

32. B. Adcock
Infinite-dimensional compressed sensing and function interpolation
Found. Comput. Math. 18(3):661-701
https://doi.org/10.1007/s10208-017-9350-3
Preprint: arXiv:1509.06073

2017

31. B. Adcock, M. Gataric and A. C. Hansen
Density theorems for nonuniform sampling of bandlimited functions using derivatives or bunched measurements
J. Fourier Anal. Appl. 23(6):1311-1347
https://doi.org/10.1007/s00041-016-9504-8
Preprint: arXiv:1411.0300

30. I. Y. Chun and B. Adcock
Compressed sensing and parallel acquisition
IEEE Trans. Inform. Theory 63(8):4860-4882
https://doi.org/10.1109/TIT.2017.2700440
Preprint: arXiv:1601.06214

29. B. Adcock
Infinite-dimensional l1 minimization and function approximation from pointwise data
Constr. Approx. 45(3):345-390
https://doi.org/10.1007/s00365-017-9369-3
Preprint: arXiv:1503.02352

28. B. Adcock, M. Gataric and A. C. Hansen
Weighted frames of exponentials and stable recovery of multidimensional functions from nonuniform Fourier samples
Appl. Comput. Harmon. Anal. 42(3):508-535
https://doi.org/10.1016/j.acha.2015.09.006
Preprint: arXiv:1405.3111

27. B. Adcock, A. C. Hansen, C. Poon and B. Roman
Breaking the coherence barrier: a new theory for compressed sensing
Forum Math. Sigma 5:e4
https://doi.org/10.1017/fms.2016.32
Preprint: arXiv:1302.0561

26. B. Adcock, J. Martin-Vaquero and M. Richardson
Resolution-optimal exponential and double-exponential transform methods for functions with endpoint singularities
SIAM J. Sci. Comput. 31(1):A164-A187
https://doi.org/10.1137/15M104517X
Preprint: arXiv:1510.07027

2016

25. B. Adcock and A. C. Hansen
Generalized sampling and infinite-dimensional compressed sensing
Found. Comput. Math. 16(5):1263-1323
https://doi.org/10.1007/s10208-015-9276-6
Preprint: DAMTP Tech. Rep. 2011/NA12

24. B. Adcock, A. C. Hansen and B. Roman
A note on compressed sensing of structured sparse wavelet coefficients from subsampled Fourier measurements
IEEE Signal Process. Lett. 23(5):732-736
https://doi.org/10.1109/LSP.2016.2550101
Preprint: arXiv:1403.6541

23. B. Adcock and R. Platte
A mapped polynomial method for high-accuracy approximations on arbitrary grids
SIAM J. Numer. Anal. 54(4):2256-2281
https://doi.org/10.1137/15M1023853
Preprint: PDF

22. A. Jones, B. Adcock and A. C. Hansen
On asymptotic incoherence and its implications for compressed sensing of inverse problems
IEEE Trans. Inform. Theory 62(2):1020-1037
https://doi.org/10.1109/TIT.2015.2508562
Preprint: arXiv:1402.5324

21. I. Y. Chun, B. Adcock and T. Talavage
Efficient compressed sensing SENSE pMRI reconstruction with joint sparsity promotion
IEEE Trans. Med. Imag. 31(1): 354-368
https://doi.org/10.1109/TMI.2015.2474383

2015

20. B. Adcock, A. C. Hansen, G. Kutyniok and J. Ma
Linear stable sampling rate: optimality of 2D wavelet reconstructions from Fourier measurements
SIAM J. Math. Anal. 47(2):1196-1233
https://doi.org/10.1137/140959365
Preprint: arXiv:1403.0172

19. B. Adcock and A. C. Hansen
Generalized sampling and the stable and accurate reconstruction of piecewise analytic functions from their Fourier coefficients
Math. Comp. 84:237-270
https://doi.org/10.1090/S0025-5718-2014-02860-3
Preprint:DAMTP Tech. Rep. 2011/NA02

2014

18. B. Adcock, M. Gataric and A. C. Hansen
On stable reconstructions from nonuniform Fourier measurements
SIAM J. Imaging Sci. 7(3):1690-1723
https://doi.org/10.1137/130943431
Preprint: arXiv:1310.7820

17. B. Adcock and M. Richardson
New exponential variable transform methods for functions with endpoint singularities
SIAM J. Numer. Anal. 52(4):1887-1912
https://doi.org/10.1137/130920460
Preprint: arXiv:1305.2643

16. B. Adcock, D. Huybrechs and J. Martin-Vaquero
On the numerical stability of Fourier extensions
Found. Comput. Math. 14(4):635-687
https://doi.org/10.1007/s10208-013-9158-8
Preprint: arXiv:1206.4111

15. B. Adcock and J. Ruan
Parameter selection and numerical approximation properties of Fourier extensions from fixed data
J. Comput. Phys. 273:453-471
https://doi.org/10.1016/j.jcp.2014.05.036
Preprint: arXiv:1405.4320

14. B. Adcock, A. C. Hansen and C. Poon
On optimal wavelet reconstructions from Fourier samples: linearity and universality of the stable sampling rate
Appl. Comput. Harmon. Anal. 36(3):387-415
https://doi.org/10.1016/j.acha.2013.07.001
Preprint: arXiv:1208.5959

13. B. Adcock, A. C. Hansen, B. Roman and G. Teschke
Generalized sampling: stable reconstructions, inverse problems and compressed sensing over the continuum
Adv. Imag. Elect. Phys. 182:187-279
https://doi.org/10.1016/B978-0-12-800146-2.00004-7
Preprint: arXiv:1310.1141

12. B. Adcock, A. C. Hansen and A. Shadrin
A stability barrier for reconstructions from Fourier samples
SIAM J. Numer. Anal. 52(1):125-139
https://doi.org/10.1137/130908221
Preprint: arXiv:1210.7831

11. B. Adcock and D. Huybrechs
On the resolution power of Fourier extensions for oscillatory functions
J. Comput. Appl. Math. 260:312-336
https://doi.org/10.1016/j.cam.2013.09.069
Preprint: arXiv:1210.7831

2013

10. B. Adcock, A. C. Hansen and C. Poon
Beyond consistent reconstructions: optimality and sharp bounds for generalized sampling, and application to the uniform resampling problem
SIAM J. Math. Anal. 45(5):3132-3167
https://doi.org/10.1137/120895846
Preprint: arXiv:1301.2831

9. B. Adcock, A. C. Hansen, E. Herrholz and G. Teschke
Generalized sampling: extensions to frames and inverse and ill-posed problems
Inverse Problems 29: 015008
https://doi.org/10.1088/0266-5611/29/1/015008
Preprint: PDF

2012

8. B. Adcock and A. C. Hansen
Stable reconstructions in Hilbert spaces and the resolution of the Gibbs phenomenon
Appl. Comput. Harmon. Anal. 32(3): 357-388
https://doi.org/10.1016/j.acha.2011.07.004
Preprint: arXiv:1011.6625

7. B. Adcock and A. C. Hansen
A generalized sampling theorem for stable reconstructions in arbitrary bases
J. Fourier Anal. Appl. 18(4):685-716
https://doi.org/10.1007/s00041-012-9221-x
Preprint: arXiv:1007.1852

6. B. Adcock, A. Iserles and S. P. Nørsett
From high oscillation to rapid approximation II: Expansions in Birkhoff series
IMA J. Numer. Anal. 32(1): 105-140
https://doi.org/10.1093/imanum/drq038
Preprint:DAMTP Tech. Rep. 2010/NA02

2011

5. B. Adcock
On the convergence of expansions in polyharmonic eigenfunctions
J. Approx. Theory 163(11): 1638-1674
https://doi.org/10.1016/j.jat.2011.06.002
Preprint: DAMTP Tech. Rep. 2010/NA06

4. B. Adcock
Gibbs phenomenon and its removal for a class of orthogonal expansions
BIT 51(1): 7-41
https://doi.org/10.1007/s10543-010-0301-5
Preprint: PDF

3. B. Adcock
Convergence acceleration of modified Fourier series in one or more dimensions
Math. Comp. 80(273): 225-261
https://doi.org/10.1090/S0025-5718-2010-02393-2
Preprint: DAMTP Tech. Rep. 2008/NA11

2010

2. B. Adcock
Multivariate modified Fourier series and application to boundary value problems
Numer. Math. 115(4): 511-552
https://doi.org/10.1007/s00211-010-0287-6
Preprint: DAMTP Tech. Rep. 2008/NA08

2009

1. B. Adcock
Univariate modified Fourier methods for second order boundary value problems
BIT 49(2): 249-280
https://doi.org/10.1007/s10543-009-0224-1
Preprint: DAMTP Tech. Rep. 2007/NA08

Preprints

7. H. Zabeti, N. Dexter, I. Lau, L. Unrah, B. Adcock and L. Chindelevitch
Group Testing Large Populations for SARS-CoV-2
Preprint: medRxiv

6. N. M. Gottschling, V. Antun, B. Adcock and A. C. Hansen
The troublesome kernel: why deep learning for inverse problems is typically unstable
Preprint: arXiv:2001.01258

5. B. Roman, R. Calderbank, D. Nietlispach, M. Bostock, I. Calvo-Almazan, M. Graves, B. Adcock and A. C. Hansen
Unlocking the potential of undersampled NMR

4. B. Roman, A. Bastounis, B. Adcock and A. C. Hansen
On fundamentals of models and sampling in compressed sensing

3. B. Adcock, R. Archibald, A. Gelb, R. B. Platte, G. Song and E. G. Walsh
Parameter assessment from time-dependent MR signals using sequential imaging

2. B. Roman, B. Adcock and A. C. Hansen
On asymptotic structure in compressed sensing
Preprint: arXiv:1406.4178

1. A. Jones, B. Adcock and A. C. Hansen
Analyzing the structure of multidimensional compressed sensing problems through coherence
Preprint: arXiv:1610.07497

Book Chapters

3. B. Adcock, J. M. Cardenas, N. Dexter and S. Moraga
Towards optimal sampling for learning sparse approximations in high dimensions
High Dimensional Optimization and Probability, Springer, 2022
https://doi.org/10.1007/978-3-031-00832-0_2
Preprint: arXiv:2202.02360

2. B. Adcock, S. Brugiapaglia and C. Webster
Compressed sensing approaches for polynomial approximation of high-dimensional functions
Compressed Sensing and its Applications, Birkhauser, 2017
https://doi.org/10.1007/978-3-319-69802-1_3
Preprint: arXiv:1703.06987

1. B. Adcock, A. C. Hansen, and B. Roman
The quest for optimal sampling: computationally efficient, structure-exploiting measurements for compressed sensing
Compressed Sensing and its Applications, Birkhauser, 2015
https://doi.org/10.1007/978-3-319-16042-9_5
Preprint: arXiv:1403.6540

News Articles

2. V. Antun, N. M. Gottschling, A. C. Hansen and B. Adcock
Deep Learning in Scientific Computing: Understanding the Instability Mystery
SIAM News, March 2021

1. B. Adcock, A. Bastounis and A. C. Hansen
From Global to Local: Getting More from Compressed Sensing
SIAM News, October 2017

Proceedings

16. B. Adcock, S. Brugiapaglia, N. Dexter and S. Moraga
Learning high-dimensional Hilbert-valued functions with deep neural networks from limited data
Proceedings of the AAAI 2021 Spring Symposium on Combining Artificial Intelligence and Machine Learning with Physics Sciences, 2021.
http://ceur-ws.org/Vol-2964/

15. B. Adcock, S. Brugiapaglia and M. King-Roskamp
Iterative and greedy algorithms for the sparsity in levels model in compressed sensing
Proc. SPIE 11138, Wavelets and Sparsity XVIII, 1113809, 2019
https://doi.org/10.1117/12.2526373

14. B. Adcock and S. Brugiapaglia
Sparse approximation of multivariate functions from small datasets via weighted orthogonal matching pursuit
Proceedings of the 12th International Conference on Spectral and High Order Methods, Imperial College, London, UK, July 2018.
https://doi.org/10.1007/978-3-030-39647-3_49
Preprint: arXiv:1810.11115

13. S. Brugiapaglia, B. Adcock and R. K. Archibald
Recovery guarantees for compressed sensing with unknown errors
Proceedings of the 12th International Conference on Sampling Theory and Applications, Tallinn, Estonia, July 2017.
https://doi.org/10.1109/SAMPTA.2017.8024421
Preprint: arXiv:1702.04424

12. I. Y. Chun, C. Li and B. Adcock
Sparsity and parallel acquisition: optimal uniform and nonuniform recovery guarantees
Proceedings of the 2016 IEEE International Conference on Multimedia and Expo, Seattle, USA, July 2016.
https://doi.org/10.1109/ICMEW.2016.7574710
Preprint: arXiv:1603.08050

11. I. Y. Chun and B. Adcock
Optimal sparse recovery for multi-sensor measurements
Proceedings of the 2016 IEEE Information Theory Workshop, Cambridge, UK, September 2016.
https://doi.org/10.1109/ITW.2016.7606838
Preprint: arXiv:1603.06934

10. B. Adcock, A. C. Hansen and B. Roman
Compressed sensing with local structure: theory, applications and benefits
Proceedings of the 11th International Conference on Sampling Theory and Applications, Washington DC, USA, May 2015.

9. B. Adcock, M. Gataric and A. C. Hansen
Stable nonuniform sampling with weighted Fourier frames and recovery in arbitrary spaces
Proceedings of the 11th International Conference on Sampling Theory and Applications, Washington DC, USA, May 2015.

8. B. Adcock, M. Gataric and A. C. Hansen
Recovering piecewise smooth functions from nonuniform Fourier measurements
Proceedings of the 10th International Conference on Spectral and High Order Methods, Salt Lake City, USA, June 2014.
https://doi.org/10.1007/978-3-319-19800-2_8
Preprint: arXiv:1410.0088

7. I. Y. Chun, B. Adcock and T. Talavage
Efficient Compressed Sensing SENSE Parallel MRI Reconstruction with Joint Sparsity Promotion and Mutual Incoherence Enhancement
Proceedings of the 36th Annual International Conference of the IEEE Engineering in Medicine and Biology Society, Chicago, USA, August 2014
https://doi.org/10.1109/EMBC.2014.6944111

6. I. Y. Chun, B. Adcock and T. Talavage
Non-Convex Compressed Sensing CT Reconstruction Based on Tensor Discrete Fourier Slice Theorem
Proceedings of the 36th Annual International Conference of the IEEE Engineering in Medicine and Biology Society, Chicago, USA, August 2014
https://doi.org/10.1109/EMBC.2014.6944782

5. B. Adcock, A. C. Hansen, C. Poon and B. Roman
Overcoming the coherence barrier in compressed sensing
Proceedings of the 10th International Conference on Sampling Theory and Applications, Bremen, Germany, July 2013.
Preprint: PDF

4. B. Adcock, A. C. Hansen and C. Poon
Optimal wavelet reconstructions from Fourier samples via generalized sampling
Proceedings of the 10th International Conference on Sampling Theory and Applications, Bremen, Germany, July 2013.
Preprint: PDF

3. B. Adcock and D. Huybrechs
Accuracy of the Fourier extension method for oscillatory phenomena
Proceedings of the 10th International Conference on Mathematical and Numerical Aspects of Waves, Vancouver, Canada, July 2011.
Preprint: PDF

2. B. Adcock and A. C. Hansen
Reduced consistency sampling in Hilbert spaces
Proceedings of the 9th International Conference on Sampling Theory and Applications, Singapore, May 2011.
Preprint: PDF

1. B. Adcock and D. Huybrechs
Multivariate modified Fourier expansions
Proceedings of the 8th International Conference on Spectral and High Order Methods (E. Rønquist et al, ed.), Trondheim, Norway, June 2009.
https://doi.org/10.1007/978-3-642-15337-2_5
Preprint: PDF

Essays

2. B. Adcock
Modified Fourier expansions: theory, construction and applications
PhD thesis PDF

1. B. Adcock
Birkhoff-Galerkin methods for linear boundary value problems
Smith-Knight/Rayleigh-Knight Prize