My Google Scholar profile can be found here.

**Submitted Papers**

56. B. Adcock, S. Brugiapaglia, N. Dexter and S. Moraga

Deep neural networks are effective at learning high-dimensional Hilbert-valued functions from limited data

Preprint: arXiv:2012.06081

55. B. Adcock, N. Dexter and Q. Xu

*Improved recovery guarantees and sampling strategies for TV minimization in compressive imaging.
*Preprint: arXiv:2009.08555

54. 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.*

Preprint: arXiv:2006.13389

53. 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

52. B. Adcock, V. Antun and A. C. Hansen

*Uniform recovery in infinite-dimensional compressed sensing and applications to structured binary sampling.
*Preprint: arXiv:1905.00126

**Journal Papers**

**2021**

51. B. Adcock and N. Dexter

*The gap between theory and practice in function approximation with deep neural networks.
*SIAM J. Math. Data Sci. (to appear)

Preprint: arXiv:2001.07523

50. 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. (to appear)

*Preprint: arXiv:1905.10028*

**2020**

49. B. Adcock and D. Huybrechs

*Frames and numerical approximation II: generalized sampling.
*J. Fourier Anal. Appl. (to appear)

*Preprint: arXiv:1802.01950*

48. B. Adcock and M. Seifi

*Frame approximation with bounded coefficients.
*Adv. Comput. Math. (to appear)

*Preprint: arXiv:2001.00983*

47. B. Adcock, C. Boyer and S. Brugiapaglia

*On oracle-type local recovery guarantees in compressed sensing.
*Inf. Inference (to appear)

*Preprint: arXiv:1806.03789*

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

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

*Preprint: arXiv:1908.01249*

44. B. Adcock and D. Huybrechs

*Approximating smooth, multivariate functions on irregular domains.
*Forum Math. Sigma 8:e27

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

*Preprint: arXiv:1610.05758*

**2019**

42. B. Adcock and D. Huybrechs

*Frames and numerical approximation.
*SIAM Rev. 61(3):443-473

*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

*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

*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

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

*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

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

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

*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

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

Preprint: arXiv:1705.10299

32. B. Adcock

*Infinite-dimensional compressed sensing and function interpolation.
*Found. Comput. Math. 18(3):661-701

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

Preprint: arXiv:1411.0300

30. I. Y. Chun and B. Adcock

*Compressed sensing and parallel acquisition.
*IEEE Trans. Inform. Theory 63(8):4860-4882

*Preprint: arXiv:1601.06214*

29. B. Adcock

*Infinite-dimensional l1 minimization and function approximation from pointwise data.
*Constr. Approx. 45(3):345-390

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

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

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

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

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

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

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

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

**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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

Preprint: PDF

3. B. Adcock

*Convergence acceleration of modified Fourier series in one or more dimensions*.

Math. Comp. 80(273): 225-261

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

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

Preprint: DAMTP Tech. Rep. 2007/NA08

**Preprints**

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**

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.

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.

Preprint: arXiv:1403.6540

**News Articles**

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

**Proceedings**

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.

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 (to appear).

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 (to appear).

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.

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 201.

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 (to appear).

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

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

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.

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.