Somantika Datta
Publications
- S. Datta, Welch bound equality sets with few distinct inner products from Delsarte-Goethals sets, Cryptography and Communications, 2023.
- S. Datta and J. Oldroyd, Properties of certain multi-angle tight frames in R^d, Linear Algebra and its Applications, Vol. 650, pp. 75 - 91, 2022.
- K. B. Datta and S. Datta, Application of Zernike polynomials in solving certain first and second order partial differential equations, JAEN Journal of Approximation, Vol. 12, pp. 111 - 154, 2021.
- S. Datta, Equiangular frames and their duals, Chapter in Excursions in Harmonic Analysis Vol. 6, pp. 163 - 183, Series: Applied and Computational Harmonic Analysis, 2021.
- S. Datta, Frames, erasures, and signal estimation with stochastic models , Acta Applicandae Mathematicae, Vol. 169 (1), pp. 411 - 431, 2020.
- O. Christensen, S. Datta and R. Y. Kim, Equiangular frames and generalizations of the Welch bound to dual pairs of frames, Linear and Multilinear Algebra, Vol. 68, Issue 12, pp. 2495 -2505, 2020.
- S. Datta and J. Oldroyd, Low coherence unit norm tight frames, Linear and Multilinear Algebra, Vol. 67, Issue 6, pp. 1174 - 1189, 2019.
- S. Datta and J. Oldroyd, Finite Frame Theory, Chapter 6 (pp. 145 - 170) in the volume A Primer for Undergraduate Research: From Groups and Tiles to Frames and Vaccines of the series Foundations for Undergraduate Research in Mathematics, Springer, 2017.
- S. Datta and J. Oldroyd, Construction of k-angle tight frames , Numerical Functional Analysis and Optimization , Vol. 37, Issue 8, pp. 975 - 989, 2016.
- S. Datta, Welch bounds for cross correlation of subspaces and generalizations , Linear and Multilinear Algebra , Vol. 64, No. 8, pp. 1484 - 1497, 2016.
- E. Au-Yeung and S. Datta, Tight frames, partial isometries, and signal reconstruction , Applicable Analysis , Vol. 94, No. 4, pp. 653 - 671, April 2015.
- S. Datta, Frame properties of low autocorrelation random sequences , Adv. Pure Appl. Math. , Vol.5, Issue 4, pp. 243 - 253, October 2014.
- E. Au-Yeung and S. Datta, Tight frames in spiral sampling , Proc. 10th International Conf. on Sampling Theory and Applications (SampTA) , pp. 472 - 475, Bremen, Germany, July 2013.
- S. Datta, S. Howard, and D. Cochran, Sampling of homogeneous polynomials and approximating multivariate functions , Adv. Pure Appl. Math. , Vol. 3, Issue 4, pp. 421- 441, 2013.
- S. Datta, K. Ni, P. Mahanti, and S. Roudenko, Stability of efficient deterministic compressed sensing for images with chirps and Reed-Muller sequences , Applied Mathematics, Vol. 4, No. 1A, pp. 183 - 196, January 2013.
- S. Datta, S. Howard, and D. Cochran, Geometry of the Welch bounds , Linear Algebra and its Applications , Vol. 437, Issue 10, pp. 2455 - 2470, 2012.
- J. J. Benedetto and S. Datta, Constructions and a generalization of perfect autocorrelation sequences on Z , Chapter 8 (pp. 183 - 207) in Multiscale Signal Analysis and Modeling , Springer, 2012.
- K. Ni, S. Datta, P. Mahanti, S. Roudenko, and D. Cochran, Efficient deterministic compressed sensing for images with chirps and Reed-Muller codes , SIAM Journal on Imaging Sciences , Vol. 4, No. 3, pp. 931 - 953, 2011.
- J.J. Benedetto and S. Datta, Discrete autocorrelation-based multiplicative MRAs and sampling on R , Sampl. Theory Signal Image Process. , Vol. 10, Number 1-2, pp. 111 - 133, 2011.
- J.J. Benedetto and S. Datta, Construction of infinite unimodular sequences with zero autocorrelation , Advances in Comp. Math. , Vol. 32, Issue 2, pp. 191 - 207, 2010.
- K. Ni, S. Datta, P. Mahanti, S. Roudenko, and D. Cochran, Using Reed-Muller codes as deterministic compressed sensing matrices for image reconstruction , Proceedings of the International Conference on Acoustics Speech and Signal Processing , 2010.
- K. Ni, P. Mahanti, S. Datta, S. Roudenko, and D. Cochran, Image reconstruction by deterministic compressed sensing with chirp matrices , SPIE International Symposium on Multispectral Image Processing and Pattern Recognition , Yichang, China, 2009.
- S. Datta, S. Howard, and D. Cochran, Sampling of homogeneous polynomials, Proceedings of the International Conference on Sampling Theory and Applications , Marseille, France, May 2009.
Grants supporting part of the above research:
- Frame theory in approximation and signal processing , Simons Foundation, Collaboration Grants for Mathematicians (2020 - 2025)
- Stochastic frames in signal processing, NSF CCF 1422252 (2014 - 2018)
- Construction of unimodular sequences for waveform-agile sensing, AFOSR Grant No. FA9550-10-1-0441 (2010 - 2013)