Dr. Matthew Fickus, Professor of Mathematics
Publications
Journal Articles:
47. M. Fickus, J. W. Iverson, J. Jasper, D. G. Mixon, Harmonic Grassmannian codes, Appl. Comput. Harmon. Anal. 65 (2023) 1-39.
46. B. Deregowska, M. Fickus, S. Foucart, B. Lewandowska, On the value of the fifth maximal projection constant, J. Funct. Anal. 283 (2022) 109634/1-16.
45. M. Fickus, J. W. Iverson, J. Jasper, E. J. King, Grassmannian codes from paired difference sets, Des. Codes Cryptogr. 89 (2021) 2553–2576.
44. M. Fickus, B. R. Mayo, Mutually unbiased equiangular tight frames, IEEE Trans. Inform. Theory 67 (2021) 1656–1667.
43. M. Fickus, J. Jasper, D. G. Mixon, J. D. Peterson, Hadamard equiangular tight frames, Appl. Comput. Harmon. Anal. 50 (2021) 281–302.
42. M. Fickus, C. A. Schmitt, Harmonic equiangular tight frames comprised of regular simplices, Linear Algebra Appl. 586 (2020) 130–169.
41. M. Fickus, J. Jasper, D. G. Mixon, J. D. Peterson, C. E. Watson, Polyphase equiangular tight frames and abelian generalized quadrangles, Appl. Comput. Harmon. Anal. 47 (2019) 628–661.
40. M. Fickus, J. Jasper, Equiangular tight frames from group divisible designs, Des. Codes Cryptogr. 87 (2019) 1673–1697.
39. M. Fickus, J. Jasper, D. G. Mixon, Packings in real projective spaces, SIAM J. Appl. Algebra Geom. 2 (2018) 377–409.
38. M. Fickus, J. Jasper, E. J. King, D. G. Mixon, Equiangular tight frames that contain regular simplices, Linear Algebra Appl. 555 (2018) 98–138.
37. M. Fickus, J. Jasper, D. G. Mixon, J. D. Peterson, C. E. Watson, Equiangular tight frames with centroidal symmetry, Appl. Comput. Harmon. Anal. 44 (2018) 476–496.
36. M. Fickus, J. Jasper, D. G. Mixon, J. D. Peterson, Tremain equiangular tight frames, J. Combin. Theory Ser. A. 153 (2018) 54–66.
35. M. Fickus, D. G. Mixon, J. Jasper, Equiangular tight frames from hyperovals, IEEE Trans. Inform. Theory. 62 (2016) 5225–5236.
34. A. S. Bandeira, M. Fickus, D. G. Mixon, J. Moreira, Derandomizing restricted isometries via the Legendre symbol, Constr. Approx. 43 (2016) 409–424.
33. M. Fickus, J. D. Marks, M. J. Poteet, A generalized Schur-Horn theorem and optimal frame completions, Appl. Comput. Harmon. Anal. 40 (2016) 505–528.
32. M. Fickus, D. G. Mixon, M. Lewis, J. Peterson, Compressive hyperspectral imaging for stellar spectroscopy, IEEE Signal Process. Lett. 22 (2015) 1829–1833.
31. M. Fickus, J. Jasper, D. G. Mixon, J. Peterson, Group-theoretic constructions of erasure-robust frames, Linear Algebra Appl. 479 (2015) 131–154.
30. R. Bhagavatula, M. T. McCann, M. Fickus, C. A. Castro, J. A. Ozolek, J. Kovacevic, A vocabulary for the identification and delineation of teratoma tissue components in hematoxylin and eosin-stained samples, J. Pathol. Inform. 5 (2014) 1–19.
29. M. T. McCann, D. G. Mixon, M. Fickus, C. A. Castro, J. A. Ozolek, J. Kovacevic, Images as occlusions of textures: a framework for segmentation, IEEE Trans. Image Process. 23 (2014) 2033–2046.
28. M. Fickus, D. G. Mixon, A. A. Nelson, Y. Wang, Phase retrieval from very few measurements, Linear Algebra Appl. 449 (2014) 475–499.
27. L. N. Smith, M. Fickus, Determining angular frequency from video with a generalized fast Fourier transform, Adv. Comput. Math. 40 (2014) 27–47.
26. J. Jasper, D. G. Mixon, M. Fickus, Kirkman equiangular tight frames and codes, IEEE Trans. Inform. Theory. 60 (2014) 170–181.
25. B. Alexeev, A. S. Bandeira, M. Fickus, D. G. Mixon, Phase retrieval with polarization, SIAM J. Imaging Sci. 7 (2014) 35–66.
24. A. S. Bandeira, M. Fickus, D. G. Mixon, P. Wong, The road to deterministic matrices with the Restricted Isometry Property, J. Fourier Anal. Appl. 19 (2013) 1123–1149.
23. M. Fickus, D. G. Mixon, M. J. Poteet, N. Strawn, Constructing all self-adjoint matrices with prescribed spectrum and diagonal, Adv. Comput. Math. 39 (2013) 585–609.
22. P. G. Casazza, M. Fickus, D. G. Mixon, J. Peterson, I. Smalyanau, Every Hilbert space frame has a Naimark complement, J. Math. Anal. Appl. 406 (2013) 111–119.
21. J. Cahill, M. Fickus, D. G. Mixon, M. J. Poteet, N. Strawn, Constructing finite frames of a given spectrum and set of lengths, Appl. Comput. Harmon. Anal. 35 (2013) 52–73.
20. M. L. Massar, R. Bhagavatula, M. Fickus, J. Kovacevic, Local histograms and image occlusion models, Appl. Comput. Harmon. Anal. 34 (2013) 469–487.
19. D. G. Mixon, C. J. Quinn, N. Kiyavash, M. Fickus, Fingerprinting with Equiangular Tight Frames, IEEE Trans. Inform. Theory. 59 (2013) 1855–1865.
18. P. G. Casazza, M. Fickus, A. Heinecke, Y. Wang, Z. Zhou, Spectral tetris fusion frame constructions, J. Fourier Anal. Appl. 18 (2012) 828–851.
17. M. Fickus, D. G. Mixon, Optimal frames and Newton’s method, Numer. Funct. Anal. Optim. 33 (2012) 971–988.
16. M. Fickus, D. G. Mixon, Numerically erasure-robust frames, Linear Algebra Appl. 437 (2012) 1394–1407.
15. D. C. Balcan, G. Srinivasa, M. Fickus, J. Kovacevic, Guaranteeing convergence of iterative skewed voting algorithms for image segmentation, Appl. Comput. Harmon. Anal. 33 (2012) 300–308.
14. M. Fickus, D. G. Mixon, J. C. Tremain, Steiner equiangular tight frames, Linear Algebra Appl. 436 (2012) 1014–1027.
13. P. G. Casazza, M. Fickus, D. G. Mixon, Auto-tuning unit norm frames, Appl. Comput. Harmon. Anal. 32 (2012) 1–15.
12. M. L. Massar, M. Fickus, E. Bryan, D. T. Petkie, A. J. Terzuoli, Fast computation of spectral centroids, Adv. Comput. Math. 35 (2011) 83–97.
11. P. G. Casazza, M. Fickus, D. G. Mixon, J. C. Tremain, The Bourgain-Tzafriri conjecture and concrete constructions of nonpavable projections, Oper. Matrices. 5 (2011) 351–363.
10. A. Chebira, M. Fickus, D. G. Mixon, Filter bank fusion frames, IEEE Trans. Signal Process. 59 (2011) 953–963.
9. P. G. Casazza, M. Fickus, D. G. Mixon, Y. Wang, Z. Zhou, Constructing tight fusion frames, Appl. Comput. Harmon. Anal. 30 (2011) 175–187.
8. G. Srinivasa, M. Fickus, Y. Guo, A. Linstedt, J. Kovacevic, Active mask segmentation of fluorescence microscope images, IEEE Trans. Image Process. 18 (2009) 1817–1829.
7. P. G. Casazza, M. Fickus, Minimizing fusion frame potential, Acta Appl. Math. 107 (2009) 7–24.
6. A. Chebira, M. Fickus, J. Kovacevic, Classifying compact convex sets with frames, Appl. Comput. Harmon. Anal. 27 (2009) 73–86.
5. M. Fickus, Maximally equiangular frames and Gauss sums, J. Fourier Anal. Appl. 15 (2009) 413–427.
4. M. Fickus, D. G. Mixon, Isotropic moments over integer lattices, Appl. Comput. Harmon. Anal. 26 (2009) 77–96.
3. P. G. Casazza, M. Fickus, Fourier transforms of finite chirps, EURASIP J. Appl. Signal Process. 2006 (2006), Article ID 70204, 7 pages.
2. M. Fickus, B. D. Johnson, K. Kornelson, K. Okoudjou, Convolutional frames and the frame potential, Appl. Comput. Harmon. Anal. 19 (2005) 77–91.
1. J. J. Benedetto, M. Fickus, Finite normalized tight frames, Adv. Comput. Math. 18 (2003) 357–385.
Peer-Reviewed Book Chapters:
3. M. Fickus, M. L. Massar, D. G. Mixon, Finite frames and filter banks, in: "Finite Frames: Theory and Applications," P. G. Casazza and G. Kutyniok eds., Birkhauser, pp.
337-379, 2012.
2. M. Fickus, D. G. Mixon, M. J. Poteet, Constructing finite frames with a given spectrum, in: "Finite Frames: Theory and Applications" P. G. Casazza and G. Kutyniok eds.,
Birkhauser, pp. 55-107, 2012.
1. P. G. Casazza, M. Fickus, J. Kovacevic, M. T. Leon, J. C. Tremain, A physical interpretation of tight frames, in: "Harmonic Analysis and Applications" C. Heil ed.,
Birkhauser, pp. 51-76, 2006.
Conference Proceedings, Fully Peer-Reviewed:
15. M. Fickus, J. W. Iverson, J. Jasper, D. G. Mixon, A note on totally symmetric equi-isoclinic tight fusion frames, Proc. IEEE Int. Conf. Acoust. Speech Signal Process. (2022).
14. M. Fickus, C. A. Schmitt, Equi-isoclinic subspaces from difference sets, Proc. Sampl. Theory Appl. (2019) 1--4.
13. M. Fickus, J. Jasper, D. G. Mixon, J. Peterson, Steiner equiangular tight frames redux, Proc. Sampl. Theory Appl. (2015) 347-351.
12. M. Fickus, D. G. Mixon, Projection retrieval: theory and algorithms, Proc. Sampl. Theory Appl. (2015) 183-186.
11. M. Fickus, M. J. Poteet, Characterizing completions of finite frames, Proc. Sampl. Theory Appl. (2013) 89-92.
10. M. T. McCann, R. Bhagavatula, M. Fickus, J. A. Ozolek, J. Kovacevic, Automated colitis detection from endoscopic biopsies as a tissue screening tool in diagnostic pathology,
Proc. IEEE Intl. Conf. Image Process. (2012) 2809-2812.
9. M. Fickus, D. G. Mixon, J. C. Tremain, Constructing a large family of equiangular tight frames, Proc. Sampl. Theory Appl. (2011) 4 pages.
8. D. G. Mixon, C. J. Quinn, N. Kiyavash, M. Fickus, Equiangular tight frame fingerprinting codes, Proc. IEEE Int. Conf. Acoust. Speech Signal Process. (2011) 1856-1859.
7. R. Bhagavatula, M. Fickus, W. Kelly, C. Guo, J. A. Ozolek, C. A. Castro, J. Kovacevic, Automatic identification and delineation of germ layer components in H&E stained images
of teratomas, Proc. IEEE Int. Symp. Biomed. Imaging (2010) 1041-1044.
6. D. C. Balcan, G. Srinivasa, M. Fickus, J. Kovacevic, Convergence behavior of the Active Mask algorithm, Proc. IEEE Int. Conf. Acoust. Speech Signal Process. (2010) 453-456.
5. A. Chebira, M. Fickus, M. Vetterli, Frame domain signal processing: framework and applications, Proc. IEEE Int. Conf. Acoust. Speech Signal Process. (2010) 4094-4097.
4. P. G. Casazza, M. Fickus, Gradient descent of the frame potential, Proc. Sampl. Theory Appl. (2009) 4 pages.
3. G. Srinivasa, V. Oak, S. Garg, M. Fickus, J. Kovacevic, Voting-based active contour segmentation of fMRI images of the brain, Proc. IEEE Int. Conf. Image Process. (2008)
1100-1103.
2. G. Srinivasa, M. Fickus, M. N. Gonzalez-Rivero, S. Hsieh, Y. Guo, A. Linstedt, J. Kovacevic, Active mask segmentation for the cell-volume computation and Golgi-body
segmentation of HeLa cell images, Proc. IEEE Int. Symp. Biomed. Imaging (2008) 348-351.
1. P. G. Casazza, M. Fickus, J. C. Tremain, E. Weber, The Kadison-Singer Problem in mathematics and engineering, Contemp. Math. 414 (2006) 299-355.
Conference Proceedings, Accepted via Peer-Review of the Abstract:
16. M. Fickus, J. Jasper, D. G. Mixon, C. E.Watson, A brief introduction to equi-chordal and equi-isoclinic tight fusion frames, Proc. SPIE 10394 (2017) 103940T/1–9.
15. M. Fickus, J. Jasper, D. G. Mixon, J. Peterson, Quasi-symmetric designs and equiangular tight frames, Proc. SPIE 9597 (2015) 95970F/1-8.
14. M. Fickus, C. E. Watson, Detailing the equivalence between real equiangular tight frames and certain strongly regular graphs, Proc. SPIE 9597 (2015) 959719/1-10.
13. R. Tervo, M. Hawks, G. Perram, M. Fickus, Effects of optical aberration on chromotomographic reconstruction, Proc. SPIE 9088 (2014) 908817/1-11.
12. P. G. Casazza, M. Fickus, A. Heinecke, Y. Wang, Z. Zhou, Spectral tetris fusion frame constructions, Proc. SPIE 8138 (2011) 813816/1-6.
11. M. L. Massar, R. Bhagavatula, J. A. Ozolek, C. A. Castro, M. Fickus, J. Kovacevic, A domain-knowledge-inspired mathematical framework for the description and classification
of H&E stained histopathology images, Proc. SPIE 8138 (2011) 81380U/1-7.
10. M. Fickus, D. G. Mixon, Deterministic matrices with the restricted isometry property, Proc. SPIE 8138 (2011) 81380A/1-6.
9. M. Fickus, D. G. Mixon, M. J. Poteet, Frame completions for optimally robust reconstruction, Proc. SPIE 8138 (2011) 81380Q/1-8.
8. M. L. Massar, R. Bhagavatula, M. Fickus, J. Kovacevic, Local histograms for classifying H&E stained tissues, Proc. South. Biomed. Eng. Conf. (2010) 348-352.
7. P. G. Casazza, M. Fickus, D. G. Mixon, Y. Wang, Z. Zhou, Constructions and existence of tight fusion frames, Proc. SPIE 7446 (2009) 744613/1-10.
6. G. Srinivasa, M. Fickus, J. Kovacevic, Multiresolution multiscale active mask segmentation of fluorescence microscope images, Proc. SPIE 7446 (2009) 744603/1-7.
5. R. Ewing, D. Quinn, Y. Zheng, M. Fickus, M. Oxley, J. Morrison, G. Seetharaman, R. Matungka, V. Sandor, Image registration using polar wavelets, Proc. IEEE Natl. Aerosp.
Electron. Conf. (2008) 316-321.
4. G. Srinivasa, M. Fickus, J. Kovacevic, Active contour-based multiresolution transforms for the segmentation of fluorescence microscope images, Proc. SPIE 6701 (2007)
67010I/1-15.
3. M. Fickus, G. S. Seetharaman, M. E. Oxley, Multiscale moment transforms over the integer lattice, Proc. SPIE 6701 (2007) 67011N/1-8.
2. P. G. Casazza, M. Fickus, Chirps on finite cyclic groups, Proc. SPIE 5914 (2005), 5914N/1-6.
1. P. G. Casazza, M. Fickus, J. Kovacevic, M. Leon, J. C. Tremain, Physical laws governing finite tight frames, Proc. SPIE 5207 (2003) 371-380.