Recent Publications

Title/Citation
Controlled scaling of Hilbert space frames for R^2

Peter G. Casazza and Shang Xu, 2020 submitted

An elementary proof of a fundamental result in phase retrieval

Peter G. Casazza (2020)

Phase retrieval by projections in R^n requires 2n-2 projections

Peter G. Casazza and Dorsa Ghoreishi, submitted (2020)

Optimal Parseval frames: Total coherence and total volume

Jameson Cahill and Peter G. Casazza, (2019) submitted.

Regular two distance sets

Peter G. Casazza, Tin T. Tran, and Janet C. Tremain, (2019) submitted.

A notion of optimal packings of subspaces with mixed-rank and solutions

Peter G. Casazza, John I. Haas IV, Joshua Stueck, and Tin T Tran, (2019) submitted.  

Constructions and properties of optimally spread subspace packings via symmetric and affine block designs and mutually unbiased bases

Peter G. Casazza, John I. Haas IV, Joshua Stueck, and Tin T. Tran, 2018 (submitted).
 

The exact constant for the l1 - l2 norm inequality

S. Bothello-Andrade, P.G. Casazza, D. Cheng, T. Tran, 2018, (submitted).

On the undefinability of Tsirelson's space and its descendants

 

Peter Casazza, Jose Iovino,  
2018 (submitted).

Phase Retrieval in l_2

Sara Botelho-Andrade, Peter G. Casazza, Desai Cheng, John Haas, Tin T. Tran, 2018, (submitted). 

Preserving Injectivity under Subgaussian Mappings and Its Application to Compressed Sensing

 

Peter G. Casazza, Xuemei Chen, Richard G. Lynch, 2018 (submitted).

 

Phase retrieval and norm retrieval by vectors and projections

P.G. Casazza and J.C. Tremain, 2018 (submitted).

The solution to the frame quantum detection problem

S. Bothello-Andrade, P.G. Casazza, D. Cheng, and T. Tran, 2018, accepted by JFAA.

Weighted fusion frame contruction via Spectral Tetris

Peter G. Casazza and Jesse Peterson, (2018) submitted.

Stability of Phase Retrievable Frames

R. Balan, Stability of Phase Retrievable Frames, to appear in the Houston Journal of Mathematics 2017

Excursions in Harmonic Analysis, vol.5

Excursions in Harmonic Analysis, vol.5, R. Balan, J.J. Benedetto, W. Czaja, M. Dellatorre, K.A. Okoudjou Eds., Birkhauser 2017.

Optimization methods for frame conditioning and application to graph Laplacian scaling

R. Balan, M. Begue, C. Clark, K. Okoudjou, Optimization methods for frame conditioning and application to graph Laplacian scaling, to appear in "Novel methods in harmonic analysis with applications to numerical analysis and data processing", Lecture Notes ANHA Series, I.Pesenson and all Eds., Birkhauser 2017

Associating vectors in C^n with rank-2 projections in R^(2n):with applications

P.Casazza, D.Cheng, Associating vectors in Cn with rank-2 projections in R(2n):with applications, submitted.

Constructions of biangular tight frames and their relationships with equiangular tight frames

P.Casazza,J.Cahill, J.Haas, J.Tremain, Constructions of biangular tight frames and their relationships with equiangular tight frames, arXiv:1703.01786

On the structures of Grassmannian frames

P.Casazza, J.Haas, On the structures of Grassmannian frames, arXiv:1703.01786

Norm retrieval phase retrieval projections

P.Casazza, D.Ghoreishi, S.Jose, J.Tremain, Norm retrieval and phase retrieval by projections, submitted.

Phase retrieval by hyperlanes

S.Botelho-Andrade, P.Casazza, D.Cheng, J.Haas, T.Tran, J.Tremain, and Z.Xu, Phase retrieval by hyperlanes, arXiv:1703.02678.

Real Phase Retrieval by orthogonal complements and hyperplanes

Sara Botelho-Andrade, Peter G. Casazza, Desai Cheng, John I. Haas, Tin T. Tran, Janet C. Tremain,
and Zhiqiang Xu, Proceedings of
SPIE (2017).

On Grassmannian frames with spectral constraints

P. Casazza and J. Haas, appeared in the special
extended issue of Sampta, 2017.

Weak phase retrieval

Sara Botelho-Andrade, Peter G. Casazza, Dorsa Ghoreishi, Shani Jose, and Janet
C. Tremain, 2017, (submitted)

Toward the classification of biangular harmonic frames

P.G.Casazza, A.Farzannia, J.Haas, T.T.Tran, Toward the classification of biangular harmonic frames, submitted, arXiv: 1610.03142.

Partitioning Hadamard vectors into Hadamard matrices

P.G.Casazza, J.C.Tremain, Partitioning Hadamard vectors into Hadamard matrices.

The unconditional constants for Hilbert space frame expansions

T.Bemrose, P.G.Casazza, V.Kaftal, R.G.Lynch, The unconditional constants for Hilbert space frame expansions, submitted, arXiv: 1602.03490.

Equiangular tight frames

M.Fickus, J.Jasper, D.G.Mixon, J.Patterson, J.Tremain, Equiangular tight frames, asXiv: 1602.03490.

Phase retrieval in infinite-dimensional Hilbert spaces

J.Cahill, P.G.Casazza, I.Daubechies, Phase retrieval in infinite-dimensional Hilbert spaces, submitted.

Reconstruction of Signals from Magnitudes of Redundant Representation: The Complex Case

R.Balan, Reconstruction of Signals from Magnitudes of Redundant Representation: The Complex Case, Apr. 2013, Foundations of Computational Mathematics, vol.16(3), (2016) 677-721.

Frames and Phaseless Reconstruction

R.Balan, Frames and Phaseless Reconstruction, AMS Short Course at the Joint Mathematics Meetings, San Antonio, January 2015, to appear in Proceedings of Symposia in Applied Mathematics, AMS 2016.

On Lipschitz Analysis and Lipschitz Synthesis for the Phase Retrieval Problem

R.Balan, D.Zhou, On Lipschitz Analysis and Lipschitz Synthesis for the Phase Retrieval Problem, to appear in Linear Algebra and Applications, 2016.

Group-theoretic constructions of erasure-robust frames

M. Fickus, J. Jasper. D. Mixon, J. Peterson, Group-theoretic constructions of erasure-robust frames, submitted.

Excursions in Harmonic Analysis, vol.3

Excursions in Harmonic Analysis, vol.3, R. Balan, M. Begue, J.J. Benedetto, W. Czaja, K.A. Okoudjou Eds., Birkhauser 2015.

Excursions in Harmonic Analysis, vol.4

Excursions in Harmonic Analysis, vol.4, R. Balan, M. Begue, J.J. Benedetto, W. Czaja, K.A. Okoudjou Eds., Birkhauser 2015.

A brief introduction to Hilbert space frame theory and its applications

P.G. Casazza, R.G. Lynch, A brief introduction to Hilbert space frame theory and its applications, submitted.

Projections and Phase Retrieval

D. Edidin, Projections and Phase Retrieval, arXiv:1506.00674, submitted,

Phase retrieval and norm retrieval

S. Bahmanpour, J. Cahill, P.G. Casazza, J. Jasper, L.M. Woodland, Phase retrieval and norm retrieval, Contemp. Math. (submitted).

An algebraic characterization of injectivity in phase retrieval

A. Conca, D. Edidin, M. Hering, C. Vinzant, An algebraic characterization of injectivity in phase retrieval, Appl. Comput. Harmon. Anal. in press (2014).

Phase retrieval from very few measurements

M. Fickus, D.G. Mixon, A.A. Nelson, Y. Wang, Phase retrieval from very few measurements, to appear in: Linear Algebra Appl.

Phase retrieval with polarization

B. Alexeev, A.S. Bandeira, M. Fickus, D.G. Mixon, Phase retrieval with polarization , SIAM J. Imaging Sci. 7 (2014) 35-66.

Kirkman equiangular tight frames and codes

J. Jasper, D.G. Mixon, M. Fickus, Kirkman equiangular tight frames and codes, IEEE Trans. Inform. Theory. 60 (2014) 170-181. 

Extensions of pure states and the Laurent operator

Y. Lonke, Extensions of pure states and the Laurent operator, M.Sc. Thesis, Hebrew University at Jerusalem - translated from Hebrew to English for the first time.

Saving phase: Injectivity and Stability for Phase Retrieval

A. Bandeira, J. Cahill, D. Mixon, A. Nelson, Saving phase: Injectivity and Stability for Phase Retrieval, submitted.

Phase retrieval by vectors and projections

P.G. Casazza and L.M. Woodland, Phase retrieval by vectors and projections, submitted.

Using Projections for Phase Retrieval

J. Cahill, P.G. Casazza, J. Peterson, L.Woodland, Using Projections for Phase Retrieval, Proceedings of SPIE, Optics and Photonics (2013).

Phase Retrieval by Projections

J. Cahill, P.G. Casazza, J. Peterson, L.Woodland, Phase Retrieval by Projections, submitted.

Excursions in Harmonic Analysis, vol.1

Excursions in Harmonic Analysis, vol.1, T.D. Andrews, R. Balan, J.J. Benedetto, W. Czaja, K.A. Okoudjou Eds., Birkhauser 2013.

Excursions in Harmonic Analysis, vol.2

Excursions in Harmonic Analysis, vol.2, T.D. Andrews, R. Balan, J.J. Benedetto, W. Czaja, K.A. Okoudjou Eds., Birkhauser 2013.

Spanning and independence properties of frame partitions

B. G. Bodmann, P. G. Casazza, V. I. Paulsen and D. Speegle, Spanning and independence properties of frame partitions, Proceedings of AMS 140, No. 7 (2012), p. 2193 - 2207

The Kadison-Singer and Paulsen problems in finite frame theory

P. C. Casazza, The Kadison-Singer and Paulsen problems in finite frame theory, in Finite Frames: Theory and Applications, Eds. P. G. Casazza and G. Kutyniok, Birkhäuser, Boston (2012).

Algebraic geometry and finite frames

J. Cahill, N. Strawn, Algebraic geometry and finite frames, in Finite Frames: Theory and Applications, Eds. P. G. Casazza and G. Kutyniok, Birkhäuser, Boston (2012).

Spanning and independence properties of finite frames

P. C. Casazza, D. Speegle, Spanning and independence properties of finite frames, in Finite Frames: Theory and Applications, Eds. P. G. Casazza and G. Kutyniok, Birkhäuser, Boston (2012).

An elementary representation of all real Hessenberg unitary matrices

J. C. Tremain, C. Vaidyanathan, An elementary representation of all real Hessenberg unitary matrices, preprint (2012).

The simplified version of the Spielman-Srivastava algorithm for proving the Bourgain-Tzafriri restricted invertibility theorem

P. G. Casazza, The simplified version of the Spielman-Srivastava algorithm for proving the Bourgain-Tzafriri restricted invertibility theorem, unpublished notes.

Necessary and sufficient conditions to perform spectral tetris

P. C. Casazza, A. Heinecke, K. Kornelson, Y. Wang, Z. Zhou, Necessary and sufficient conditions to perform spectral tetris, preprint (2012).

An elementary, illustrative proof of the Rado-Horn theorem

P. C. Casazza, J. Peterson, An elementary, illustrative proof of the Rado-Horn theorem, preprint (2012).

Operators and frames

J. Cahill, P. C. Casazza, G. Kutyniok, Operators and frames, preprint (2012).

Finite Frames: Theory and Applications

Eds. P.G. Casazza and G. Kutyniok, Finite Frames: Theory and Applications, Birkhäuser, Boston (2012). Amazon

Auto-tuning unit norm frames

P. G. Casazza, M. Fickus and D. G. Mixon, Auto-tuning unit norm frames, Appl. Comput. Harmon. Anal. 32 (2012), p 1-15.

Fusion frames

P. C. Casazza, G. Kutyniok, Fusion frames, in Finite Frames: Theory and Applications, Eds. P. G. Casazza and G. Kutyniok, Birkhäuser, Boston (2012).

The Kadison-Singer and Paulsen problems in finite frame theory

P. C. Casazza, The Kadison-Singer and Paulsen problems in finite frame theory, in Finite Frames: Theory and Applications, Eds. P. G. Casazza and G. Kutyniok, Birkhäuser, Boston (2012).

Spectral tetris fusion frame constructions

P. G. Casazza, M. Fickus, A. Heinecke, Y. Wang and Z. Zhou, Spectral tetris fusion frame constructions, Jour. Fourier Anal. and Appls. 18 No. 4 (2012) 828-851.

Introduction to finite frame theory

P. C. Casazza, G. Kutyniok, Introduction to finite frame theory, in Finite Frames: Theory and Applications, Eds. P. G. Casazza and G. Kutyniok, Birkhäuser, Boston (2012).

A quantitive notion of redundancy and its applications

B. G. Bodmann, P. G. Casazza and G. Kutyniok, A quantitive notion of redundancy and its applications, Proceedings of SampTA 2011, Singapore. 

Full spark frames

B. Alexeev, J. Cahill, D. G. Mixon, Full spark frames, preprint (2011).

Constructing a large family of equiangular tight frames

M. Fickus, D. G. Mixon, J. C. Tremain, Constructing a large family of equiangular tight frames, Proceedings of SampTA 2011, Singapore. 

Every Hilbert space frame has a Naimark complement

P. G. Casazza, M. Fickus, D. Mixon, J. Peterson and I. Smalyanau, Every Hilbert space frame has a Naimark complement, preprint (2011).

Algorithmic constructions of unitary matrices and tight frames

J. C. Tremain, Algorithmic constructions of unitary matrices and tight frames, preprint (2011).

The Paulsen problem in operator theory

J. Cahill and P. G. Casazza, The Paulsen problem in operator theory, submitted to Operators and Matrices (2011).

Constructing finite frames of a given spectrum and set of lengths

J. Cahill, M. Fickus, D. G. Mixon, M. J. Poteet and N. K. Strawn, Constructing finite frames of a given spectrum and set of lengths, submitted (2011).

A Quantitative Notion of Redundancy for Finite Frames

B. G. Bodmann, P. G. Casazza and G. Kutyniok, A Quantitative Notion of Redundancy for Finite Frames, Appl. and Comput. Harmonic Anal. 30 (2011) 348-362.

Fusion frames and the restricted isometry property

B. G. Bodmann, J. Cahill, P. G. Casazza, Fusion frames and the restricted isometry property, preprint (2011).

Fusion frames and unbiased basic sequences

B. G. Bodmann, P. G. Casazza, J. Peterson, I. Smalyanau, Fusion frames and unbiased basic sequences, preprint (2011).

Optimally sparse fusion frames: Existence and construction

P. G. Casazza, A. Heinecke, G. Kutyniok, Optimally sparse fusion frames: Existence and construction, Proceedings of SampTA 2011, Singapore.

Sparse Fusion Frames: Existence and Construction

R. Calderbank, P. G. Casazza, A. Heinecke, G. Kutyniok, and A. Pezeshki, Sparse Fusion Frames: Existence and Construction. Advances in Computational Mathematics, 35 No. 1 (2011) pp. 1-31.

Constructing tight fusion frames

P.G. Casazza, M. Fickus, D. Mixon, Y. Wang and Z. Zhou, Constructing tight fusion frames, Appl. Comput. Harmon. Anal. 30 (2011) 175-187.

Optimally Sparse Frames

P. GP. G. Casazza, A. Heinecke, F. Krahmer and G. Kutyniok, Optimally Sparse Frames, IEEE Trans. Inform.Theory 57 (2011), 7279-7287.. Casazza, A. Heinecke, F. Krahmer and G. Kutyniok, Optimally Sparse Frames, IEEE Trans. Inform.Theory 57 (2011), 7279-7287.

A notion of redundancy for infinite frames

J. Cahill, P. G. Casazza and A. Heinecke, A notion of redundancy for infinite frames, Proceedings of SampTA 2011, Singapore. 

Existence and Construction of Finite Frames with a Given Frame Operator

P.G. Casazza and M. Leon, Existence and Construction of Finite Frames with a Given Frame Operator, International Journal of Pure and Applied Mathematics, Vol. 63, No. 2 (2010), p. 149 - 158.

The road to equal-norm Parseval frames

B. G. Bodmann and P. G. Casazza, The road to equal-norm Parseval frames. Journal of Functional Analysis, Vol. 258 (2010) p. 397-420.

Upper and Lower Redundancy of Finite Frames

B. G. Bodmann, P. G. Casazza and G. Kutyniok, Upper and Lower Redundancy of Finite Frames. 43nd Annual Conference on Information Sciences and Systems (CISS) (Princeton University, NJ, 2010). 

Steiner equiangular tight frames

M. Fickus, D. G. Mixon, J. C. Tremain, Steiner equiangular tight frames, preprint submitted to Linear Algebra and Applications (2010). 

Non-orthogonal fusion frames and the sparsity of fusion frame operators

J. Cahill, P. G. Casazza, S. Li, Non-orthogonal fusion frames and the sparsity of fusion frame operators, submitted to JFAA.

The Bourgain-Tzafriri conjecture and concrete constructions of non-pavable projections

P. G. Casazza, M. Fickus, D.G. Mixon, and J.C. Tremain, The Bourgain-Tzafriri conjecture and concrete constructions of non-pavable projections, submitted to: Operators and Matrices (2010).

Gradient descent of the frame potential

P.G. Casazza and M. Fickus, Gradient descent of the frame potential, Proc. Sampl. Theory Appl. (2009). 

When are frames close to equal-norm Parseval frames?

B. Bodmann and P.G. Casazza, When are frames close to equal-norm Parseval frames?, preprint (2009). 

Sums of Hilbert Space Frames

P.G. Casazza, S. Obeidat, S. Samarah and J.C. Tremain, Sums of Hilbert Space Frames, J. Math. Analysis and Appl. Vol. 351, Issue 2 (2009), 579-585. 

Redundancy for localized and Gabor frames

R. Balan, P. Casazza and Z. Landau, Redundancy for localized and Gabor frames, preprint. 

Error Correction for Erasures of Quantized Frame Coefficients

B. Bodmann, P.G. Casazza, G. Kutyniok and S. Senger, Error Correction for Erasures of Quantized Frame Coefficients, SampTA'09 (Marseille, France, 2009), Proc., 2009. 

A Low Complexity Replacement Scheme for Erased Frame Coefficients

B. Bodmann, P.G. Casazza, G. Kutyniok and S. Senger, A Low Complexity Replacement Scheme for Erased Frame Coefficients, Wavelets XIII (San Diego, CA, 2009), 74460O-1 - 74460O-10, SPIE Proc. 7446, SPIE, Bellingham, WA, 2009. 

Revisiting the Bourgain-Tzafriri Restricted Invertibility Theorem

P.G. Casazza and J.C. Tremain, Revisiting the Bourgain-Tzafriri Restricted Invertibility Theorem, Operators and Matrices, Vol. 3, No. 1 (2009), 97-110.

Redundancy for localized frames

R. Balan, P.G. Casazza and Z. Landau, Redundancy for localized frames, Submitted (2009).

Concrete Constructions of Real Equiangular Line Sets

J.C. Tremain, Concrete Constructions of Real Equiangular Line Sets, preprint (2009).

Concrete Constructions of Equiangular Line Sets II

J.C. Tremain, Concrete Constructions of Equiangular Line Sets II, preprint (2009). 

A Mathematician's Survival Guide

P.G. Casazza, preprint.

Sums of Hilbert Space Frames

P.G. Casazza, S. Obeidat, S. Samarah and J.C. Tremain, Sums of Hilbert Space Frames, J. Math. Analysis and Appl. Vol. 351, Issue 2 (2009), 579-585

Infinite Dimensional Restricted Invertibility

P.G. Casazza and G.E. Pfander, Infinite Dimensional Restricted Invertibility, preprint.

The Bourgain-Tzafriri Conjecture for Operators with Small Coefficients

J.C. Tremain, The Bourgain-Tzafriri Conjecture for Operators with Small Coefficients, preprint (2009).

Concrete Constructions of Non-Pavable Projections

P.G. Casazza, M. Fickus, D. Mixon and J.C. Tremain, Concrete Constructions of Non-Pavable Projections, preprint (2009).

A Frame Theory Primer for the Kadison-Singer Problem

P.G. Casazza, A Frame Theory Primer for the Kadison-Singer Problem, Preprint (2009).

Constructing Fusion Frames with Desired Parameters

R. Calderbank, P. G. Casazza, A. Heinecke, G. Kutyniok, and A. Pezeshki, Constructing Fusion Frames with Desired Parameters. Wavelets XIII (San Diego, CA, 2009), 744612-1 - 744612-10, SPIE Proc. 7446, SPIE, Bellingham, WA, 2009.

Constructions and existence of tight fusion frames

P.G. Casazza, M. Fickus, D. Mixon, Y.Wang and Z. Zhou, Constructions and existence of tight fusion frames, Proc. SPIE. 7446 (2009) 744613/1-10.

Painless Reconstruction from Magnitudes of Frame Vectors

B. Balan, B.G.Bodmann, P.G. Casazza and D. Edidin, Painless Reconstruction from Magnitudes of Frame Vectors, J. Fourier Anal. Appl., Vol. 15, No. 4 (2009), 488-501.

Minimizing Fusion Frame Potentials

P.G. Casazza and M. Fickus, Minimizing Fusion Frame Potentials, Acta Applicandae Mathematicae, Volume 107, Numbers 1-3 (2009), pp. 7-24.

Redundancy for localized and Gabor frames

R. Balan, P. Casazza and Z. Landau, Redundancy for localized and Gabor frames, preprint.