Teaching
Publications
Qiyu Sun, Localized
nonlinear functional equations and two
sampling problems in signal processing Dorin Ervin Dutkay,
Deguang Han and Qiyu Sun, Divergence
of mock and scrambled Fourier series , submitted Michael Unser, Pouya
D. Tafti and Qiyu Sun, A
unified formulation of Gaussian vs. sparse stochastic process—Part I M. Z. Nashed and Qiyu
Sun, Function spaces
for sampling expansions Multiscale
Signal Analysis and Modelling ”, edited by X. Shen and A. Zayed,
Lecture Notes in Electrical Engineering, Springer. M. Z. Nashed, Qiyu Sun
and Jun Xian, Convolution
sampling and reconstruction of signals in a reproducing kernel
subspaces, Proceeding of
American Mathematical Society , Accepted Kyung Soo Rim, Chang
Eon Shin and Qiyu Sun, Stability
of localized integral operators on weighted $L^p$ spaces , Numerical Functional Analysis and
Optimization, special issue on Operator Algebra and Representation Theory: Frames, Wavelets and
Fractals, Accepted Qiyu Sun and Michael
Unser, Left-inverse
of fractional Laplacian and sparse stochastic processes Advances
in Computational Mathematics, 36(2012), 399-441. Qiyu Sun, Recovery
of sparsest signals via $\ell^q$-minimization , Applied and Computational Harmonic
Analysis, 32(2012), 329—341. Qiyu Sun, Sparse
approximation property and stable recovery of sparse signals from noisy
measurements, IEEE Trans.
Signal Processing, 19(2011), 5086-5090. Qiyu Sun, Wiener’s
lemma for infinite matrices II , Constructive Approximation, 34(2011), 209--235. Dorin Ervin Dutkay,
Deguang Han, Qiyu Sun, and Eric Weber, On
the Beurling dimension of exponential frames Advances in Mathematics, 226(2011),
285-297. Akram Aldroubi, Qiyu
Sun and Haichao Wang, Uncertainty
principles and Balian-Low type theorems in principal shift-invariant
spaces Applied and Computational Harmonic
Analysis, 30(2011), 337--347 Deguang Han, Qiyu Sun
and Wai-Shing Tang, Topological
and geometric properties of refinable functions and MRA affine frames , Applied and Computational Harmonic Analysis , 30(2011),
151-174. More
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Research
Activities
The candidacy
examination of Gayatri Ramesh for the degree of Doctor of Philosophy on
April 23, 2012. Co-chaired with Ram N. Mohapatra. Final examination of
Christopher Huff for the degree of Master of Science on March 27, 2012.
The thesis title is Applications
of Compressive Sensing To Surveillance Problems. Co-chaired with Ram
N. Mohapatra. Attended the 2012
Spring Eastern sectional meeting at George Washington University,
Washington DC, March 17-18 and gave a talk on “Nonlinear
Wiener’s lemma and its application to a sampling problem ” in the special session on Analysis of Wavelets, Frames and Fractals, which is organized
by Keri Kornelson and Judy
Packer. The article “Left-inverse
of fractional Laplacian and sparse stochastic processes ” with
Michael Unser was assigned in the paginated issue (Volume 37, 2012,
399-441) of the journal “Advances in Computational Mathematics” . The paper can be Download
from Journal Website free The article “Recovery
of sparsest signals via $\ell^q$-minimization ” was assigned in the
paginated issue (Volume 32, 2012, 329—341 )
of the journal Applied and
Computational Harmonic Analysis . This article is the third
most downloaded paper in the last 90 days according to the journal
website data on April 15, 2012. Guihui Song from Arizona State
University visited from February 21 to 27, 2012 and gave a colloquium
talk in the department.Chang-Eon
Shin from Sogang University, Korea visited from January 26 to
February 6, 2012.The article Convolution
sampling and reconstruction of signals in a reproducing kernel subspaces with M. Z. Nashed and Jun Xian
was accepted by the journal “Proceeding
of American Mathematical Society”. Attend the Joint
Mathematical meeting at Boston, January 4-7, 2012 and present a talk on sampling
signals with finite rate of innovation at SIAM Minisymposium on Sparsity in
Inverse Problems and Signal Processing. The article “Stability
of localized integral operators on weighted $L^p$ spaces ” with Operator Algebra and Representation
Theory: Frames, Wavelets and Fractal of the journal Numerical Functional Analysis and Optimization. Weekly learning
seminar on signals on finite rate of innovation started from October 28,
2011. Alexander Singh
Alvarado from, CNEL, University of Florida, visited on Oct. 13,
2011.The article “Sparse approximation
property and stable recovery of sparse signals from noisy measurements ” was assigned in the paginated
issue (Volume 19, No 10, 2011, pages 5086-5090 ) of the journal IEEE
Trans. Signal Processing Awarded by the National Science Foundation . Visit Sogang
University, Korea from August 7 to 14, 2011. The article “Wiener’s
lemma for infinite matrices II ” was assigned in the paginated issue
(Volume 34, Issue 2, 2011, pages 209-235) of the journal “Constructive
Approximation ” . Attend the International Conference on
Applied Harmonic Analysis and Multiscale Computing from July 25 to
July 28, 2011 at University of Alberta, and give a talk on Wiener’s
lemma and two nonlinear sampling problems in signal processing on July
26, 2011. The article “Recovery
of sparsest signals via $\ell^q$-minimization ” was accepted for the
publication in the journal Applied
and Computational Harmonic Analysis in
press . The article “Sparse
approximation property and stable recovery of sparse signals from noisy
measurements ” was
accepted for the publication in the journal IEEE
Trans. Signal Processing . More
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Academic
Services
Research
Interests
Wiener’s lemma Compressive Sampling (Average) Sampling
Theorem Multiband Wavelets Shift-invariant Spaces
Frame Theory Singular Integral
Operator
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