Positive Trigonometric Polynomials and Signal Processing Applications

By B. Dumitrescu. 2007

319 citations recorded by the source corpus.

Subfields: Computer Networks and Communications, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/729461c1402501457de24faa095fa494b739eb92

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In Computer Networks and Communications

In Statistical and Nonlinear Physics

Citations in the corpus

Regret Bounds for Robust Adaptive Control of the Linear Quadratic Regulator (2018, unknown): “Theorem G.1 (Theorem 5.8, [10]) .”
Finite-Data Performance Guarantees for the Output-Feedback Control of an Unknown System (2018, background): “ptimizationModel Let vec(F) := F T 0...F n−1 T , vec(F) := [F ...F n−1], and I be the (static) identity transfer function. Furthermore, appealing to the SDP characterization of H ∞-bounded FIRsystems([16]Thm. 5.8),deﬁne H(Q,F,γ) := Q vec(F) vec(F)T γI . Then,undertheapproximateassumptionthatR˜,N˜,”
Bispectrum Inversion with Application to Multireference Alignment (2017, background): “2 One example is a minimum phase signal in which the signal can be recovered from its power spectrum by solving a convex program [47].”
Atomic Norm Denoising With Applications to Line Spectral Estimation (2012, background): “[35, Theorem 4.24] For any given causal trigonometric polynomial and only if there exists complex Hermitian matrix Q such that Here, e 1 is the ﬁrst canonical basis vector with a one at the ﬁrst component and zeros elsewhere and v ∗ denotes the Hermitian adjoint (conjugate transpose) of v .”
Towards a Mathematical Theory of Super‐resolution (2012, background): “24 in [17] allows to express this constraint as the intersection between the cone of positive semidefinite matrices {X : X 0} and an affine hyperplane.”
Super-Resolution from Noisy Data (2012, unknown): “The dual can be recast as the semideﬁnite program (SDP) where X is an n × n Hermitian matrix, leveraging a corollary to Theorem 4.24 in [11] (see also [3,6,45]).”
On the Sample Complexity of the Linear Quadratic Regulator (2017, background): “8 of Dumitrescu’s text to take advantage of the FIR structure in our problem [17].”
Compressed Sensing Off the Grid (2012, methodology): “Thus, proofs based on Bochner’s Theorem [29], the bounded real lemma [30], [31], or spectral factorization [32] would also provide a tight characterization.”
Safely Learning to Control the Constrained Linear Quadratic Regulator (2018, background): “Next, considering the system norm constraints, theH∞ norm can be reduced to a compact SDP over Φx,Φu, γ as in Theorem 5.8 of Dumitrescu [26], described explicitly for this setting in Appendix G.3 of Dean et al. [7].”