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Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：Fourier analysis on finite abelian groups and the uncertainty principles
有限阿贝尔群 傅里叶分析 不确定性原理
2023/4/18
Let G be a finite abelian group. If f: G → C is a nonzero function with Fourier transform f , the Donoho-Stark uncertainty principle states that|supp(f)||supp(f )|≥|G|. The purpose of this talk is two...
Uncertainty Principles and Ideal Atomic Decomposition
Uncertainty Principles Ideal Atomic Decomposition
2015/8/21
Suppose a discrete-time signal S(t), 0 t is a superposition of atoms taken
from a combined time/frequency dictionary made of spike sequences 1ft= g and sinu- soids expf2iwt=N)=p
N. Can one re...
Robust Uncertainty Principles: Exact Signal Reconstruction from Highly Incomplete Frequency Information
Random matrices free probability sparsity trigonometric expansions uncertainty principle convex optimization duality in optimization total-variation minimization image reconstruction linear programming
2015/6/17
This paper considers the model problem of reconstructing an object from incomplete frequency samples. Consider a discrete-time signal f ∈ CN and a randomly chosen set of frequencies Ω. Is it pos...
Quantitative Robust Uncertainty Principles and Optimally Sparse Decompositions
Uncertainty principle applications of uncertainty principles random matrices eigenvalues of random matrices sparsity trigonometric expansion convex optimization duality in optimization basis pursuit wavelets linear programming
2015/6/17
In this paper, we develop a robust uncertainty principle for finite signals in CN which states that for nearly all choices T,Ω ⊂ {0, . . . , N − 1} such that |T| + |Ω| (log N...
Uncertainty principles for integral operators
Uncertainty principles annihilating pairs Dunkl transform Fourier-Clifford transform integral operators
2012/6/25
The aim of this paper is to prove new uncertainty principles for an integral operator $\tt$ with a bounded kernel for which there is a Plancherel theorem. The first of these results is an extension of...
On Heisenberg and Local Uncertainty Principles for the $q$-Dunkl Transform
$q$-Dunkl transform Heisenberg-Weyl inequality Local uncertainty principles
2010/1/22
In this paper, we provide, for the q-Dunkl transform studied in [2], a Heisenberg uncertainty principle and two local uncertainty principles leading to a new Heisenberg-Weyl type inequality.
Heisenberg Uncertainty Principles for Some $q^2$-Analogue Fourier Transforms
Heisenberg inequality $q$-Fourier transforms
2010/1/22
The aim of this paper is to state -analogues of the Heisenberg uncertainty principles for some -analogue Fourier transforms introduced and studied in [7,8].