Universal Spatiotemporal Sampling Sets for Discrete Spatially Invariant Evolution Processes

作者：Tang Sui^*

来源：IEEE Transactions on Information Theory, 2017, 63(9): 5518-5528.

DOI：10.1109/TIT.2017.2696019

• Spatiotemporal sampling
• finite frames
• discrete fourier transform
• interpolation
• full spark matrix

Let (I,+) be a finite abelian group and A be a circular convolution operator on l(2)(I). The problem under consideration is how to construct minimal Omega subset of I and l(i) such that Y = {e(i), Ae(i), . . . , A(li) e(i) : i is an element of Omega} is a frame for l(2)(I), where {e(i) : i is an element of I} is the canonical basis of l(2)(I). This problem is motivated by the spatiotemporal sampling problem in discrete spatially invariant evolution processes. We will show that the cardinality of Omega should be at least equal to the largest geometric multiplicity of eigenvalues of A, and consider the universal spatiotemporal sampling sets (Omega, l(i)) for convolution operators whose eigenvalues subject to the same largest geometric multiplicity. We will give an algebraic characterization for such sampling sets and show how this problem is linked with sparse signal processing theory and polynomial interpolation theory.

• 出版日期2017-9