Reconstruction of vector and tensor fields from sampled discrete data

We construct atomic spaces S ⊂ L2(R, T 1 1 ) that are appropriate for the representation and processing of discrete tensor field data. We give conditions for these spaces to be well defined, atomic subspaces of the Wiener amalgam space W (C,L2(R, T 1 1 )) which is locally continuous and globally L2. We show that the sampling or discretization operator R from S to l2(Z, T 1 1 ) is a bounded linear operator. We introduce the dilated spaces S∆ = D∆ S parametrized by the coarseness ∆, and show that the discretization operator is also bounded with a bounded inverse for any ∆ ∈ Zn. This allows us to represent discrete tensor field data in terms of continuous tensor fields in S∆, and to obtain continous representations with fast filtering algorithms.

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