A Friendly Guide to the Proof of Optimal Approximation for Compactly Supported Shearlets
نویسنده
چکیده
This report provides an expository summary of the proof of optimal shearlet approximation (compact support case). We only discuss the non-smooth part of the approximation. For further details, the readers are referred to [1], [2] and the references therein. I. COMPACTLY SUPPORTED SHEARLET FRAME A. Some Notations • parabolic scaling matrices: A2j = 2j 0 0 2 or Ã2j = 2j/2 0 0 2 , for j ∈ Z. • shear matrices: Sk = 1 k 0 1 or S k = 1 0 k 1 , for k ∈ Z. • partition of frequency plane: R = ( 4 ∪ l=1 Cl )∪ R, where the four cones {Cl}l=1 are defined as Cl = {(ξ1, ξ2) ∈ R : ξ1 ≥ 1, |ξ2/ξ1| ≤ 1} l = 1 {(ξ1, ξ2) ∈ R : ξ2 ≥ 1, |ξ1/ξ2| ≤ 1} l = 2 {(ξ1, ξ2) ∈ R : ξ1 ≤ −1, |ξ2/ξ1| ≤ 1} l = 3 {(ξ1, ξ2) ∈ R : ξ2 ≤ −1, |ξ1/ξ2| ≤ 1} l = 4 December 12, 2011 DRAFT
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