Some refined results on convergence of curvelet transform
Jouni Sampo
TL;DR
This paper proves that for functions with smooth regions separated by edges, the curvelet transform provides an approximation error that decreases proportionally to M^(-2) when using M-term non-linear approximation.
Contribution
It offers a refined proof establishing the convergence rate of curvelet-based approximation for functions with C^3 smoothness apart from edges.
Findings
Squared L^2 approximation error bounded by M^(-2)
Improved understanding of curvelet approximation efficiency
Theoretical validation of curvelet transform's convergence rate
Abstract
Article presents proof that M-term non-linear approximation of functions that are C^3 apart from C^3 edges in curvelet frame have squared L^2 approximation bounded by M^(-2).
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Taxonomy
TopicsAdvanced Numerical Analysis Techniques · Approximation Theory and Sequence Spaces · Mathematical Analysis and Transform Methods