Curvelets and Shearlets
Directional multiscale systems for sparse image representation.
Curvelets and Shearlets. Directional multiscale systems for sparse image representation.
Foundations and canonical references
The standard treatments of curvelets and shearlets approach the subject from complementary angles. Kutyniok, Shearlets: Multiscale Analysis for Multivariate Data (2012) is the anchor reference for the subject and lays out the core definitions, theorems, and worked examples that practitioners return to.
Recent technical contributions
A handful of recent papers carry the methodological frontier of curvelets and shearlets forward. New tight frames of curvelets and optimal representations of objects with piecewise C2 singularities (Candes et al., 2004) is a primary reference for this area and develops new techniques or results that downstream work builds on.
Open methodological questions for curvelets and shearlets include sharpening the bridges between foundational theory and computational practice, extending classical results to broader or more structured settings, and integrating the techniques surveyed above with adjacent mathematical disciplines. The references listed in this page are the entry points that current work builds on.
Prerequisites
Sources
- paper · primary · 2004New tight frames of curvelets and optimal representations of objects with piecewise C2 singularitiescandes-2004, donoho-2004
- textbook · primary · 2012Shearlets: Multiscale Analysis for Multivariate Datakutyniok-2012, labate-2012
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