Ridgelets and their Derivatives: Representation of Images with Edges
STANFORD UNIV CA DEPT OF STATISTICS
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This paper reviews the development of several recent tools from computational harmonic analysis. These new systems are presented under a coherent perspective, namely, the representation of bivariate functions that are singular along smooth curves edges. First, the representation of functions that are smooth away from straight edges is presented, and ridgelets will be shown to provide near optimal nonlinear approximations to these objects. Motivated by the limitations of the ridgelet methodology, new representation systems, namely, monoscale ridgelets and curvelets - both of which use the ridgelet transform as a building block - will be introduced. Curvelets are shown to provide concrete and constructive optimal nonlinear approximations to smooth functions with twice differentiable singularities. In addition, these approximations are obtained simply by thresholding the curvelet series.
- Numerical Mathematics
- Theoretical Mathematics