Kanghui Guo

OPTIMALLY SPARSE MULTIDIMENSIONAL REPRESENTATION USING SHEARLETS

In this paper we show that shearlets, an affine-like system of functions recently introduced by the authors and their collaborators, are essentially optimal in representing 2-dimensional functions f which are

Wavelets with composite dilations

C^2

Characterization and Analysis of Edges Using the Continuous Shearlet Transform

except for discontinuities along

The Theory of Wavelets with Composite Dilations

C^2

Optimally Sparse Representations of 3D Data with

curves. More specifically, if

C^2

f_N^S

Surface Singularities Using Parseval Frames of Shearlets

is the N-term reconstruction of f obtained by using the N largest coefficients in the shearlet representation, then the asymptotic approximation error decays as

Microlocal Analysis of Singularities from Directional Multiscale Representations

\norm{f-f_N^S}_2^2 \asymp N^{-2} (\log N)^3, N \to \infty,

Optimally sparse shearlet approximations of 3D data

which is essentially optimal, and greatly outperforms the corresponding asymptotic approximation rate

Optimal recovery of 3D X-ray tomographic data via shearlet decomposition

N^{-1}