Demetrio Labate

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

Sparse multidimensional representation using shearlets

C^2

A Shearlet Approach to Edge Analysis and Detection

except for discontinuities along

Resolution of the wavefront set using continuous shearlets

C^2

Shearlet-Based Total Variation Diffusion for Denoising

curves. More specifically, if

A unified characterization of reproducing systems generated by a finite family, II

f_N^S

Wavelets with composite dilations

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

Characterization and Analysis of Edges Using the Continuous Shearlet Transform

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

The Theory of Wavelets with Composite Dilations

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

3-D Discrete Shearlet Transform and Video Processing

N^{-1}