Adaptive Multiresolution Analysis Structures and Shearlet Systems

Authors:
Bin Han;Gitta Kutyniok;Zuowei Shen
Affiliations:
bhan@ualberta.ca;kutyniok@math.uni-osnabrueck.de;matzuows@nus.edu.sg
Venue:
SIAM Journal on Numerical Analysis
Year:
2011

Citing 6
Cited 0

Approximation properties of multivariate wavelets

Mathematics of Computation
Compactly supported tight wavelet frames and orthonormal wavelets of exponential decay with a general dilation matrix

Journal of Computational and Applied Mathematics - Special issue: Approximation theory, wavelets, and numerical analysis
Linearized Bregman Iterations for Frame-Based Image Deblurring

SIAM Journal on Imaging Sciences
Full length article: Compactly supported shearlets are optimally sparse

Journal of Approximation Theory
An Accelerated Proximal Gradient Algorithm for Frame-Based Image Restoration via the Balanced Approach

SIAM Journal on Imaging Sciences
The contourlet transform: an efficient directional multiresolution image representation

IEEE Transactions on Image Processing

Quantified Score

Hi-index	0.00

Visualization

Abstract

In this paper, we first introduce the concept of an adaptive multiresolution analysis (AMRA) structure, which is a variant of the classical MRA structure well suited to the main goal of a fast flexible decomposition strategy adapted to the data at each decomposition level. We then study this novel methodology for the general case of affine-like systems and derive a unitary extension principle (UEP) for filter design. Finally, we apply our results to the directional representation system of shearlets. This leads to a comprehensive theory for fast decomposition algorithms associated with shearlet systems which encompasses tight shearlet frames with spatially compactly supported generators within such an AMRA structure. Also, shearlet-like systems associated with parabolic scaling and unimodular shear matrices are studied within this framework.