Discrete shearlet transform: faithful digitization concept and its applications

Wang-Q Lim

doi:10.1117/12.893105

27 September 2011 Discrete shearlet transform: faithful digitization concept and its applications

Wang-Q Lim

Proceedings Volume 8138, Wavelets and Sparsity XIV; 813810 (2011) https://doi.org/10.1117/12.893105
Event: SPIE Optical Engineering + Applications, 2011, San Diego, California, United States

Abstract

Over the past years, various representation systems which sparsely approximate functions governed by anisotropic features such as edges in images have been proposed. Alongside the theoretical development of these systems, algorithmic realizations of the associated transforms were provided. However, one of the most common short-comings of these frameworks is the lack of providing a unified treatment of the continuum and digital world, i.e., allowing a digital theory to be a natural digitization of the continuum theory. Shearlets were introduced as means to sparsely encode anisotropic singularities of multivariate data while providing a unified treatment of the continuous and digital realm. In this paper, we introduce a discrete framework which allows a faithful digitization of the continuum domain shearlet transform based on compactly supported shearlets. Finally, we show numerical experiments demonstrating the potential of the discrete shearlet transform in several image processing applications.

Citation Download Citation

Wang-Q Lim "Discrete shearlet transform: faithful digitization concept and its applications", Proc. SPIE 8138, Wavelets and Sparsity XIV, 813810 (27 September 2011); https://doi.org/10.1117/12.893105

ACCESS THE FULL ARTICLE

INSTITUTIONAL
Select your institution to access the SPIE Digital Library.

SELECT YOUR INSTITUTION

PERSONAL
Sign in with your SPIE account to access your personal subscriptions or to use specific features such as save to my library, sign up for alerts, save searches, etc.

PERSONAL SIGN IN

No SPIE Account? Create one

PURCHASE THIS CONTENT

SUBSCRIBE TO DIGITAL LIBRARY

50 downloads per 1-year subscription

Members: $195

Non-members: $335 ADD TO CART

25 downloads per 1 - year subscription

Members: $145

Non-members: $250 ADD TO CART

PURCHASE SINGLE ARTICLE

Includes PDF, HTML & Video, when available