Digital Shearlet Transform
Gitta Kutyniok, Wang-Q Lim, Xiaosheng Zhuang

TL;DR
This paper introduces a unified digital shearlet theory that bridges continuum and digital representations, providing implementations and performance evaluation tools for shearlet transforms in image processing.
Contribution
It presents a comprehensive digital shearlet framework with implementations, enabling optimal sparse approximation of images and objective comparison with other transforms.
Findings
Unified digital and continuum shearlet theory developed.
Two shearlet transform implementations provided in Matlab.
Quantitative measures for performance comparison discussed.
Abstract
Over the past years, various representation systems which sparsely approximate functions governed by anisotropic features such as edges in images have been proposed. We exemplarily mention the systems of contourlets, curvelets, and shearlets. Alongside the theoretical development of these systems, algorithmic realizations of the associated transforms were provided. However, one of the most common shortcomings 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. In fact, shearlet systems are the only systems so far which satisfy this property, yet still deliver optimally sparse approximations of cartoon-like images. In this chapter, we provide an introduction to digital shearlet theory with a particular focus on a unified treatment of the continuum and…
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Taxonomy
TopicsSensor Technology and Measurement Systems · Optical measurement and interference techniques · Image and Signal Denoising Methods
