02-02-2015, 06:43 PM
edge directional image interpolation using shearlet transform ppt
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shearlet transform ppt
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edge directional image interpolation using shearlet transform ppt
20-03-2017, 10:10 AM
In the last years, diverse systems of representation have been proposed that approach scarcely the functions governed by anisotropic characteristics such as edges in the images. The systems of contourlets, curvelets and shearlets. Along with the theoretical development of these systems, algorithmic embodiments of the associated transforms were provided. However, one of the most common defects of these frames is the failure to provide a unified treatment of the continuous and digital world, ie, to allow a digital theory to be a natural digitization of continuum theory. In fact, shearlet systems are the only systems so far that satisfy this property, but still offer optimally scarce approximations of cartoon images. In this chapter, we offer an introduction to digital shearlet theory with a particular focus on a unified treatment of the digital continuum and realm. In our survey we present the implementation of two shearlet transformations, one based on limited band shearlets and the other based on compactly supported shearlets. In addition we will discuss several quantitative measures, which allow an objective comparison with other directional transformations and an objective adjustment of the parameters. The codes for the two transformations presented, as well as the framework for quantifying performance are provided in the Matlab ShearLab toolbox.
In recent years, shearlets have emerged among the most successful frameworks for efficient multidimensional data representation. In fact, after recognizing that traditional multiple-scale methods are not very efficient in edge trapping and other anisotropic features that frequently dominate multidimensional phenomena, several methods were introduced to overcome their limitations. The shearlet representation stands out as it offers a unique combination of some highly desirable properties: it has a unique or finite set of generating functions, provides optimally scattered representations for a large class of multidimensional data, it is possible to use compactly supported Fast algorithmic implementations and allows a unified treatment of the continuous and digital realms. In this chapter we present an autonomous overview of the main results concerning the theory and applications of shearlets.
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