Current Development in Theory and Applications of Wavelets
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Abstract: The aim is to introduce an application of the novel
tool from Computational Harmonic Analysis (CHA) technology-wave atoms. Wave
atoms, encompassing both the wave atom orthobasis and the wave atom frame, have
some good properties, such as the uniformly bounded location in both time and
frequency, the parabolic scaling relationship, namely wavelength and most important, a significantly
sparser representation of the warped oscillatory functions or oriented textures
(e.g., Fingerprint, seismic profile, engineering surfaces) than other fixed
standard representations like wavelets, Gabor atoms, or curvelets. As a result,
we propose a variational image decomposition model using wave atoms and also
obtain a scale-dependent thresholding rule, which can be seen as a
complementarity of papers available. Finally, we give some experimental results
with our method.
