SHEARLET SHRINKAGE WITH INTEGRO-DIFFERENTIAL EQUATIONS USING 3-DIMENSIONAL CONTINUOUS SHEARLET TRANSFORM

SHEARLET SHRINKAGE WITH INTEGRO-DIFFERENTIAL EQUATIONS USING 3-DIMENSIONAL CONTINUOUS SHEARLET TRANSFORM

D. Kumar

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Abstract

The generalization of continuous wavelet, a directional multiscale is known as continuous shearlet which is able to study the directional functions and distributions. Many useful features do not carry from 2-dimensional to 3-dimensional cases due to the complexity of singularity sets de ned on surfaces rather than along curves. Therefore, we obtained a relation between 3-dimensional continuous shearlet transform and sum of smoothed partial derivative operators. The transform has been explained as a weighted average of pseudo-di erential equations. Our results are applicable in medical and seis- mic imaging related problems.

Keywords

Directional multiscale transform, shearlet shrinkage, integro-di erential equa- tions and smoothed partial operators.