Shearlet shrinkage with integro-differential equations using 3-dimensional continuous shearlet transform

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 defined 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-differential equations. Our results are applicable in medical and seismic imaging related problems.