Seislet-based morphological component analysis using scale-dependent exponential shrinkage |

Connections between seislet frame and seislet-MCA algorithm

The complete data is regarded to be superposition of several different geometrical components, and each component can be sparely represented using a seislet dictionary , i.e.,

(29) |

where is a combined seislet dictionary (i.e. seislet frame), and the backward operator is chosen to be

(30) |

in the sense that

(31) |

The difference between seislet-MCA algorithm and seislet frame minimization is the use of BCR technique (Bruce et al., 1998): We sparsify one component while keeping all others fixed. At the -th iteration applying the backward operator on the -th component leads to

(32) |

where the terms are the crosstalk between the -th component and the others. An intuitive approach to filter out the undesired crosstalk is shrinkage/thresholding. The proposed exponential shrinkage provides us a flexible control on the performance of the shrinkage/thresholding operator.

Seislet-based morphological component analysis using scale-dependent exponential shrinkage |

2021-08-31