LULU Operators and Discrete Pulse Transform for Multidimensional Arrays

@article{Anguelov2010LULUOA,
  title={LULU Operators and Discrete Pulse Transform for Multidimensional Arrays},
  author={Roumen Anguelov and Inger Fabris-Rotelli},
  journal={IEEE Transactions on Image Processing},
  year={2010},
  volume={19},
  pages={3012-3023}
}
The LULU operators for sequences, that is Ln, Un and their compositions, are extended to multidimensional arrays in a way which preserves their essential properties, e.g., consistent separation, total variation and shape preservation. The power of the operators is demonstrated by deriving the discrete pulse transform (DPT), which is a hierarchical decomposition of the input array into pulses. Similar to its 1-D counterpart this transform satisfies a basic consistency property. 

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