The convolution is done with the filter *h* by keeping one sample out
of two (see figure 14.7):

(14.38) |

To reconstruct *c*_{j} from *c*_{j+1}, we need to calculate the difference
signal *w*_{j+1}.

(14.39) |

where is the signal reconstructed by the following operation (see figure 14.8):

(14.40) |

In two dimensions, the method is similar. The convolution is done
by keeping one sample out of two in the two directions. We have:

(14.41) |

and is:

(14.42) |

The number of samples is divided by four. If the image size is , then the pyramid size is . We get a pyramidal structure (see figure 14.9).

The laplacian pyramid leads to an analysis with four wavelets [3] and there is no invariance to translation.