GNGTS 2023 - Atti del 41° Convegno Nazionale

Session 3.3 ______ ___ GNGTS 2023 End-to-end self-supervised equivariant learning Figure 1: Equivariant imaging systems for seismic data interpolation To avoid the training datasets collection, we leverage the equivariant imaging strategy (Chen et al, 2021) to train a CNN . It is clear that for the CNN training, we need to impose the measurement consistency (4) However, this alone is not sufficient because it cannot capture information about m outside the range of the operator (Chen et al, 2021). In order to overcome this limitation, besides the measurement consistency, we introduce the equivariance of seismic data with respect to shift and undersampling. We assume that the seismic data is shift invariant, i.e. shifted undersampled data are equivalent to undersampled shifted data, or interpolated shifted data are equivalent to shifted interpolated data. As illustrated in Figure 1, based on this equivariance assumption, the composition should then be equivariant to the shift transformation (5)