pylops.Smoothing1D¶
- pylops.Smoothing1D(nsmooth, dims, axis=-1, dtype='float64')[source]¶
1D Smoothing.
Apply smoothing to model (and data) to a multi-dimensional array along
axis.- Parameters
Notes
The Smoothing1D operator is a special type of convolutional operator that convolves the input model (or data) with a constant filter of size \(n_\text{smooth}\):
\[\mathbf{f} = [ 1/n_\text{smooth}, 1/n_\text{smooth}, ..., 1/n_\text{smooth} ]\]When applied to the first direction:
\[y[i,j,k] = 1/n_\text{smooth} \sum_{l=-(n_\text{smooth}-1)/2}^{(n_\text{smooth}-1)/2} x[l,j,k]\]Similarly when applied to the second direction:
\[y[i,j,k] = 1/n_\text{smooth} \sum_{l=-(n_\text{smooth}-1)/2}^{(n_\text{smooth}-1)/2} x[i,l,k]\]and the third direction:
\[y[i,j,k] = 1/n_\text{smooth} \sum_{l=-(n_\text{smooth}-1)/2}^{(n_\text{smooth}-1)/2} x[i,j,l]\]Note that since the filter is symmetrical, the Smoothing1D operator is self-adjoint.
