pylops.Smoothing2D¶
-
pylops.
Smoothing2D
(nsmooth, dims, nodir=None, dtype='float64')[source]¶ 2D Smoothing.
Apply smoothing to model (and data) along two directions of a multi-dimensional array depending on the choice of
nodir
.Parameters: See also
pylops.signalprocessing.Convolve2D
- 2D convolution
Notes
The 2D Smoothing operator is a special type of convolutional operator that convolves the input model (or data) with a constant 2d filter of size \(n_{\text{smooth}, 1} \times n_{\text{smooth}, 2}\):
Its application to a two dimensional input signal is:
\[y[i,j] = 1/(n_{\text{smooth}, 1}\cdot n_{\text{smooth}, 2}) \sum_{l=-(n_{\text{smooth},1}-1)/2}^{(n_{\text{smooth},1}-1)/2} \sum_{m=-(n_{\text{smooth},2}-1)/2}^{(n_{\text{smooth},2}-1)/2} x[l,m]\]Note that since the filter is symmetrical, the Smoothing2D operator is self-adjoint.
Attributes: