import numpy as np
from pylops.signalprocessing import Convolve2D
[docs]def Smoothing2D(nsmooth, dims, nodir=None, dtype='float64'):
r"""2D Smoothing.
Apply smoothing to model (and data) along two directions of a
multi-dimensional array depending on the choice of ``nodir``.
Parameters
----------
nsmooth : :obj:`tuple` or :obj:`list`
Lenght of smoothing operatorin 1st and 2nd dimensions (must be odd)
dims : :obj:`tuple`
Number of samples for each dimension
nodir : :obj:`int`, optional
Direction along which smoothing is NOT applied (set to None for 2d
arrays)
dtype : :obj:`str`, optional
Type of elements in input array.
Attributes
----------
shape : :obj:`tuple`
Operator shape
explicit : :obj:`bool`
Operator contains a matrix that can be solved explicitly (``True``) or
not (``False``)
See Also
--------
lops.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
:math:`n_{smooth, 1} \quad x \quad n_{smooth, 2}`:
Its application to a two dimensional input signal is:
.. math::
y[i,j] = 1/(n_{smooth, 1}*n_{smooth, 2})
\sum_{l=-(n_{smooth,1}-1)/2}^{(n_{smooth,1}-1)/2}
\sum_{m=-(n_{smooth,2}-1)/2}^{(n_{smooth,2}-1)/2} x[l,m]
Note that since the filter is symmetrical, the *Smoothing2D* operator is
self-adjoint.
"""
if isinstance(nsmooth, tuple):
nsmooth = list(nsmooth)
if nsmooth[0] % 2 == 0:
nsmooth[0] += 1
if nsmooth[1] % 2 == 0:
nsmooth[1] += 1
h = np.ones((nsmooth[0], nsmooth[1]))/float(nsmooth[0]*nsmooth[1])
return Convolve2D(np.prod(np.array(dims)), h=h,
offset=[(nsmooth[0]-1)/2, (nsmooth[1]-1)/2],
dims=dims, nodir=nodir, dtype=dtype)