import logging
import numpy as np
from pylops.basicoperators import BlockDiag, Diagonal, HStack, Restriction
from pylops.signalprocessing.Sliding2D import _slidingsteps
from pylops.utils.tapers import taper2d
logging.basicConfig(format="%(levelname)s: %(message)s", level=logging.WARNING)
[docs]def Patch2D(Op, dims, dimsd, nwin, nover, nop, tapertype="hanning", design=False):
"""2D Patch transform operator.
Apply a transform operator ``Op`` repeatedly to patches of the model
vector in forward mode and patches of the data vector in adjoint mode.
More specifically, in forward mode the model vector is divided into
patches, each patch is transformed, and patches are then recombined
together. Both model and data are internally reshaped and
interpreted as 2-dimensional arrays: each patch contains a portion
of the array in both the first and second dimension.
This operator can be used to perform local, overlapping transforms (e.g.,
:obj:`pylops.signalprocessing.FFT2D`
or :obj:`pylops.signalprocessing.Radon2D`) on 2-dimensional arrays.
.. note:: The shape of the model has to be consistent with
the number of windows for this operator not to return an error. As the
number of windows depends directly on the choice of ``nwin`` and
``nover``, it is recommended to use ``design=True`` if unsure about the
choice ``dims`` and use the number of windows printed on screen to
define such input parameter.
.. warning:: Depending on the choice of `nwin` and `nover` as well as the
size of the data, patches may not cover the entire size of the data.
The start and end indices of each window can be displayed using
``design=True`` while defining the best patching approach.
Parameters
----------
Op : :obj:`pylops.LinearOperator`
Transform operator
dims : :obj:`tuple`
Shape of 2-dimensional model. Note that ``dims[0]`` and ``dims[1]``
should be multiple of the model size of the transform in their
respective dimensions
dimsd : :obj:`tuple`
Shape of 2-dimensional data
nwin : :obj:`tuple`
Number of samples of window
nover : :obj:`tuple`
Number of samples of overlapping part of window
nop : :obj:`tuple`
Size of model in the transformed domain
tapertype : :obj:`str`, optional
Type of taper (``hanning``, ``cosine``, ``cosinesquare`` or ``None``)
design : :obj:`bool`, optional
Print number of sliding window (``True``) or not (``False``)
Returns
-------
Sop : :obj:`pylops.LinearOperator`
Sliding operator
Raises
------
ValueError
Identified number of windows is not consistent with provided model
shape (``dims``).
See Also
--------
Sliding2d: 2D Sliding transform operator.
"""
# model windows
mwin0_ins, mwin0_ends = _slidingsteps(dims[0], nop[0], 0)
mwin1_ins, mwin1_ends = _slidingsteps(dims[1], nop[1], 0)
# data windows
dwin0_ins, dwin0_ends = _slidingsteps(dimsd[0], nwin[0], nover[0])
dwin1_ins, dwin1_ends = _slidingsteps(dimsd[1], nwin[1], nover[1])
nwins0 = len(dwin0_ins)
nwins1 = len(dwin1_ins)
nwins = nwins0 * nwins1
# create tapers
if tapertype is not None:
tap = taper2d(nwin[1], nwin[0], nover, tapertype=tapertype).astype(Op.dtype)
taps = {itap: tap for itap in range(nwins)}
# topmost tapers
taptop = tap.copy()
taptop[: nover[0]] = tap[nwin[0] // 2]
for itap in range(0, nwins1):
taps[itap] = taptop
# bottommost tapers
tapbottom = tap.copy()
tapbottom[-nover[0] :] = tap[nwin[0] // 2]
for itap in range(nwins - nwins1, nwins):
taps[itap] = tapbottom
# leftmost tapers
tapleft = tap.copy()
tapleft[:, : nover[1]] = tap[:, nwin[1] // 2][:, np.newaxis]
for itap in range(0, nwins, nwins1):
taps[itap] = tapleft
# rightmost tapers
tapright = tap.copy()
tapright[:, -nover[1] :] = tap[:, nwin[1] // 2][:, np.newaxis]
for itap in range(nwins1 - 1, nwins, nwins1):
taps[itap] = tapright
# lefttopcorner taper
taplefttop = tap.copy()
taplefttop[:, : nover[1]] = tap[:, nwin[1] // 2][:, np.newaxis]
taplefttop[: nover[0]] = taplefttop[nwin[0] // 2]
taps[0] = taplefttop
# righttopcorner taper
taprighttop = tap.copy()
taprighttop[:, -nover[1] :] = tap[:, nwin[1] // 2][:, np.newaxis]
taprighttop[: nover[0]] = taprighttop[nwin[0] // 2]
taps[nwins1 - 1] = taprighttop
# leftbottomcorner taper
tapleftbottom = tap.copy()
tapleftbottom[:, : nover[1]] = tap[:, nwin[1] // 2][:, np.newaxis]
tapleftbottom[-nover[0] :] = tapleftbottom[nwin[0] // 2]
taps[nwins - nwins1] = tapleftbottom
# rightbottomcorner taper
taprightbottom = tap.copy()
taprightbottom[:, -nover[1] :] = tap[:, nwin[1] // 2][:, np.newaxis]
taprightbottom[-nover[0] :] = taprightbottom[nwin[0] // 2]
taps[nwins - 1] = taprightbottom
# check that identified number of windows agrees with mode size
if design:
logging.warning("%d-%d windows required...", nwins0, nwins1)
logging.warning(
"model wins - start:%s, end:%s / start:%s, end:%s",
str(mwin0_ins),
str(mwin0_ends),
str(mwin1_ins),
str(mwin1_ends),
)
logging.warning(
"data wins - start:%s, end:%s / start:%s, end:%s",
str(dwin0_ins),
str(dwin0_ends),
str(dwin1_ins),
str(dwin1_ends),
)
if nwins0 * nop[0] != dims[0] or nwins1 * nop[1] != dims[1]:
raise ValueError(
"Model shape (dims=%s) is not consistent with chosen "
"number of windows. Choose dims[0]=%d and "
"dims[1]=%d for the operator to work with "
"estimated number of windows, or create "
"the operator with design=True to find out the"
"optimal number of windows for the current "
"model size..." % (str(dims), nwins0 * nop[0], nwins1 * nop[1])
)
# transform to apply
if tapertype is None:
OOp = BlockDiag([Op for _ in range(nwins)])
else:
OOp = BlockDiag(
[Diagonal(taps[itap].ravel(), dtype=Op.dtype) * Op for itap in range(nwins)]
)
hstack = HStack(
[
Restriction(
dimsd[1] * nwin[0],
range(win_in, win_end),
dims=(nwin[0], dimsd[1]),
dir=1,
dtype=Op.dtype,
).H
for win_in, win_end in zip(dwin1_ins, dwin1_ends)
]
)
combining1 = BlockDiag([hstack] * nwins0)
combining0 = HStack(
[
Restriction(
np.prod(dimsd),
range(win_in, win_end),
dims=dimsd,
dir=0,
dtype=Op.dtype,
).H
for win_in, win_end in zip(dwin0_ins, dwin0_ends)
]
)
Pop = combining0 * combining1 * OOp
return Pop