__all__ = [
"patch3d_design",
"Patch3D",
]
import logging
from typing import Optional, Sequence, Tuple
import numpy as np
from pylops import LinearOperator
from pylops.basicoperators import BlockDiag, Diagonal, HStack, Restriction
from pylops.signalprocessing.sliding2d import _slidingsteps
from pylops.utils.tapers import tapernd
from pylops.utils.typing import InputDimsLike, NDArray
logging.basicConfig(format="%(levelname)s: %(message)s", level=logging.WARNING)
[docs]def patch3d_design(
dimsd: InputDimsLike,
nwin: Tuple[int, int, int],
nover: Tuple[int, int, int],
nop: Tuple[int, int, int],
) -> Tuple[
Tuple[int, int, int],
Tuple[int, int, int],
Tuple[Tuple[NDArray, NDArray], Tuple[NDArray, NDArray], Tuple[NDArray, NDArray]],
Tuple[Tuple[NDArray, NDArray], Tuple[NDArray, NDArray], Tuple[NDArray, NDArray]],
]:
"""Design Patch3D operator
This routine can be used prior to creating the :class:`pylops.signalprocessing.Patch3D`
operator to identify the correct number of windows to be used based on the dimension of the data (``dimsd``),
dimension of the window (``nwin``), overlap (``nover``),a and dimension of the operator acting in the model
space.
Parameters
----------
dimsd : :obj:`tuple`
Shape of 3-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.
Returns
-------
nwins : :obj:`tuple`
Number of windows.
dims : :obj:`tuple`
Shape of 3-dimensional model.
mwins_inends : :obj:`tuple`
Start and end indices for model patches (stored as tuple of tuples).
dwins_inends : :obj:`tuple`
Start and end indices for data patches (stored as tuple of tuples).
"""
# data windows
dwin0_ins, dwin0_ends = _slidingsteps(dimsd[0], nwin[0], nover[0])
dwin1_ins, dwin1_ends = _slidingsteps(dimsd[1], nwin[1], nover[1])
dwin2_ins, dwin2_ends = _slidingsteps(dimsd[2], nwin[2], nover[2])
dwins_inends = (
(dwin0_ins, dwin0_ends),
(dwin1_ins, dwin1_ends),
(dwin2_ins, dwin2_ends),
)
nwins0 = len(dwin0_ins)
nwins1 = len(dwin1_ins)
nwins2 = len(dwin2_ins)
nwins = (nwins0, nwins1, nwins2)
# model windows
dims = (nwins0 * nop[0], nwins1 * nop[1], nwins2 * nop[2])
mwin0_ins, mwin0_ends = _slidingsteps(dims[0], nop[0], 0)
mwin1_ins, mwin1_ends = _slidingsteps(dims[1], nop[1], 0)
mwin2_ins, mwin2_ends = _slidingsteps(dims[2], nop[2], 0)
mwins_inends = (
(mwin0_ins, mwin0_ends),
(mwin1_ins, mwin1_ends),
(mwin2_ins, mwin2_ends),
)
# print information about patching
logging.warning("%d-%d-%d windows required...", nwins0, nwins1, nwins2)
logging.warning(
"data wins - start:%s, end:%s / start:%s, end:%s / start:%s, end:%s",
dwin0_ins,
dwin0_ends,
dwin1_ins,
dwin1_ends,
dwin2_ins,
dwin2_ends,
)
logging.warning(
"model wins - start:%s, end:%s / start:%s, end:%s / start:%s, end:%s",
mwin0_ins,
mwin0_ends,
mwin1_ins,
mwin1_ends,
mwin2_ins,
mwin2_ends,
)
return nwins, dims, mwins_inends, dwins_inends
[docs]def Patch3D(
Op,
dims: InputDimsLike,
dimsd: InputDimsLike,
nwin: Tuple[int, int, int],
nover: Tuple[int, int, int],
nop: Tuple[int, int, int],
tapertype: str = "hanning",
scalings: Optional[Sequence[float]] = None,
name: str = "P",
) -> LinearOperator:
"""3D 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 3-dimensional arrays: each patch contains a portion
of the array in every axis.
This operator can be used to perform local, overlapping transforms (e.g.,
:obj:`pylops.signalprocessing.FFTND`
or :obj:`pylops.signalprocessing.Radon3D`) on 3-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 first run ``patch3d_design`` to obtain
the corresponding ``dims`` and number of windows.
.. warning:: Depending on the choice of `nwin` and `nover` as well as the
size of the data, sliding windows may not cover the entire data.
The start and end indices of each window will be displayed and returned
with running ``patch3d_design``.
Parameters
----------
Op : :obj:`pylops.LinearOperator`
Transform operator
dims : :obj:`tuple`
Shape of 3-dimensional model. Note that ``dims[0]``, ``dims[1]``
and ``dims[2]`` should be multiple of the model size of the
transform in their respective dimensions
dimsd : :obj:`tuple`
Shape of 3-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``)
scalings : :obj:`tuple` or :obj:`list`, optional
Set of scalings to apply to each patch. If ``None``, no scale will be
applied
name : :obj:`str`, optional
Name of operator (to be used by :func:`pylops.utils.describe.describe`)
Returns
-------
Sop : :obj:`pylops.LinearOperator`
Sliding operator
Raises
------
ValueError
Identified number of windows is not consistent with provided model
shape (``dims``).
See Also
--------
Sliding1D: 1D Sliding transform operator.
Sliding2D: 2D Sliding transform operator.
Sliding3D: 3D Sliding transform operator.
Patch2D: 2D Patching transform operator.
"""
# data windows
dwin0_ins, dwin0_ends = _slidingsteps(dimsd[0], nwin[0], nover[0])
dwin1_ins, dwin1_ends = _slidingsteps(dimsd[1], nwin[1], nover[1])
dwin2_ins, dwin2_ends = _slidingsteps(dimsd[2], nwin[2], nover[2])
nwins0 = len(dwin0_ins)
nwins1 = len(dwin1_ins)
nwins2 = len(dwin2_ins)
nwins = nwins0 * nwins1 * nwins2
# check patching
if (
nwins0 * nop[0] != dims[0]
or nwins1 * nop[1] != dims[1]
or nwins2 * nop[2] != dims[2]
):
raise ValueError(
f"Model shape (dims={dims}) is not consistent with chosen "
f"number of windows. Run patch3d_design to identify the "
f"correct number of windows for the current "
"model size..."
)
# create tapers
if tapertype is not None:
tap = tapernd(nwin, nover, tapertype=tapertype).astype(Op.dtype)
taps = {itap: tap for itap in range(nwins)}
# 1, sides
# topmost tapers
taptop = tap.copy()
taptop[: nover[0]] = tap[nwin[0] // 2]
for itap in range(0, nwins1 * nwins2):
taps[itap] = taptop
# bottommost tapers
tapbottom = tap.copy()
tapbottom[-nover[0] :] = tap[nwin[0] // 2]
for itap in range(nwins - nwins1 * nwins2, nwins):
taps[itap] = tapbottom
# frontmost tapers
tapfront = tap.copy()
tapfront[:, :, : nover[2]] = tap[:, :, nwin[2] // 2][:, :, np.newaxis]
for itap in range(0, nwins, nwins2):
taps[itap] = tapfront
# backmost tapers
tapback = tap.copy()
tapback[:, :, -nover[2] :] = tap[:, :, nwin[2] // 2][:, :, np.newaxis]
for itap in range(nwins2 - 1, nwins, nwins2):
taps[itap] = tapback
# leftmost tapers
tapleft = tap.copy()
tapleft[:, : nover[1]] = tap[:, nwin[1] // 2][:, np.newaxis, :]
for itap in range(0, nwins, nwins1 * nwins2):
for i in range(nwins2):
taps[itap + i] = tapleft
# rightmost tapers
tapright = tap.copy()
tapright[:, -nover[1] :] = tap[:, nwin[1] // 2][:, np.newaxis, :]
for itap in range(nwins2 * (nwins1 - 1), nwins, nwins2 * nwins1):
for i in range(nwins2):
taps[itap + i] = tapright
# 2. pillars
# topleftmost tapers
taplefttop = tap.copy()
taplefttop[:, : nover[1]] = tap[:, nwin[1] // 2][:, np.newaxis, :]
taplefttop[: nover[0]] = taplefttop[nwin[0] // 2]
for itap in range(nwins2):
taps[itap] = taplefttop
# toprightmost tapers
taprighttop = tap.copy()
taprighttop[:, -nover[1] :] = tap[:, nwin[1] // 2][:, np.newaxis, :]
taprighttop[: nover[0]] = taprighttop[nwin[0] // 2]
for itap in range(nwins2):
taps[nwins2 * (nwins1 - 1) + itap] = taprighttop
# topfrontmost tapers
tapfronttop = tap.copy()
tapfronttop[:, :, : nover[2]] = tap[:, :, nwin[2] // 2][:, :, np.newaxis]
tapfronttop[: nover[0]] = tapfronttop[nwin[0] // 2]
for itap in range(0, nwins1 * nwins2, nwins2):
taps[itap] = tapfronttop
# topbackmost tapers
tapbacktop = tap.copy()
tapbacktop[:, :, -nover[2] :] = tap[:, :, nwin[2] // 2][:, :, np.newaxis]
tapbacktop[: nover[0]] = tapbacktop[nwin[0] // 2]
for itap in range(nwins2 - 1, nwins1 * nwins2, nwins2):
taps[itap] = tapbacktop
# bottomleftmost tapers
tapleftbottom = tap.copy()
tapleftbottom[:, : nover[1]] = tap[:, nwin[1] // 2][:, np.newaxis, :]
tapleftbottom[-nover[0] :] = tapleftbottom[nwin[0] // 2]
for itap in range(nwins2):
taps[(nwins0 - 1) * nwins1 * nwins2 + itap] = tapleftbottom
# bottomrightmost tapers
taprightbottom = tap.copy()
taprightbottom[:, -nover[1] :] = tap[:, nwin[1] // 2][:, np.newaxis, :]
taprightbottom[-nover[0] :] = taprightbottom[nwin[0] // 2]
for itap in range(nwins2):
taps[
(nwins0 - 1) * nwins1 * nwins2 + (nwins1 - 1) * nwins2 + itap
] = taprightbottom
# bottomfrontmost tapers
tapfrontbottom = tap.copy()
tapfrontbottom[:, :, : nover[2]] = tap[:, :, nwin[2] // 2][:, :, np.newaxis]
tapfrontbottom[-nover[0] :] = tapfrontbottom[nwin[0] // 2]
for itap in range(0, nwins1 * nwins2, nwins2):
taps[(nwins0 - 1) * nwins1 * nwins2 + itap] = tapfrontbottom
# bottombackmost tapers
tapbackbottom = tap.copy()
tapbackbottom[:, :, -nover[2] :] = tap[:, :, nwin[2] // 2][:, :, np.newaxis]
tapbackbottom[-nover[0] :] = tapbackbottom[nwin[0] // 2]
for itap in range(0, nwins1 * nwins2, nwins2):
taps[(nwins0 - 1) * nwins1 * nwins2 + nwins2 + itap - 1] = tapbackbottom
# leftfrontmost tapers
tapleftfront = tap.copy()
tapleftfront[:, : nover[1]] = tap[:, nwin[1] // 2][:, np.newaxis, :]
tapleftfront[:, :, : nover[2]] = tapleftfront[:, :, nwin[2] // 2][
:, :, np.newaxis
]
for itap in range(0, nwins, nwins1 * nwins2):
taps[itap] = tapleftfront
# rightfrontmost tapers
taprightfront = tap.copy()
taprightfront[:, -nover[1] :] = tap[:, nwin[1] // 2][:, np.newaxis, :]
taprightfront[:, :, : nover[2]] = taprightfront[:, :, nwin[2] // 2][
:, :, np.newaxis
]
for itap in range(0, nwins, nwins1 * nwins2):
taps[(nwins1 - 1) * nwins2 + itap] = taprightfront
# leftbackmost tapers
tapleftback = tap.copy()
tapleftback[:, : nover[1]] = tap[:, nwin[1] // 2][:, np.newaxis, :]
tapleftback[:, :, -nover[2] :] = tapleftback[:, :, nwin[2] // 2][
:, :, np.newaxis
]
for itap in range(0, nwins, nwins1 * nwins2):
taps[nwins2 + itap - 1] = tapleftback
# rightbackmost tapers
taprightback = tap.copy()
taprightback[:, -nover[1] :] = tap[:, nwin[1] // 2][:, np.newaxis, :]
taprightback[:, :, -nover[2] :] = taprightback[:, :, nwin[2] // 2][
:, :, np.newaxis
]
for itap in range(0, nwins, nwins1 * nwins2):
taps[(nwins1 - 1) * nwins2 + nwins2 + itap - 1] = taprightback
# 3. corners
# lefttopfrontcorner taper
taplefttop = tap.copy()
taplefttop[: nover[0]] = tap[nwin[0] // 2]
taplefttop[:, : nover[1]] = taplefttop[:, nwin[1] // 2][:, np.newaxis, :]
taplefttop[:, :, : nover[2]] = taplefttop[:, :, nwin[2] // 2][:, :, np.newaxis]
taps[0] = taplefttop
# lefttopbackcorner taper
taplefttop = tap.copy()
taplefttop[: nover[0]] = tap[nwin[0] // 2]
taplefttop[:, : nover[1]] = taplefttop[:, nwin[1] // 2][:, np.newaxis, :]
taplefttop[:, :, -nover[2] :] = taplefttop[:, :, nwin[2] // 2][:, :, np.newaxis]
taps[nwins2 - 1] = taplefttop
# righttopfrontcorner taper
taprighttop = tap.copy()
taprighttop[: nover[0]] = tap[nwin[0] // 2]
taprighttop[:, -nover[1] :] = taprighttop[:, nwin[1] // 2][:, np.newaxis, :]
taprighttop[:, :, : nover[2]] = taprighttop[:, :, nwin[2] // 2][
:, :, np.newaxis
]
taps[(nwins1 - 1) * nwins2] = taprighttop
# righttopbackcorner taper
taprighttop = tap.copy()
taprighttop[: nover[0]] = tap[nwin[0] // 2]
taprighttop[:, -nover[1] :] = taprighttop[:, nwin[1] // 2][:, np.newaxis, :]
taprighttop[:, :, -nover[2] :] = taprighttop[:, :, nwin[2] // 2][
:, :, np.newaxis
]
taps[(nwins1 - 1) * nwins2 + nwins2 - 1] = taprighttop
# leftbottomfrontcorner taper
tapleftbottom = tap.copy()
tapleftbottom[-nover[0] :] = tap[nwin[0] // 2]
tapleftbottom[:, : nover[1]] = tapleftbottom[:, nwin[1] // 2][:, np.newaxis, :]
tapleftbottom[:, :, : nover[2]] = tapleftbottom[:, :, nwin[2] // 2][
:, :, np.newaxis
]
taps[(nwins0 - 1) * nwins1 * nwins2] = tapleftbottom
# leftbottombackcorner taper
tapleftbottom = tap.copy()
tapleftbottom[-nover[0] :] = tap[nwin[0] // 2]
tapleftbottom[:, : nover[1]] = tapleftbottom[:, nwin[1] // 2][:, np.newaxis, :]
tapleftbottom[:, :, -nover[2] :] = tapleftbottom[:, :, nwin[2] // 2][
:, :, np.newaxis
]
taps[(nwins0 - 1) * nwins1 * nwins2 + nwins2 - 1] = tapleftbottom
# rightbottomfrontcorner taper
taprightbottom = tap.copy()
taprightbottom[-nover[0] :] = tap[nwin[0] // 2]
taprightbottom[:, -nover[1] :] = taprightbottom[:, nwin[1] // 2][
:, np.newaxis, :
]
taprightbottom[:, :, : nover[2]] = taprightbottom[:, :, nwin[2] // 2][
:, :, np.newaxis
]
taps[(nwins0 - 1) * nwins1 * nwins2 + (nwins1 - 1) * nwins2] = taprightbottom
# rightbottombackcorner taper
taprightbottom = tap.copy()
taprightbottom[-nover[0] :] = tap[nwin[0] // 2]
taprightbottom[:, -nover[1] :] = taprightbottom[:, nwin[1] // 2][
:, np.newaxis, :
]
taprightbottom[:, :, -nover[2] :] = taprightbottom[:, :, nwin[2] // 2][
:, :, np.newaxis
]
taps[
(nwins0 - 1) * nwins1 * nwins2 + (nwins1 - 1) * nwins2 + nwins2 - 1
] = taprightbottom
# define scalings
if scalings is None:
scalings = [1.0] * nwins
# transform to apply
if tapertype is None:
OOp = BlockDiag([scalings[itap] * Op for itap in range(nwins)])
else:
OOp = BlockDiag(
[
scalings[itap] * Diagonal(taps[itap].ravel(), dtype=Op.dtype) * Op
for itap in range(nwins)
]
)
hstack2 = HStack(
[
Restriction(
(nwin[0], nwin[1], dimsd[2]),
range(win_in, win_end),
axis=2,
dtype=Op.dtype,
).H
for win_in, win_end in zip(dwin2_ins, dwin2_ends)
]
)
combining2 = BlockDiag([hstack2] * (nwins1 * nwins0))
hstack1 = HStack(
[
Restriction(
(nwin[0], dimsd[1], dimsd[2]),
range(win_in, win_end),
axis=1,
dtype=Op.dtype,
).H
for win_in, win_end in zip(dwin1_ins, dwin1_ends)
]
)
combining1 = BlockDiag([hstack1] * nwins0)
combining0 = HStack(
[
Restriction(dimsd, range(win_in, win_end), axis=0, dtype=Op.dtype).H
for win_in, win_end in zip(dwin0_ins, dwin0_ends)
]
)
Pop = LinearOperator(combining0 * combining1 * combining2 * OOp)
Pop.dims, Pop.dimsd = (
nwins0,
nwins1,
nwins2,
int(dims[0] // nwins0),
int(dims[1] // nwins1),
int(dims[2] // nwins2),
), dimsd
Pop.name = name
return Pop