Source code for pylops.signalprocessing.Patch2D

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(, 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