Source code for pylops.signalprocessing.Sliding2D

import logging
import numpy as np

from pylops.basicoperators import Diagonal, BlockDiag, Restriction, \
from pylops.utils.tapers import taper2d

logging.basicConfig(format='%(levelname)s: %(message)s', level=logging.WARNING)

def _slidingsteps(ntr, nwin, nover):
    """Identify sliding window initial and end points given overall
    trace length, window length and overlap

    ntr : :obj:`int`
        Number of samples in trace
    nwin : :obj:`int`
        Number of samples of window
    nover : :obj:`int`
        Number of samples of overlapping part of window

    starts : :obj:`np.ndarray`
        Start indices
    ends : :obj:`np.ndarray`
        End indices

    if nwin > ntr:
        raise ValueError('nwin=%d is bigger than ntr=%d...'
                         % (nwin, ntr))
    step = nwin - nover
    starts = np.arange(0, ntr - nwin + 1, step,
    ends = starts + nwin
    return starts, ends

[docs]def Sliding2D(Op, dims, dimsd, nwin, nover, tapertype='hanning', design=False): """2D Sliding transform operator. Apply a transform operator ``Op`` repeatedly to slices of the model vector in forward mode and slices of the data vector in adjoint mode. More specifically, in forward mode the model vector is divided into slices, each slice is transformed, and slices are then recombined in a sliding window fashion. Both model and data are internally reshaped and interpreted as 2-dimensional arrays: each slice contains a portion of the array in the first dimension (and the entire 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, sliding windows may not cover the entire first dimension. The start and end indices of each window can be displayed using ``design=True`` while defining the best sliding window approach. Parameters ---------- Op : :obj:`pylops.LinearOperator` Transform operator dims : :obj:`tuple` Shape of 2-dimensional model. Note that ``dims[0]`` should be multiple of the model size of the transform in the first dimension dimsd : :obj:`tuple` Shape of 2-dimensional data nwin : :obj:`int` Number of samples of window nover : :obj:`int` Number of samples of overlapping part of window 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``). """ # model windows mwin_ins, mwin_ends = _slidingsteps(dims[0], Op.shape[1]//dims[1], 0) # data windows dwin_ins, dwin_ends = _slidingsteps(dimsd[0], nwin, nover) nwins = len(dwin_ins) # create tapers if tapertype is not None: tap = taper2d(dimsd[1], nwin, nover, tapertype=tapertype) tapin = tap.copy() tapin[:nover] = 1 tapend = tap.copy() tapend[-nover:] = 1 taps = {} taps[0] = tapin for i in range(1, nwins - 1): taps[i] = tap taps[nwins - 1] = tapend # check that identified number of windows agrees with mode size if design: logging.warning('%d windows required...', nwins) logging.warning('model wins - start:%s, end:%s', str(mwin_ins), str(mwin_ends)) logging.warning('data wins - start:%s, end:%s', str(dwin_ins), str(dwin_ends)) if nwins*Op.shape[1]//dims[1] != dims[0]: raise ValueError('Model shape (dims=%s) is not consistent with chosen ' 'number of windows. Choose dims[0]=%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), nwins*Op.shape[1]//dims[1])) # transform to apply if tapertype is None: OOp = BlockDiag([Op for _ in range(nwins)]) else: OOp = BlockDiag([Diagonal(taps[itap].flatten()) * Op for itap in range(nwins)]) combining = HStack([Restriction(, range(win_in, win_end), dims=dimsd).H for win_in, win_end in zip(dwin_ins, dwin_ends)]) Sop = combining * OOp return Sop