Source code for pylops.signalprocessing.convolve2d

__all__ = ["Convolve2D"]

from typing import Union

from pylops.signalprocessing import ConvolveND
from pylops.utils.typing import DTypeLike, InputDimsLike, NDArray

[docs]class Convolve2D(ConvolveND): r"""2D convolution operator. Apply two-dimensional convolution with a compact filter to model (and data) along a pair of ``axes`` of a two or three-dimensional array. Parameters ---------- dims : :obj:`list` or :obj:`int` Number of samples for each dimension h : :obj:`numpy.ndarray` 2d compact filter to be convolved to input signal offset : :obj:`tuple`, optional Indices of the center of the compact filter axes : :obj:`int`, optional .. versionadded:: 2.0.0 Axes along which convolution is applied method : :obj:`str`, optional Method used to calculate the convolution (``direct`` or ``fft``). dtype : :obj:`str`, optional Type of elements in input array. name : :obj:`str`, optional .. versionadded:: 2.0.0 Name of operator (to be used by :func:`pylops.utils.describe.describe`) Notes ----- The Convolve2D operator applies two-dimensional convolution between the input signal :math:`d(t,x)` and a compact filter kernel :math:`h(t,x)` in forward model: .. math:: y(t,x) = \iint\limits_{-\infty}^{\infty} h(t-\tau,x-\chi) d(\tau,\chi) \,\mathrm{d}\tau \,\mathrm{d}\chi This operation can be discretized as follows .. math:: y[i,n] = \sum_{j=-\infty}^{\infty} \sum_{m=-\infty}^{\infty} h[i-j,n-m] d[j,m] as well as performed in the frequency domain. .. math:: Y(f, k_x) = \mathscr{F} (h(t,x)) * \mathscr{F} (d(t,x)) Convolve2D operator uses :py:func:`scipy.signal.convolve2d` that automatically chooses the best domain for the operation to be carried out. As the adjoint of convolution is correlation, Convolve2D operator applies correlation in the adjoint mode. In time domain: .. math:: y(t,x) = \iint\limits_{-\infty}^{\infty} h(t+\tau,x+\chi) d(\tau,\chi) \,\mathrm{d}\tau \,\mathrm{d}\chi or in frequency domain: .. math:: y(t, x) = \mathscr{F}^{-1} (H(f, k_x)^* * X(f, k_x)) """ def __init__(self, dims: Union[int, InputDimsLike], h: NDArray, offset: InputDimsLike = (0, 0), axes: InputDimsLike = (-2, -1), method: str = "fft", dtype: DTypeLike = "float64", name: str = "C", ): if h.ndim != 2: raise ValueError("h must be 2-dimensional") super().__init__(dims=dims, h=h, offset=offset, axes=axes, method=method, dtype=dtype, name=name)