Source code for pylops.signalprocessing.Convolve2D

from pylops.signalprocessing import ConvolveND

[docs]def Convolve2D(N, h, dims, offset=(0, 0), nodir=None, dtype="float64", method="fft"): r"""2D convolution operator. Apply two-dimensional convolution with a compact filter to model (and data) along a pair of specific directions of a two or three-dimensional array depending on the choice of ``nodir``. Parameters ---------- N : :obj:`int` Number of samples in model h : :obj:`numpy.ndarray` 2d compact filter to be convolved to input signal dims : :obj:`list` Number of samples for each dimension offset : :obj:`tuple`, optional Indeces of the center of the compact filter nodir : :obj:`int`, optional Direction along which convolution is NOT applied (set to ``None`` for 2d arrays) dtype : :obj:`str`, optional Type of elements in input array. method : :obj:`str`, optional Method used to calculate the convolution (``direct`` or ``fft``). Returns ------- cop : :obj:`pylops.LinearOperator` Convolve2D linear operator 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)) """ if h.ndim != 2: raise ValueError("h must be 2-dimensional") if nodir is None: dirs = (0, 1) elif nodir == 0: dirs = (1, 2) elif nodir == 1: dirs = (0, 2) else: dirs = (0, 1) cop = ConvolveND(N, h, dims, offset=offset, dirs=dirs, method=method, dtype=dtype) return cop