import logging
import numpy as np
from pylops import LinearOperator
from ._ChirpRadon3D import _chirp_radon_3d
try:
import pyfftw
from ._ChirpRadon3D import _chirp_radon_3d_fftw
except ModuleNotFoundError:
pyfftw = None
pyfftw_message = (
"Pyfftw not installed, use numpy or run "
'"pip install pyFFTW" or '
'"conda install -c conda-forge pyfftw".'
)
except Exception as e:
pyfftw = None
pyfftw_message = "Failed to import pyfftw (error:%s), use numpy." % e
logging.basicConfig(format="%(levelname)s: %(message)s", level=logging.WARNING)
[docs]class ChirpRadon3D(LinearOperator):
r"""3D Chirp Radon transform
Apply Radon forward (and adjoint) transform using Fast Fourier Transform
and Chirp functions to a 3-dimensional array of size
:math:`[n_y \times n_x \times n_t]` (both in forward and adjoint mode).
Note that forward and adjoint are swapped compared to the time-space
implementation in :class:`pylops.signalprocessing.Radon3D` and a direct
`inverse` method is also available for this implementation.
Parameters
----------
taxis : :obj:`np.ndarray`
Time axis
hxaxis : :obj:`np.ndarray`
Fast patial axis
hyaxis : :obj:`np.ndarray`
Slow spatial axis
pmax : :obj:`np.ndarray`
Two element array :math:`(p_{y,\text{max}}, p_{x,\text{max}})` of :math:`\tan`
of maximum stacking angles in :math:`y` and :math:`x` directions
:math:`(\tan(\alpha_{y,\text{max}}), \tan(\alpha_{x,\text{max}}))`. If one operates
in terms of minimum velocity :math:`c_0`, then
:math:`p_{y,\text{max}}=c_0\,\mathrm{d}y/\mathrm{d}t` and :math:`p_{x,\text{max}}=c_0\,\mathrm{d}x/\mathrm{d}t`
engine : :obj:`str`, optional
Engine used for fft computation (``numpy`` or ``fftw``)
dtype : :obj:`str`, optional
Type of elements in input array.
**kwargs_fftw
Arbitrary keyword arguments for :py:class:`pyfftw.FTTW`
(reccomended: ``flags=('FFTW_ESTIMATE', ), threads=NTHREADS``)
Attributes
----------
shape : :obj:`tuple`
Operator shape
explicit : :obj:`bool`
Operator contains a matrix that can be solved explicitly (``True``) or
not (``False``)
Notes
-----
Refer to [1]_ for the theoretical and implementation details.
.. [1] Andersson, F and Robertsson J. "Fast :math:`\tau-p` transforms by
chirp modulation", Geophysics, vol 84, NO.1, pp. A13-A17, 2019.
"""
def __init__(
self,
taxis,
hyaxis,
hxaxis,
pmax,
engine="numpy",
dtype="float64",
**kwargs_fftw
):
self.dt = taxis[1] - taxis[0]
self.dy = hyaxis[1] - hyaxis[0]
self.dx = hxaxis[1] - hxaxis[0]
self.nt, self.nx, self.ny = taxis.size, hxaxis.size, hyaxis.size
self.pmax = pmax
self.engine = engine
if self.engine not in ["fftw", "numpy"]:
raise NotImplementedError("engine must be numpy or fftw")
self.kwargs_fftw = kwargs_fftw
self.shape = (self.nt * self.nx * self.ny, self.nt * self.nx * self.ny)
self.dtype = np.dtype(dtype)
self.explicit = False
def _matvec(self, x):
x = x.reshape(self.ny, self.nx, self.nt)
if self.engine == "fftw" and pyfftw is not None:
y = _chirp_radon_3d_fftw(
x, self.dt, self.dy, self.dx, self.pmax, mode="f", **self.kwargs_fftw
)
else:
y = _chirp_radon_3d(x, self.dt, self.dy, self.dx, self.pmax, mode="f")
return y.ravel()
def _rmatvec(self, x):
x = x.reshape(self.ny, self.nx, self.nt)
if self.engine == "fftw" and pyfftw is not None:
y = _chirp_radon_3d_fftw(
x, self.dt, self.dy, self.dx, self.pmax, mode="a", **self.kwargs_fftw
)
else:
y = _chirp_radon_3d(x, self.dt, self.dy, self.dx, self.pmax, mode="a")
return y.ravel()
def inverse(self, x):
x = x.reshape(self.ny, self.nx, self.nt)
if self.engine == "fftw" and pyfftw is not None:
y = _chirp_radon_3d_fftw(
x, self.dt, self.dy, self.dx, self.pmax, mode="i", **self.kwargs_fftw
)
else:
y = _chirp_radon_3d(x, self.dt, self.dy, self.dx, self.pmax, mode="i")
return y.ravel()