pylops.signalprocessing.Radon3D¶
-
pylops.signalprocessing.
Radon3D
(taxis, hyaxis, hxaxis, pyaxis, pxaxis, kind='linear', centeredh=True, interp=True, onthefly=False, engine='numpy', dtype='float64')[source]¶ Three dimensional Radon transform.
Apply three dimensional Radon forward (and adjoint) transform to a 3-dimensional array of size \([n_{p_y} \times n_{p_x} \times n_t]\) (and \([n_y \times n_x \times n_t]\)).
In forward mode this entails to spreading the model vector along parametric curves (lines, parabolas, or hyperbolas depending on the choice of
kind
), while stacking values in the data vector along the same parametric curves is performed in adjoint mode.Parameters: - taxis :
np.ndarray
Time axis
- hxaxis :
np.ndarray
Fast patial axis
- hyaxis :
np.ndarray
Slow spatial axis
- pyaxis :
np.ndarray
Axis of scanning variable \(p_y\) of parametric curve
- pxaxis :
np.ndarray
Axis of scanning variable \(p_x\) of parametric curve
- kind :
str
, optional Curve to be used for stacking/spreading (
linear
,parabolic
, andhyperbolic
are currently supported)- centeredh :
bool
, optional Assume centered spatial axis (
True
) or not (False
). IfTrue
the originalhaxis
is ignored and a new axis is created.- interp :
bool
, optional Apply linear interpolation (
True
) or nearest interpolation (False
) during stacking/spreading along parametric curve- onthefly :
bool
, optional Compute stacking parametric curves on-the-fly as part of forward and adjoint modelling (
True
) or at initialization and store them in look-up table (False
). Using a look-up table is computationally more efficient but increases the memory burden- engine :
str
, optional Engine used for computation (
numpy
ornumba
)- dtype :
str
, optional Type of elements in input array.
Returns: - r3op :
pylops.LinearOperator
Radon operator
Raises: - KeyError
If
engine
is neithernumpy
nornumba
- NotImplementedError
If
kind
is notlinear
,parabolic
, orhyperbolic
See also
pylops.signalprocessing.Radon2D
- Two dimensional Radon transform
pylops.Spread
- Spread operator
Notes
The Radon3D operator applies the following linear transform in adjoint mode to the data after reshaping it into a 3-dimensional array of size \([n_y \times n_x \times n_t]\) in adjoint mode:
\[m(p_y, p_x, t_0) = \int{d(y, x, t = f(p_y, p_x, y, x, t))} \,\mathrm{d}x \,\mathrm{d}y\]where \(f(p_y, p_x, y, x, t) = t_0 + p_y y + p_x x\) in linear mode, \(f(p_y, p_x, y, x, t) = t_0 + p_y y^2 + p_x x^2\) in parabolic mode, and \(f(p_y, p_x, y, x, t) = \sqrt{t_0^2 + y^2 / p_y^2 + x^2 / p_x^2}\) in hyperbolic mode. Note that internally the \(p_x\) and \(p_y\) axes will be normalized by the ratio of the spatial and time axes and used alongside unitless axes. Whilst this makes the linear mode fully unitless, users are required to apply additional scalings to the \(p_x\) axis for other relationships
- \(p_x\) should be pre-multipled by \(d_x / d_y\) for the parabolic relationship;
- \(p_x\) should be pre-multipled by \((d_t/d_x)^2 / (d_t/d_y)^2\) for the hyperbolic relationship.
As the adjoint operator can be interpreted as a repeated summation of sets of elements of the model vector along chosen parametric curves, the forward is implemented as spreading of values in the data vector along the same parametric curves. This operator is actually a thin wrapper around the
pylops.Spread
operator.- taxis :