pylops.signalprocessing.Convolve2D¶
-
pylops.signalprocessing.
Convolve2D
(dims, h, offset=(0, 0), axes=(-2, -1), method='fft', dtype='float64', name='C')[source]¶ 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 :
list
orint
Number of samples for each dimension
- h :
numpy.ndarray
2d compact filter to be convolved to input signal
- offset :
tuple
, optional Indices of the center of the compact filter
- axes :
int
, optional New in version 2.0.0.
Axes along which convolution is applied
- method :
str
, optional Method used to calculate the convolution (
direct
orfft
).- dtype :
str
, optional Type of elements in input array.
- name :
str
, optional New in version 2.0.0.
Name of operator (to be used by
pylops.utils.describe.describe
)
Returns: - cop :
pylops.LinearOperator
Convolve2D linear operator
Notes
The Convolve2D operator applies two-dimensional convolution between the input signal \(d(t,x)\) and a compact filter kernel \(h(t,x)\) in forward model:
\[y(t,x) = \iint\limits_{-\infty}^{\infty} h(t-\tau,x-\chi) d(\tau,\chi) \,\mathrm{d}\tau \,\mathrm{d}\chi\]This operation can be discretized as follows
\[y[i,n] = \sum_{j=-\infty}^{\infty} \sum_{m=-\infty}^{\infty} h[i-j,n-m] d[j,m]\]as well as performed in the frequency domain.
\[Y(f, k_x) = \mathscr{F} (h(t,x)) * \mathscr{F} (d(t,x))\]Convolve2D operator uses
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:
\[y(t,x) = \iint\limits_{-\infty}^{\infty} h(t+\tau,x+\chi) d(\tau,\chi) \,\mathrm{d}\tau \,\mathrm{d}\chi\]or in frequency domain:
\[y(t, x) = \mathscr{F}^{-1} (H(f, k_x)^* * X(f, k_x))\]- dims :