pylops.signalprocessing.Convolve2D¶

class 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:

dimslist or int: Number of samples for each dimension
hnumpy.ndarray: 2d compact filter to be convolved to input signal
offsettuple, optional: Indices of the center of the compact filter
axesint, optional: Added in version 2.0.0.

Axes along which convolution is applied
methodstr, optional: Method used to calculate the convolution (auto, direct or fft) - see scipy.signal.convolve for details.
dtypestr, optional: Type of elements in input array.
namestr, optional: Added in version 2.0.0.

Name of operator (to be used by pylops.utils.describe.describe)

Attributes:

nhtuple

Length of the filter

convolvecallable

Convolution function

correlatecallable

Correlation function

dimstuple

Shape of the array after the adjoint, but before flattening.

For example, x_reshaped = (Op.H * y.ravel()).reshape(Op.dims).

dimsdtuple

Shape of the array after the forward, but before flattening. In this case, same as dims.

shapetuple

Operator shape.

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:

\[y(t, x) = \mathscr{F}^{-1} (H(f, k_x)^* * X(f, k_x))\]

Methods

`__init__`(dims, h[, offset, axes, method, ...])
`adjoint`()
`apply_columns`(cols)	Apply subset of columns of operator
`cond`([uselobpcg])	Condition number of linear operator.
`conj`()	Complex conjugate operator
`div`(y[, niter, densesolver])	Solve the linear problem \(\mathbf{y}=\mathbf{A}\mathbf{x}\).
`dot`(x)	Matrix-matrix or matrix-vector multiplication.
`eigs`([neigs, symmetric, niter, uselobpcg])	Most significant eigenvalues of linear operator.
`matmat`(X)	Matrix-matrix multiplication.
`matvec`(x)	Matrix-vector multiplication.
`reset_count`()	Reset counters
`rmatmat`(X)	Matrix-matrix multiplication.
`rmatvec`(x)	Adjoint matrix-vector multiplication.
`todense`([backend])	Return dense matrix.
`toimag`([forw, adj])	Imag operator
`toreal`([forw, adj])	Real operator
`tosparse`()	Return sparse matrix.
`trace`([neval, method, backend])	Trace of linear operator.
`transpose`()