# pylops.signalprocessing.ConvolveND¶

class pylops.signalprocessing.ConvolveND(N, h, dims, offset=(0, 0, 0), dirs=None, method='fft', dtype='float64')[source]

ND convolution operator.

Apply n-dimensional convolution with a compact filter to model (and data) along a set of directions dirs of a n-dimensional array.

Parameters: N : int Number of samples in model h : numpy.ndarray nd compact filter to be convolved to input signal dims : list Number of samples for each dimension offset : tuple, optional Indices of the center of the compact filter dirs : tuple, optional Directions along which convolution is applied (set to None for filter of same dimension as input vector) method : str, optional Method used to calculate the convolution (direct or fft). dtype : str, optional Type of elements in input array.

Notes

The ConvolveND operator applies n-dimensional convolution between the input signal $$d(x_1, x_2, ..., x_N)$$ and a compact filter kernel $$h(x_1, x_2, ..., x_N)$$ in forward model. This is a straighforward extension to multiple dimensions of pylops.signalprocessing.Convolve2D operator.

Attributes: shape : tuple Operator shape explicit : bool Operator contains a matrix that can be solved explicitly (True) or not (False)

Methods

 __init__(self, N, h, dims[, offset, dirs, …]) Initialize this LinearOperator. adjoint(self) Hermitian adjoint. apply_columns(self, cols) Apply subset of columns of operator cond(self, \*\*kwargs_eig) Condition number of linear operator. conj(self) Complex conjugate operator div(self, y[, niter]) Solve the linear problem $$\mathbf{y}=\mathbf{A}\mathbf{x}$$. dot(self, x) Matrix-matrix or matrix-vector multiplication. eigs(self[, neigs, symmetric, niter]) Most significant eigenvalues of linear operator. matmat(self, X) Matrix-matrix multiplication. matvec(self, x) Matrix-vector multiplication. rmatmat(self, X) Adjoint matrix-matrix multiplication. rmatvec(self, x) Adjoint matrix-vector multiplication. todense(self) Return dense matrix. transpose(self) Transpose this linear operator.

## Examples using pylops.signalprocessing.ConvolveND¶ 2D Smoothing Causal Integration Convolution 05. Image deblurring