pylops.SmoothingND

class pylops.SmoothingND(nsmooth, dims, axes=(-2, -1), dtype='float64', name='S')

ND Smoothing.

Apply smoothing to model (and data) along the axes of a n-dimensional array.

Parameters:

nsmoothtuple or list

Length of smoothing operator in the chosen dimensions (must be odd, if even it will be increased by 1).

dimstuple

Number of samples for each dimension

axesint, optional

Axes along which model (and data) are smoothed.

dtypestr, optional

Type of elements in input array.

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.

See also

pylops.signalprocessing.ConvolveND

ND convolution

Notes

The ND Smoothing operator is a special type of convolutional operator that convolves the input model (or data) with a constant nd filter of size \(n_{\text{smooth}, 1} \times n_{\text{smooth}, 2} \times n_{\text{smooth}, 3}\):

Its application to a three dimensional input signal is:

\[y[i,j,k] = 1/(n_{\text{smooth}, 1}\cdot n_{\text{smooth}, 2}\cdot n_{\text{smooth}, 3}) \sum_{l=-(n_{\text{smooth},1}-1)/2}^{(n_{\text{smooth},1}-1)/2} \sum_{m=-(n_{\text{smooth},2}-1)/2}^{(n_{\text{smooth},2}-1)/2} \sum_{n=-(n_{\text{smooth},3}-1)/2}^{(n_{\text{smooth},3}-1)/2} x[l,m,n]\]

Note that since the filter is symmetrical, the Smoothing3D operator is self-adjoint.

Methods

__init__(nsmooth, dims[, axes, dtype, name])
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()

Examples using pylops.SmoothingND

3D Smoothing

3D Smoothing