pylops.Smoothing1D(nsmooth, dims, axis=-1, dtype='float64')[source]

1D Smoothing.

Apply smoothing to model (and data) to a multi-dimensional array along axis.


Length of smoothing operator (must be odd)

dimstuple or int

Number of samples for each dimension

axisint, optional

New in version 2.0.0.

Axis along which model (and data) are smoothed.

dtypestr, optional

Type of elements in input array.


The Smoothing1D operator is a special type of convolutional operator that convolves the input model (or data) with a constant filter of size \(n_\text{smooth}\):

\[\mathbf{f} = [ 1/n_\text{smooth}, 1/n_\text{smooth}, ..., 1/n_\text{smooth} ]\]

When applied to the first direction:

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

Similarly when applied to the second direction:

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

and the third direction:

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

Note that since the filter is symmetrical, the Smoothing1D operator is self-adjoint.


Operator shape


Operator contains a matrix that can be solved explicitly (True) or not (False)

Examples using pylops.Smoothing1D

1D Smoothing

1D Smoothing

1D Smoothing
Causal Integration

Causal Integration

Causal Integration
Wavelet estimation

Wavelet estimation

Wavelet estimation
03. Solvers

03. Solvers

03. Solvers