Bilinear Interpolation#

This example shows how to use the pylops.signalprocessing.Bilinar operator to perform bilinear interpolation to a 2-dimensional input vector.

import matplotlib.pyplot as plt
import numpy as np
from scipy import misc

import pylops


First of all, we create a 2-dimensional input vector containing an image from the scipy.misc family.

x = misc.face()[::5, ::5, 0]
nz, nx = x.shape
/home/docs/checkouts/ DeprecationWarning: scipy.misc.face has been deprecated in SciPy v1.10.0; and will be completely removed in SciPy v1.12.0. Dataset methods have moved into the scipy.datasets module. Use scipy.datasets.face instead.
  x = misc.face()[::5, ::5, 0]

We can now define a set of available samples in the first and second direction of the array and apply bilinear interpolation.

At this point we try to reconstruct the input signal imposing a smooth solution by means of a regularization term that minimizes the Laplacian of the solution.

D2op = pylops.Laplacian((nz, nx), weights=(1, 1), dtype="float64")

xadj = Bop.H * y
xinv = pylops.optimization.leastsquares.normal_equations_inversion(
    Bop, y, [D2op], epsRs=[np.sqrt(0.1)], **dict(maxiter=100)
xadj = xadj.reshape(nz, nx)
xinv = xinv.reshape(nz, nx)

fig, axs = plt.subplots(1, 3, figsize=(10, 4))
fig.suptitle("Bilinear interpolation", fontsize=14, fontweight="bold", y=0.95)
axs[0].imshow(x, cmap="gray_r", vmin=0, vmax=250)
axs[1].imshow(xadj, cmap="gray_r", vmin=0, vmax=250)
axs[2].imshow(xinv, cmap="gray_r", vmin=0, vmax=250)
axs[2].set_title("2D Regularization")
Bilinear interpolation, Original, Sampled, 2D Regularization

Total running time of the script: (0 minutes 0.901 seconds)

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