For the sake of simplicity, I demonstrate the method by interpolating
one dimensional time sequences.
The data sequence shown in the following examples is a segment of a trace from
a field dataset. The original trace has a uniform time
sampling interval of 2 ms
and a maximum frequency of 160 Hz. To prevent the signal from aliasing
after random sub-sampling, the signal is low-passed to 100 Hz. Figure
shows two examples of interpolating the randomly sub-sampled
signal. Both examples have 32% randomly missing samples, but the distributions
of the missing samples are different. The distribution of
the missing samples in the first example is close to uniform,
while the missing samples in the second example are clustered
into a few groups. From Figure , we see that the results of
the interpolation are satisfactory. Figure compares the
amplitude spectra computed from the original signal and from the signal
with random missing samples, respectively. The results indicate that
the algorithm can accurately estimate the spectrum of an irregularly
sampled signal.

interp
Figure 2 Two examples of interpolating irregularly sampled data. The top trace shows
a segment of seismic data. The three traces in the middle show data before
and after interpolation, and interpolation error, which is magnified by a factor
of 500. The three traces at the bottom show another example in which the
missing samples are clustered. The error in this second example is
magnified by a factor of 40.

specirre
Figure 3 Amplitude spectra: The solid curve is computed from the original signal; The
dashed curve is computed from the signal with random missing samples.