Interpolating irregularly missing data points of regularly spaced data If I have a set of regularly spaced sample data (spacing $\delta x$) and some of my data is missing (zero) but not at regular intervals, i.e.

$[a_0, (missing), (missing), (missing), a_4, a_5, (missing), a_7, a_8, a_9, a_{10}, ...]$

Can digital signal processing techniques be used to interpolate the missing data?

I've only read of interpolating by a FIR or IIR when the missing data is every nth element.

There is a lot more data present than missing.

The interpolation can be done offline.

The first or last data point(s) might be missing.
I found a method similar to the zero-padding FFT interpolation but in which the missing samples can be nonuniformly spaced. I think it exactly solves the problem you have. The method is described here:

J. Selva, "FFT interpolation from nonuniform samples lying in a regular grid", IEEE Trans. on Signal Processing, vol. 63, n. 11, June 2015.

The code is available here.