Estimate the Discrete Fourier Series of a Signal with Missing Samples

Assuming we have a discrete signal ${ \left\{ x \left[ n \right] \right\}}_{n = 1}^{N}$.
Which has a Discrete Fourier Series.

Now, assume I'd like to estimate its Discrete Fourier Series coefficient yet some samples of $x [ n]$ are missing (The indices are known).

How could that be done efficiently without computing the Pseudo Inverse of the adapting Fourier Series matrix?

Thank You.