  We propose and test a method to interpolate sparsely sampled signals by a
stochastic process with a broad range of spatial and/or temporal scales. To
this end, we extend the notion of a fractional Brownian bridge, defined as
fractional Brownian motion with a given scaling (Hurst) exponent $H$ and with
prescribed start and end points, to a bridge process with an arbitrary number
of intermediate and non-equidistant points. Determining the optimal value of
the Hurst exponent, $H_{opt}$, appropriate to interpolate the sparse signal, is
a very important step of our method. We demonstrate the validity of our method
on a signal from fluid turbulence in a high Reynolds number flow and discuss
the implications of the non-self-similar character of the signal. The method
introduced here could be instrumental in several physical problems, including
astrophysics, particle tracking, specific tailoring of surrogate data, as well
as in domains of natural and social sciences.
