  Interferometric observations of the mm dust distribution in protoplanetary
discs are now showing a ubiquity of annular gap and ring substructures. Their
identification and accurate characterization is critical to probing the
physical processes responsible. We present Frankenstein (frank), an open source
code that recovers axisymmetric disc structures at sub-beam resolution. By
fitting the visibilities directly, the model reconstructs a disc's 1D radial
brightness profile nonparametrically using a fast (<~1 min) Gaussian process.
The code avoids limitations of current methods that obtain the radial
brightness profile by either extracting it from the disc image via nonlinear
deconvolution at the cost of reduced fit resolution, or by assumptions placed
on the functional forms of disc structures to fit the visibilities
parametrically. We use mock ALMA observations to quantify the method's
intrinsic capability and its performance as a function of baseline-dependent
signal-to-noise. Comparing the technique to profile extraction from a CLEAN
image, we motivate how our fits accurately recover disc structures at a
sub-beam resolution. Demonstrating the model's utility in fitting real high and
moderate resolution observations, we conclude by proposing applications to
address open questions on protoplanetary disc structure and processes.
