  Extrasolar analogues of the Solar System's Kuiper belt offer unique
constraints on outer planetary system architecture. Radial features such as the
sharpness of disk edges and substructures such as gaps may be indicative of
embedded planets within a disk. Vertically, the height of a disk can constrain
the mass of embedded bodies. Edge-on debris disks offer a unique opportunity to
simultaneously access the radial and vertical distribution of material, however
recovering either distribution in an unbiased way is challenging. In this
study, we present a non-parametric method to recover the surface brightness
profile (face-on surface brightness as a function of radius) and height profile
(scale height as a function of radius) of azimuthally symmetric, edge-on debris
disks. The method is primarily designed for observations at thermal emission
wavelengths, but is also applicable to scattered light observations under the
assumption of isotropic scattering. By removing assumptions on underlying
functional forms, this algorithm provides more realistic constraints on disk
structures. We also apply this technique to ALMA observations of the AU Mic
debris disk and derive a surface brightness profile consistent with estimates
from parametric approaches, but with a more realistic range of possible models
that is independent of parametrisation assumptions. Our results are consistent
with a uniform scale height of 0.8 au, but a scale height that increases
linearly with radius is also possible.
