  The derivation by Alan Hodgkin and Andrew Huxley of their famous neuronal
conductance model relied on experimental data gathered using neurons of the
giant squid. It becomes clear that determining experimentally the conductances
of neurons is hard, in particular under the presence of spatial and temporal
heterogeneities. Moreover it is reasonable to expect variations between species
or even between types of neurons of a same species. Determining conductances
from one type of neuron is no guarantee that it works across the board.
  We tackle the inverse problem of determining, given voltage data,
conductances with non-uniform distribution computationally. In the simpler
setting of a cable equation, we consider the Landweber iteration, a
computational technique used to identify non-uniform spatial and temporal ionic
distributions, both in a single branch or in a tree. Here, we propose and
(numerically) investigate an iterative scheme that consists in numerically
solving two partial differential equations in each step. We provide several
numerical results showing that the method is able to capture the correct
conductances given information on the voltages, even for noisy data.
