Recovering iodine from activated carbon
Based on Recovery of Iodine with Activated Carbon from Dilute Aqueous Solutions,Petrochemical Center of Excellence, Department of Chemical Engineering, Amirkabir University of Technology, No.424, Hafez Ave., Tehran, Iran , you should get good recovery of your iodine by heating in a solution of NaOH. According to the paper:  


  The optimal desorption conditions obtained by the software are as
  follows: temperature of NaOH solution: $\mathrm{50^oC}$, concentration of NaOH
  solution: 0.5 % and agitation speed: 300rpm. Desorption experiments
  under these optimal conditions showed 98.9% desorption. The Taguchi
  design software results also showed that in the desorption section,
  the contributions of each factor on desorption percentage are as
  follows: concentration of NaOH solution (55%), temperature of NaOH
  solution (39.4%) and agitation speed (4.6%).
  [...]
  the necessary time for equilibrium desorption is obtained as 6h.  


The paper does not discuss the algorithms used to calculate the relative importance of the different parameters, but obviously temperature and NaOH concentration are the important factors to getting such good recovery.