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Determination of the calcium channel distribution in the olfactory system

Authors: C. Conca, R. Lecaros, J. H. Ortega and L. Rosier, Journal of Inverse and Ill-Posed Problems, vol 22 no 5, pp. 671--711, 2014, DOI: 10.1515/jip-2013-0033
In this paper we study a linear inverse problem with a biological interpretation, which is modeled by a Fredholm integral equation of the first kind. When the kernel in the Fredholm equation is represented by step functions, we obtain identifiability, stability and reconstruction results. Furthermore, we provide a numerical reconstruction algorithm for the kernel, whose main feature is that a non-regular mesh has to be used to ensure the invertibility of the matrix representing the numerical discretization of the system. Finally, a second identifiability result for a polynomial approximation of degree less than nine of the kernel is also established.
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author = {R. Lecaros C. Conca, J. H. Ortega and L. Rosier},
title = {Determination of the calcium channel distribution in the olfactory system},
journal = {Journal of Inverse and Ill-Posed Problems},
volume = {22},
number = {5},
pages = {671-671},
year = {2014},