Determination of the Calcium channel distribution in the olfactory system

作者：Conca Carlos^*; Lecaros Rodrigo; Ortega Jaime H; Rosier Lionel

来源：Journal of Inverse and Ill-Posed Problems, 2014, 22(5): 671-711.

DOI：10.1515/jip-2013-0033

• Inverse problems
• olfactory system
• kernel determination
• partial differential equations
• numerical reconstruction

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.

• 出版日期2014-10
• 单位INRIA