Reconstruction of the timewise conductivity using a linear combination of heat flux measurements

The reconstruction of the timewise conductivity in the heat equation from an observation consisting of a linear combination of heat flux measurement data is considered. This inverse formulation results in a local uniquely solvable problem. The two-dimensional inverse problem is discretized using an alternating direction explicit method. The resulting constrained optimization problem is minimized iteratively by employing a MATLAB toolbox subroutine.