Sparse Approximation-Based Maximum Likelihood Approach for Estimation of Radiological Source Terms

Abstract

A computationally efficient and accurate method is presented for identifying the number, intensity and location of stationary multiple radiological sources. The proposed method uniformly grids the region of interest resulting in a finite set of solutions for the source locations. The resulting problem is a sparse convex optimization problem based on ${{\cal L}_1}$ -norm minimization. The solution of this convex optimization encapsulates all information needed for the estimation of source terms; the values of the nonzero elements of the solution vector approximates the source intensity, the grid points corresponding to the nonzero elements approximates the source locations, and the number of nonzero elements is the number of sources. The accuracy limited by the resolution of the grid is further improved by making use of the maximum likelihood estimation approach. The performance of sparse approximation based maximum likelihood estimation is verified using real experimental data acquired from radiological field trials in the presence of up to three point sources of gamma radiation. The numerical results show that the proposed approach efficiently and accurately identifies the source terms simultaneously, and it outperforms existing methods which have been used for stationary multiple radiological source terms estimation.