An efficient quadratic programming optimization method for deconvolution of gamma-ray spectra

The relationship between incident and observed gamma-ray spectrum can be described by a linear equation system. The solution of this system (called deconvolution), is generally a complex problem, because the solution is unstable with respect to the uncertainty of the measurement. The equation system is extremely sensitive to errors in the measured data, because the matrix of the system is always singular or ill conditioned. The existence of error and the singularity of the system-matrix affects the process of deconvolution, and can lead to difficulties in solving the equation system. Classical methods for solving equation systems are not efficient enough, therefore, in order to find stable solution the method of regularization must be applied. This means, that the original problem is replaced by an approximate one, the solutions of which are significantly less sensitive to errors in the data. This work describes physical and mathematical background of this problem, after that presents an efficient deconvolution method, which is significantly less sensitive to errors in the data. From mathematical point of view the applied algorithm is based on the quadratic programming optimization theory, and active set method. (author)