Combining singular value decomposition and a non-negative constraint in a hybrid method for photothermal depth profiling

We present a method to solve the inverse problem in pulsed photothermal radiometry sPPTRd that exploits advantages of truncated singular value decomposition sT-SVDd while imposing a non-negativity constraint to the solution. The presented method is a hybrid in the sense that it expresses the solution vector as a linear superposition of right singular vectors, but with a non-negative constraint applied to it. The weights for the superposition are determined using an optimization algorithm. In one-dimensional PPTR simulation examples, the best reconstruction results are of comparable quality to those of the conjugate gradient method. Furthermore, the hybrid method exhibits a sharper knee in the L-curve and small susceptibility to over-iteration in presence of experimental noise, thus facilitating the regularization process. As a result, the reconstructed temperature profiles are more likely to be closer to the original initial profiles. © 2005 American Institute of Physics. fDOI: 10.1063/1.1851473g