Sparse non-negative volume reconstruction using non-linear substitution and spectral projected gradient methods

Sparse non-negative reconstruction problems arise as part of the tomographic particle image velocimetry technique for volumetric flow measurement. Current state-of-the-art algebraic reconstruction algorithms for these kinds of problems are MART/SMART-based. This paper intends to make a case for an alternative algebraic reconstruction algorithm for sparse non-negative volumes called S-SPG. It is based on the spectral projected gradient method and enhanced by a non-linear substitution that acts as a preconditioner. S-SPG offers a couple of interesting properties in comparison with the MART/SMART-based solvers which are discussed in this paper along with results of simulations with varying numbers of cameras and particle densities