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The data processing algorithm with tomographic reconstruction of volume particle images and a subsequent three-dimensional cross-correlation procedure to estimate a velocity field inside a measurement volume is now getting the standard tool for Tomographic Particle Image Velocimetry (Tomo-PIV). Up to now, it has already been successfully applied in several experimental studies of turbulent flows and also two-phase flows. The essential problems of the experimental Tomo PIV data processing are a high computational cost and the need in a large amount of disk space and RAM memory. The objective of the present work is to discuss alternative algorithms for the estimation of 3D3C velocity fields from a Tomo-PIV experiment that have an advantage in terms of running time. The idea is to replace 3D correlation analysis of particle patterns by several two dimensional correlations that sometimes is sufficient to have reliable 3C velocity vector assessment without significant loss of accuracy. An approach for the parallel projection correlation (PPC) proposed in this work seems to have a potential in practical applications for speeding up the correlation stage of the Tomo-PIV data processing. The results of the application of the described algorithms to the synthetic and real experimental data are discussed in the paper.