Dual-basis reconstruction techniques for tomographic PIV

As an inverse problem, particle reconstruction in tomographic particle image velocimetry attempts to solve a large-scale underdetermined linear system using an optimization technique. The most popular approach, the multiplicative algebraic reconstruction technique (MART), uses entropy as an objective function in the optimization. All available MART-based methods are focused on improving the efficiency and accuracy of particle reconstruction. However, those methods do not perform very well on dealing with ghost particles in highly seeded measurements. In this report, a new technique called dual-basis pursuit (DBP), which is based on the basis pursuit technique, is proposed for tomographic particle reconstruction. A template basis is introduced as a priori knowledge of a particle intensity distribution combined with a correcting basis to enable a full span of the solution space of the underdetermined linear system. A numerical assessment test with 2D synthetic images indicated that the DBP technique is superior to MART method, can completely recover a particle field when the number of particles per pixel (ppp) is less than 0.15, and can maintain a quality factor Q of above 0.8 for ppp up to 0.30. Unfortunately, the DBP method is difficult to utilize in 3D applications due to the cost of its excessive memory usage. Therefore, a dual-basis MART was designed that performed better than the traditional MART and can potentially be utilized for 3D applications.