Comparative studies of total-variation-regularized sparse reconstruction algorithms in projection tomography

Projection tomography techniques, such as optical projection tomography and stimulated Raman projection tomography, can efficiently provide quantitative distributions of compositions in three-dimensional volumes that are isotropic and exhibit high spatial resolutions. A projection model and a reconstruction algorithm are two important elements of such techniques. This research explores the quality vs. efficiency tradeoffs for combinations of existing algorithms in a performance study. Two projection models are used. This first is the pixel vertex driven projection model; and the second is the distance driven projection model (DDM). These models are integrated with three TV-regularized iterative reconstruction algorithms: the algebraic reconstruction technique, the simultaneous algebra reconstruction technique (SART), and the two-step iterative shrinkage/thresholding algorithm. The performance of the combinations of these projection models and reconstruction algorithms are evaluated with a sparsely sampled data set in simulation experiments. The experiments consider both the reconstruction image quality and the time complexity. The comparative results indicate the combination of the SART and DDM algorithms provide a good balance between the quality and efficiency of reconstructed images. The exploratory results of this study are expected to provide some useful guidance on algorithmic development and applications in the projection tomography field.