SIRT 3D (ToMoBAR)#
Description
Simultaneous Iterative Reconstruction Technique (SIRT) is a widely used iterative algorithm for image reconstruction. It updates the system of linear algebraic equations simultaneously using averages and therefore faster than Algebraic Reconstruction Technique. The following iterations are performed: \(x^{k+1} = \mathbf{C}\mathbf{A}^{\intercal}\mathbf{R}(b - \mathbf{A}x^{k})\), where \(\mathbf{A}\) is the forward projection or geometry matrix, \(x\) is the sought solution (reconstructed image), \(b\) is the vectorised projection data, and \(\mathbf{A}^{\intercal}\) is the inverse projection operator. Matrices \(\mathbf{R}\) and \(\mathbf{C}\) are the preconditioning matrices which are pre-calculated before the main iterations.
Where and how to use it:
When the data is noisy, incomplete, or limited-angle data. Normally direct methods do not work well with that kind of data so it is recommended to use iterative methods. Note the SIRT method is slow in convergence and it also requires hundreds of iterations normally, we recommended to use faster iterative methods, such as CGLS 3D (ToMoBAR) or even more advanced FISTA 3D (ToMoBAR).
What are the adjustable parameters:
The number of
iterationsis an important parameter for the method as as too few iterations leave the reconstruction blurry, while too many lead to noise amplification. SIRT might require 200-400 iterations, so one can also try a faster CGLS 3D (ToMoBAR) method.
Fig. 56 Log-Polar 3D (ToMoBAR) reconstruction is extremely noisy as the data is undersampled with a rapid exposure to the X-ray beam.# |
Fig. 57 SIRT reconstruction with |
Fig. 58 SIRT reconstruction with |