ADMM 3D (ToMoBAR)

ADMM 3D (ToMoBAR)#

Description

The Alternating Direction Method of Multipliers (ADMM) [3] in tomography is an iterative reconstruction algorithm that optimises image quality by breaking complex, large-scale, and non-smooth optimization problems into smaller, manageable subproblems. It is particularly effective for high-quality, 3D imaging from sparse-view or low-dose data, where traditional methods like filtered back-projection (FBP) produce severe artifacts. It can also employ various regularisation [6] models to suppress the noise. There are few types of regularisation that can be used, please see method’s API httomolibgpu.recon.algorithm.ADMM3d_tomobar.

Where and how to use it:

When the data is highly inaccurate, noisy, incomplete, or limited-angle data. Due to added regularisation, the quality of ADMM reconstruction is expected to be better than other classical methods, such as, CGLS 3D (ToMoBAR) or SIRT 3D (ToMoBAR).

What are the adjustable parameters:

  • The number of iterations is an important parameter as one would like to achieve a trade-off between the resolution and SNR. For ADMM-OS method (when subsets_number > 1) the range of iterations depends on how many subsets_number used. For 24 subsets, 3-5 iterations is usually enough.

  • subsets_number usually helps with the faster convergence of the reconstruction algorithm. Fortunately, ADMM is much more robust for higher numbers of subsets, compared to FISTA 3D (ToMoBAR). 24 or larger number of subsets can be used and iterations can be reduced when the subsets grow.

  • initialisation Initialise ADMM iterations using another reconstruction algorithm, like FBP, for instance. A so-called warm-start. Usually helps significantly to reduce the number of iterations. However, for very noise, undersampled, data it is recommended to use ‘CGLS’ as initialisation to avoid boosting up the noise and artifacts of the FBP reconstruction.

  • regularisation_parameter is probably the second most important parameter after iterations. When one increases the value of regularisation_parameter, one can expect the image to be smoother. The type of smoothing usually depends on the regularisation type, and for Total-Variation is the piecewise-constant smoothness.

  • regularisation_iterations defines how many inner iterations for regularisation performed on every step of the outer algorithm. This can depend on regularisation_type and subsets_number. The general rule is when subsets_number is smaller then regularisation_iterations should be increased.

  • nonnegativity. By setting this parameter to True imposes positivity constraint on the solution.