Lessons for building a fast, modular EIT reconstruction library. They follow from the structure of the problem described in this wiki.
Exploit the pattern-level parallelism. All state and adjoint solves of one iteration share a single matrix (see Adjoint State Method).
- Batch them as block solves (block CG or block MINRES; see Block Krylov Methods) and run them on the GPU.
- Solve state and adjoint systems in the same batch once residuals are available.
- Assemble the gradient contributions in parallel as well.
Split the work between CPU and GPU. Sparse assembly of , setup of the preconditioner, mesh adaptation, and processing of the incoming residuals and gradients suit the CPU. Bulk linear algebra suits the accelerator. Avoid global synchronisation points: a Gauss–Newton solve that waits for all patterns stalls the pipeline, so asynchronous or stochastic updates over patterns are worth considering.
Control accuracy and error. Tie linear solver tolerances to the optimisation progress. Estimate discretisation errors (see A Posteriori Error Estimation and Adaptive Meshing). Adapt meshes near electrodes and conductivity jumps. Always test gradients.
Keep components exchangeable. Forward discretisation (FEM, spectral), metric (Data Fidelity Terms), regulariser (classical or learned), and optimiser (L-BFGS-B, Gauss–Newton, ADMM) should be independent modules behind small interfaces.
Prefer schedule-free learned priors. Priors that do not need a synchronised diffusion time (RED-Diff, Diffusion Proximal Operator) can run concurrently with the physics solver. Guidance-based samplers interleave the two tightly.
Respect the geometry. Generic regularisers such as TV and Tikhonov ignore the structure of EIT. Spectral information from the boundary operator (Truncated SVD Regularization) and the Symmetries of the EIT Problem are underused sources of prior knowledge.
References
- A. Adler, W. R. B. Lionheart (2006). Uses and abuses of EIDORS: an extensible software base for EIT. Physiol. Meas. 27(5), S25–S42. doi:10.1088/0967-3334/27/5/S03
- W. R. B. Lionheart (2004). EIT reconstruction algorithms: pitfalls, challenges and recent developments. Physiol. Meas. 25(1), 125–142. doi:10.1088/0967-3334/25/1/021