Open Access
Table A.1
Tabellaric overview of the properties, advantages and disadvantages of imaging frameworks that are frequently used in VLBI and for STIX.
| Method | (MS-)CLEAN | MEM |
|---|---|---|
| Software | Difmap, MrBeam, Casa, Aips, SSW-IDL | Casa, ehtim, MrBeam, SSW-IDL |
| Idea | Deconvolve dirty image and dirty beam | Minimize entropy |
| Data term | Residual (or in basis functions for MS-CLEAN) | Visibilities, Closures |
| Minimizer/solver | Matching Pursuit | Forward-Backward Splitting, SQP, trust-constr |
| Output | Model = image (except for DoB-CLEAN, U-CLEAN) | Regularized model |
| Resolution | Clean beam | Super-resolution |
| Accuracy | Small due to suboptimal representation | High |
| Dynamic range | High | Medium |
| Regularization properties | ||
| −> Calibration | Self-calibration during imaging | Closure-only possible |
| −> Thermal Noise | Divergence!, manual stopping | Entropy assures simplicity |
| −> (u, v) coverage | Spurious, copy covered features in gaps (−>DoB-CLEAN, U-CLEAN: better extrapolation) | Entropy |
| Speed | Fast | Fast |
| Supervision | Huge human bias | Small |
| Resources | Small, only shifts and subtractions performed | Medium, FFT evaluated in every iteration |
| Adaptability | Small, not all extensions could be written as a deconvolution problem | Medium, new entropy functionals needed |
| Maternity | Probed for decades, de-facto standard | Probed for decades |
| Method | RML | CS |
| Software | ehtim, SMILI | MrBeam |
| Idea | Generalized Tikhonov method | Sparsity promoting regularization |
| Data term | Visibilities, closures | Visibilities, closures |
| Reg term | L1, L2, TV, TSV, Entropy, Flux | L1 in wavelet basis |
| Minimizer/solver | Newton type | Forward-backward splitting |
| Output | Regularized model | Regularized model |
| Resolution | Super-resolution | Super-resolution |
| Accuracy | Highest (for correct parameter weighting) | High |
| Dynamic tange | Medium, limited by field of view | High (multiscalar representation) |
| Regularization properties | ||
| −> Calibration | Closure-only | Closure-only |
| −> Thermal noise | By balancing reg. terms with data terms | By balancing |
| −> (u, v) coverage | By balancing | Multiscalar dictionary adapts to the (u, υ) coverage |
| Speed | Fast (but parameter surveys needed) | Fast, no survey needed |
| Supervision | Small, but parameter survey needed | Unsupervised |
| Resources | Medium, FFT evaluated in every iteration | Medium, FFT evaluated in every iteration |
| Adaptability | Medium, new data terms needed | High, same multiresolution support information could be reused |
| Maternity | Intensively tested for the EHT, rare application outside | Relatively young |
| Methods | Bayesian | Multiobjective |
| Software | Resolve, Themis, Comrade | MrBeam |
| Idea | Posterior exploration | Multiobjective Pareto optimality |
| Data term | Likelihood (Visibilities, closures) | Closures |
| Reg term | Prior distribution | Multiobjective combination of L1,L2,TV, TSV, entropy, flux |
| Minimizer and posterior estimation | Newton type: VI, MCMC | Genetic Algorithm |
| Output | Posterior distribution from posterior samples | Pareto front (clusters of solutions) |
| Resolution | Super-resolution | Super-resolved clusters |
| determined by averaging | as well as blurred clusters | |
| Accuracy | Highest | Limited by number of pixels and genetic optimization |
| Dynamic tange | High | Limited by number of pixels and genetic optimization |
| Regularization properties | ||
| −> Calibration | Built in Bayesian model | Closure-only |
| −> Thermal noise | By prior distribution | By balancing multiobjective functionals |
| −> (u, v) coverage | By prior distribution | By balancing |
| Speed | Slow | Slow, but no survey needed |
| Supervision | Small, but larger number of parameters | Unsupervised |
| Resources | High due to the high | High, FFT evaluated in every iteration |
| -dimensionality of the problem | on the full population | |
| Adaptability | Medium, need to be built in the prior model | Medium, new reg. terms needed |
| Maternity | Probed in practice | In development |
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