Open Access
Table 2
Wavelet forward–backward splitting: pipeline round 2.
| Input: Visibilities: V |
| Input: Stepsize: τ (chosen artificially, such that algorithm converges) |
| Input: Regularization Parameter: α |
| Input: Total flux: f |
| ▷ Precompute needed data terms and operators |
| Define a dictionary of basis functions(wavelets): Γ |
| Define a forward operator: G : I ↦ FΓI (note G is linear) |
| Define a data-fidelity functional: df : I ↦ Slca(V, GI) + Scph(V, ΓI) |
| Precompute gradient of data-fidelity functional: df′[I] |
| Define a penalty term: pen : I ↦ |support(x)| (l0-norm) |
| Precompute proximal operator of penalty term: proxτ (hard thrinkage operator, Eq. (25)) |
| I = initialguess |
| ▷ Find initial image thresholding by minimizing Eq. (26) on a predefined grid of thresholds |
| Define grid of possible thresholds: ti |
| for i = 1, 2, 3, … do |
Hard thresholding:  |
| mini = df (testi) + αpen(testi) |
Find minimum i and update initial guess  |
| mintot = mini |
| for j = 0, 1, 2, …, J do |
| for i = 1, 2, 3, … do |
Hard thresholding single scale:  |
| mini,j = df (testi,j) + αpen(testi,j) |
| if mini,j < mintot then |
| mintot = mini,j |
 |
| ▷ Start forward–backward iterations from this guess |
| while stopping-rule 1 do |
| while stopping-rule 2 do |
| I = I - τ d f′ [I] |
| I = proxτ·α(I) |
| I = I·f/sum(ΓI) |
| Compute Multiresolution support M = {I ≠ 0} |
| Output: I is approximate minimizer to Eq. (26) |
| Output: Î = ΓI is an approximation to the true sky brightness distribution |
| Output: As a byproduct M is a reasonable multi-resolution support |
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