Mercurial > repos > pointsource_algs / file comparison
comparison: README.md
README.md
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| 4 This package contains [Rust][] codes for the manuscript “_Proximal methods for | 4 This package contains [Rust][] codes for the manuscript “_Proximal methods for |
| 5 point source localisation_” by Tuomo Valkonen ⟨tuomov@iki.fi⟩. It concerns | 5 point source localisation_” by Tuomo Valkonen ⟨tuomov@iki.fi⟩. It concerns |
| 6 solution of problems of the type | 6 solution of problems of the type |
| 7 $$ | 7 $$ |
| 8 \min_{μ ∈ ℳ(Ω)}~ F(x) + λ \|μ\|_{ℳ(Ω)} + δ_{≥ 0}(x), | 8 \min_{μ ∈ ℳ(Ω)}~ F(μ) + λ \|μ\|_{ℳ(Ω)} + δ_{≥ 0}(μ), |
| 9 $$ | 9 $$ |
| 10 where $F$ is a data term, and $ℳ(Ω)$ is the space of Radon measures on the | 10 where $F$ is a data term, and $ℳ(Ω)$ is the space of Radon measures on the |
| 11 (rectangular) domain $Ω ⊂ ℝ^n$. Implemented are $F(x)=\frac12\|Ax-b\|_2^2$ and | 11 (rectangular) domain $Ω ⊂ ℝ^n$. Implemented are $F(μ)=\frac12\|Aμ-b\|_2^2$ and |
| 12 $F(x)=\|Ax-b\|_1$ for the forward operator $A \in 𝕃(ℳ(Ω); ℝ^m)$ modelling a | 12 $F(μ)=\|Aμ-b\|_1$ for the forward operator $A \in 𝕃(ℳ(Ω); ℝ^m)$ modelling a |
| 13 simple sensor grid. For the 2-norm-squared data term implemented are the | 13 simple sensor grid. For the 2-norm-squared data term implemented are the |
| 14 algorithms μFB, μFISTA, and μPDPS from the aforementioned manuscript along with | 14 algorithms μFB, μFISTA, and μPDPS from the aforementioned manuscript along with |
| 15 comparison relaxed and fully corrective conditional gradient methods from the | 15 comparison relaxed and fully corrective conditional gradient methods from the |
| 16 literature. For the 1-norm data term only the μPDPS is applicable. | 16 literature. For the 1-norm data term only the μPDPS is applicable. |
| 17 | 17 |
