Inverse Problems

Pathway

Pages are grouped by how many dependency steps into this group they sit. Everything a page needs from this group appears above it.

1. Level 0

   13 pages
   • level 0Active network tomography and identifiability by design4 results
     2 definitions, 1 algorithm, 1 theoremExamples & counterexamples →
   • level 0Analytic double fibrations and Bolker visibility17 results
     4 definitions, 10 lemmas, 3 theoremsExamples & counterexamples →
   • level 0Credible sets and frequentist coverage2 results
     1 definition, 1 exampleExamples & counterexamples →
   • level 0Dynamical observations and finite system realization5 results
     1 definition, 1 algorithm, 3 theoremsExamples & counterexamples →
   • level 0Euclidean Radon transform and filtered backprojection4 results
     1 definition, 1 algorithm, 2 theoremsExamples & counterexamples →
   • level 0Geodesic X-ray transforms on simple surfaces7 results
     2 definitions, 3 lemmas, 1 theoremExamples & counterexamples →
   • level 0Inverse maps, identifiability, and stability3 results
     2 definitions, 1 theoremExamples & counterexamples →
   • level 0Open frontiers in calibrated and robust learned inversion2 results
     Examples & counterexamples →
   • level 0Posterior computation and error accounting2 results
     1 definition, 1 propositionExamples & counterexamples →
   • level 0Score and diffusion methods for inverse data4 results
     1 definition, 1 algorithm, 1 lemma, 1 propositionExamples & counterexamples →
   • level 0Sparse recovery and nullspace certificates3 results
     1 definition, 1 lemma, 1 theoremExamples & counterexamples →
   • level 0Spatial BV, finite perimeter, and TV conventions23 results
     2 definitions, 21 lemmasExamples & counterexamples →
   • level 0Statistical inverse experiments and white noise2 results
     1 definition, 1 theoremExamples & counterexamples →

2. Level 1

   11 pages
   • level 1Compact linear inverse maps and the Picard criterion4 results
     2 definitions, 2 theoremsExamples & counterexamples →
   • level 1Function-space priors and sample regularity4 results
     1 definition, 3 lemmasExamples & counterexamples →
   • level 1Hyperbolic inverse problems and finite-time visibility16 results
     2 definitions, 11 lemmas, 2 theorems, 1 corollaryExamples & counterexamples →
   • level 1Limited-angle visibility and instability10 results
     2 definitions, 4 lemmas, 2 propositions, 1 corollaryExamples & counterexamples →
   • level 1Linear feature identifiability and Gaussian MAP tests5 results
     1 definition, 1 algorithm, 3 theoremsExamples & counterexamples →
   • level 1Nonlinear maps and tangential cone control5 results
     3 definitions, 1 lemma, 1 theoremExamples & counterexamples →
   • level 1Nonlinear Tikhonov existence and stability8 results
     3 definitions, 1 lemma, 4 theoremsExamples & counterexamples →
   • level 1Real phase retrieval and phaseless ambiguity9 results
     3 definitions, 1 algorithm, 2 lemmas, 2 theorems, 1 corollaryExamples & counterexamples →
   • level 1Scalar Calderón maps and conditional uniqueness21 results
     4 definitions, 11 lemmas, 5 theorems, 1 corollaryExamples & counterexamples →
   • level 1Stable compressed sensing with noise10 results
     2 definitions, 1 algorithm, 6 lemmas, 1 theoremExamples & counterexamples →
   • level 1Unknown operators, model mismatch, and robustness limits2 results
     1 definition, 1 theoremExamples & counterexamples →

3. Level 2

   12 pages
   • level 2Anisotropic gauge and unresolved uniqueness5 results
     1 definition, 2 lemmas, 1 theoremExamples & counterexamples →
   • level 2Bregman distances and variational source rates6 results
     3 definitions, 2 lemmas, 1 theoremExamples & counterexamples →
   • level 2Data, operator, discretization, and solve errors2 results
     1 definition, 1 propositionExamples & counterexamples →
   • level 2Deterministic source classes and optimal recovery7 results
     3 definitions, 2 lemmas, 2 theoremsExamples & counterexamples →
   • level 2Fixed-frequency inverse scattering and Born linearization4 results
     1 definition, 1 algorithm, 2 lemmasExamples & counterexamples →
   • level 2Gaussian sequence inversion and exact risk4 results
     2 definitions, 1 algorithm, 1 theoremExamples & counterexamples →
   • level 2Likelihood potentials and posterior propriety2 results
     1 definition, 1 theoremExamples & counterexamples →
   • level 2Nonlinear Landweber with discrepancy stopping2 results
     1 algorithm, 1 theoremExamples & counterexamples →
   • level 2Parameter rules and the noise-free veto2 results
     1 definition, 1 theoremExamples & counterexamples →
   • level 2PDE-constrained inversion and adjoint error control6 results
     1 definition, 1 algorithm, 2 lemmas, 1 proposition, 1 theoremExamples & counterexamples →
   • level 2Physical constraints and manifold-valued inversion4 results
     1 definition, 1 algorithm, 1 lemma, 1 propositionExamples & counterexamples →
   • level 2Regularized nonlinear Levenberg–Marquardt6 results
     1 definition, 1 algorithm, 3 lemmas, 1 theoremExamples & counterexamples →

4. Level 3

   11 pages
   • level 3Adaptive spectral regularization by SOLIT5 results
     1 definition, 1 algorithm, 2 lemmas, 1 theoremExamples & counterexamples →
   • level 3Banach range invariance and EIT rates19 results
     2 definitions, 14 lemmas, 2 theorems, 1 remarkExamples & counterexamples →
   • level 3Factorized and composite linear inversion3 results
     1 definition, 1 theoremExamples & counterexamples →
   • level 3Function-space pCN and invariant posterior kernels6 results
     1 algorithm, 3 lemmas, 2 theoremsExamples & counterexamples →
   • level 3Hellinger stability and posterior discretization3 results
     1 lemma, 2 theoremsExamples & counterexamples →
   • level 3Learned reconstruction targets and risk3 results
     2 definitions, 1 propositionExamples & counterexamples →
   • level 3Linear Gaussian inverse posteriors and Tikhonov3 results
     1 lemma, 1 theorem, 1 corollaryExamples & counterexamples →
   • level 3Minimax estimation over inverse source classes4 results
     2 lemmas, 1 theorem, 1 corollaryExamples & counterexamples →
   • level 3Minimax signal detection and separation rates10 results
     1 definition, 6 lemmas, 2 theorems, 1 corollaryExamples & counterexamples →
   • level 3Small-ball MAP and Cameron–Martin geometry4 results
     1 definition, 2 lemmas, 1 theoremExamples & counterexamples →
   • level 3TV source certificates and level-set convergence15 results
     4 definitions, 10 lemmas, 1 theoremExamples & counterexamples →

5. Level 4

   7 pages
   • level 4Bayesian measurement design and information gain6 results
     2 definitions, 1 algorithm, 3 theoremsExamples & counterexamples →
   • level 4Benchmarks, prior shift, and solver admissibility2 results
     1 definition, 1 remarkExamples & counterexamples →
   • level 4Conditional flow matching for inverse posteriors6 results
     1 algorithm, 3 lemmas, 1 theoremExamples & counterexamples →
   • level 4Logarithmic EIT stability on explicit conductivity classes28 results
     2 definitions, 25 lemmas, 1 theoremExamples & counterexamples →
   • level 4Plug-and-play MMSE denoisers and stationarity4 results
     1 algorithm, 1 lemma, 1 theorem, 1 remarkExamples & counterexamples →
   • level 4Posterior contraction in Gaussian sequence inversion2 results
     1 definition, 1 theoremExamples & counterexamples →
   • level 4Unrolled reconstruction and finite-iteration limits3 results
     1 definition, 1 lemma, 1 propositionExamples & counterexamples →

6. Level 5

   1 page
   • level 5Noise-robust neural-operator approximation for EIT19 results
     2 definitions, 12 lemmas, 4 theoremsExamples & counterexamples →