Stability and Error Estimates of BV Solutions to the Abel Inverse Problem
| Autor: | Linan Zhang, Hayden Schaeffer |
|---|---|
| Rok vydání: | 2018 |
| Předmět: |
Stability (learning theory)
ComputingMethodologies_IMAGEPROCESSINGANDCOMPUTERVISION 010103 numerical & computational mathematics 02 engineering and technology Classification of discontinuities 01 natural sciences Theoretical Computer Science Mathematics - Analysis of PDEs 0202 electrical engineering electronic engineering information engineering FOS: Mathematics Applied mathematics Reconstructed image 0101 mathematics Mathematical Physics Mathematics Applied Mathematics Minimization problem Total variation denoising Inverse problem Computer Science Applications Functional Analysis (math.FA) Mathematics - Functional Analysis Noise Signal Processing A priori and a posteriori 020201 artificial intelligence & image processing Analysis of PDEs (math.AP) |
| DOI: | 10.48550/arxiv.1806.09451 |
| Popis: | Reconstructing images from ill-posed inverse problems often utilizes total variation regularization in order to recover discontinuities in the data while also removing noise and other artifacts. Total variation regularization has been successful in recovering images for (noisy) Abel transformed data, where object boundaries and data support will lead to sharp edges in the reconstructed image. In this work, we analyze the behavior of BV solutions to the Abel inverse problem, deriving a priori estimates on the recovery. In particular, we provide L2-stability bounds on BV solutions to the Abel inverse problem. These bounds yield error estimates on images reconstructed from a proposed total variation regularized minimization problem. Comment: 40 pages, 3 figures, 2 tables |
| Databáze: | OpenAIRE |
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