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PreprintCC BY 4.0arXiv

Computing Data-Aware Diagonal Frame Decompositions

  • Andrea Ebner
  • Dirk Lorenz
  • Mathias Staudigl
Open at sourcePDFDOICite

Abstract

We present a method for computing a specific type of matrix decomposition that combines a structured framework with data-driven adaptation. This framework allows for an efficient and stable representation of signals or images using frames by identifying sets of vectors that naturally capture the essential features of the given data. The resulting decomposition enables the development of regularization techniques that enhance the quality of reconstruction by preserving important signal characteristics while suppressing noise. We develop an optimization-based algorithm to compute the decomposition and establish convergence properties of the resulting iterates. Numerical experiments on synthetic data and tomographic image reconstruction illustrate the behavior of the proposed method and its performance compared to conventional spectral regularization methods.

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Cite

BibTeXRIS
BibTeX
@misc{ebner2026computing,
  title = {{Computing Data-Aware Diagonal Frame Decompositions}},
  author = {Andrea Ebner and Dirk Lorenz and Mathias Staudigl},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2610.35691},
  eprint = {2610.35691},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2610.35691},
  note = {CC BY 4.0},
}
RIS
TY  - UNPB
TI  - Computing Data-Aware Diagonal Frame Decompositions
AU  - Andrea Ebner
AU  - Dirk Lorenz
AU  - Mathias Staudigl
PY  - 2026
DA  - 2026/10/26
PB  - arXiv
DO  - 10.48550/arxiv.2610.35691
UR  - https://arxiv.org/abs/2610.35691
AB  - We present a method for computing a specific type of matrix decomposition that combines a structured framework with data-driven adaptation. This framework allows for an efficient and stable representation of signals or images using frames by identifying sets of vectors that naturally capture the essential features of the given data. The resulting decomposition enables the development of regularization techniques that enhance the quality of reconstruction by preserving important signal characteristics while suppressing noise. We develop an optimization-based algorithm to compute the decomposition and establish convergence properties of the resulting iterates. Numerical experiments on synthetic data and tomographic image reconstruction illustrate the behavior of the proposed method and its performance compared to conventional spectral regularization methods.
ER  -