Orthogonal Matching Pursuit based Reconstruction for Modulo Hysteresis Operators
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arXiv
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866915233467990016 |
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| author | Beckmann, Matthias Jeschke, Jürgen |
| author_facet | Beckmann, Matthias Jeschke, Jürgen |
| contents | Unlimited sampling provides an acquisition scheme for high dynamic range signals by folding the signal into the dynamic range of the analog-to-digital converter (ADC) using modulo non-linearity prior to sampling to prevent saturation. Recently, a generalized scheme called modulo hysteresis was introduced to account for hardware non-idealities. The encoding operator, however, does not guarantee that the output signal is within the dynamic range of the ADC. To resolve this, we propose a modified modulo hysteresis operator and show identifiability of bandlimited signals from modulo hysteresis samples. We propose a recovery algorithm based on orthogonal matching pursuit and validate our theoretical results through numerical experiments. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2504_05895 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Orthogonal Matching Pursuit based Reconstruction for Modulo Hysteresis Operators Beckmann, Matthias Jeschke, Jürgen Numerical Analysis Signal Processing Unlimited sampling provides an acquisition scheme for high dynamic range signals by folding the signal into the dynamic range of the analog-to-digital converter (ADC) using modulo non-linearity prior to sampling to prevent saturation. Recently, a generalized scheme called modulo hysteresis was introduced to account for hardware non-idealities. The encoding operator, however, does not guarantee that the output signal is within the dynamic range of the ADC. To resolve this, we propose a modified modulo hysteresis operator and show identifiability of bandlimited signals from modulo hysteresis samples. We propose a recovery algorithm based on orthogonal matching pursuit and validate our theoretical results through numerical experiments. |
| title | Orthogonal Matching Pursuit based Reconstruction for Modulo Hysteresis Operators |
| topic | Numerical Analysis Signal Processing |
| url | https://arxiv.org/abs/2504.05895 |