arXiv subjects

Jürgen Jeschke

Publications and source records attributed to Jürgen Jeschke.

3 recordsLinked to original sources

arXiv2026

Enhanced attenuation modelling for multispectral computed tomography

We revisit the modelling of the material decomposition problem in multispectral computed tomography and propose to leverage the known absorption spectra of different materials. With this we both derive new uniqueness conditions for the material decomposition and also offer a three-step reconstruction model. Our uniqueness criterion only requires certain characteristics of the bin sensitivity functions and the material attenuation spectra and hence, can be computed a-priori before measurements are taken.

math.NA↗

arXiv2026

Generalized Modulo Hysteresis Encoding

Unlimited sensing and its extension via modulo hysteresis provide an efficient encoding scheme for high dynamic range signals by folding the signal's amplitude into the range of the analog-to-digital converter prior to sampling. Motivated by shortcomings of the modulo hysteresis model, in this work we introduce generalized modulo encoders that flexibly design the folding by incorporating a general transition function and allowing the folding times to depend on the nonideality of the folding transition. We rigorously study mathematical properties of the respective operators and derive conditions under which a bandlimited signal is uniquely determined by its generalized modulo samples. Finally, we propose a recovery algorithm backed by mathematical guarantees and illustrate our theoretical results through numerical experiments.

math.NA↗

arXiv2025

Orthogonal Matching Pursuit based Reconstruction for Modulo Hysteresis Operators

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.

math.NA↗