On Reconstruction Guarantees for Modulo Radon Transform Based Tomography

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• Matthias Beckmann
• Monday 27 November 2023, 15:00-16:30
• Denis Gabor Seminar Room, 611.

If you have a question about this talk, please contact Ayush Bhandari.

In the recent years, the topic of high dynamic range (HDR) tomography has started to gather attention due to recent advances in hardware technology. The issue is that registering high-intensity projections that exceed the dynamic range of the detector cause sensor saturation, which, in turn, leads to a loss of information. Inspired by the multi-exposure fusion strategy in computational photography, a common approach is to acquire multiple Radon projections at different exposure levels that are algorithmically fused to facilitate HDR reconstructions.

In our recent line of work, a single-shot approach has been proposed which is based on the Modulo Radon Transform, a novel generalization of the conventional Radon transform. In this case, Radon projections are folded via a modulo non-linearity, which allows HDR values to be mapped into the dynamic range of the sensor and, thus, avoids saturation or clipping. The folded measurements are then mapped back to their ambient range using reconstruction algorithms.

In this talk we introduce two conceptually different reconstruction approaches and show mathematical recovery guarantees and error estimates for target functions from Sobolev spaces of fractional order. The US-FBP method operates in the spatial domain and makes use of a variant of the Unlimited Sampling (US) algorithm. As opposed to this, the OMP -FBP method operates in the Fourier domain and is based on the Orthogonal Matching Pursuit (OMP) algorithm. We discuss pros and cons of both methods and illustrate our theoretical results by numerical experiments.

This talk is part of the Ayush Bhandari's list series.

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