
Infimal Models for Denoising and Super-Resolution of Raw Sinograms in Tomographic Medical Imaging Problems
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Raw sinogram data in computed tomography (CT) represent a critical yet underexplored domain, where photon absorption measurements are influenced by mixed noise components arising from both the physical process of photon scattering and engineering aspects of the CT machinery. These noise contributions, combining Poisson and Gaussian characteristics, are intrinsically linked to the physics of photon absorption as governed by Lambert-Beer's law. The statistical interplay of such noise types complicates image reconstruction, particularly when limited detector resolution is involved. To address this challenge, we introduce an infimal convolution model designed to denoise and super-resolve raw sinograms, thereby enhancing subsequent CT reconstruction quality. Our approach exploits the inherent coupling between noise sources and the detector’s spatial resolution by combining statistical noise modeling with algorithmic super-resolution. Specifically, we enhance the vertical resolution of sinograms through an algorithmic framework that simulates finer detector granularity, without the need for hardware upgrades. The infimal convolution framework allows us to incorporate domain-specific priors for mixed noise suppression, ensuring high fidelity in pre-log data representation. We demonstrate the effectiveness of this method on low-cost CT systems, where hardware limitations exacerbate noise and resolution constraints. Results show a substantial improvement in denoising performance and sinogram resolution, leading to enhanced reconstruction quality even in resource-constrained setups. This study lays the groundwork for future research into advanced denoising and super-resolution strategies while considering the entire medical image reconstruction process, bridging the gap between physical limitations of CT hardware and mathematical modeling for diagnostic imaging.