LpL^p-LqL^q off-diagonal estimates for the Ornstein--Uhlenbeck semigroup: some positive and negative results

We investigate $L^p(\gamma)$-$L^q(\gamma)$ off-diagonal estimates for the Ornstein-Uhlenbeck semigroup $(e^{tL})_{t > 0}$. For sufficiently large $t$ (quantified in terms of $p$ and $q$) these estimates hold in an unrestricted sense, while for sufficiently small $t$ they fail when restricted to maximal admissible balls and sufficiently small annuli. Our counterexample uses Mehler kernel estimates.Comment: Final version. To appear in the Bulletin of the Australian Mathematical Societ

End-to-end Memory-Efficient Reconstruction for Cone Beam CT

Cone Beam CT plays an important role in many medical fields nowadays, but the potential of this imaging modality is hampered by lower image quality compared to the conventional CT. A lot of recent research has been directed towards reconstruction methods relying on deep learning. However, practical application of deep learning to CBCT reconstruction is complicated by several issues, such as exceedingly high memory costs of deep learning methods for fully 3D data. In this work, we address these limitations and propose LIRE: a learned invertible primal-dual iterative scheme for Cone Beam CT reconstruction. Memory requirements of the network are substantially reduced while preserving its expressive power, enabling us to train on data with isotropic 2mm voxel spacing, clinically-relevant projection count and detector panel resolution on current hardware with 24 GB VRAM. Two LIRE models for small and for large Field-of-View setting were trained and validated on a set of 260 + 22 thorax CT scans and tested using a set of 142 thorax CT scans plus an out-of-distribution dataset of 79 head \& neck CT scans. For both settings, our method surpasses the classical methods and the deep learning baselines on both test sets. On the thorax CT set, our method achieves PSNR of 33.84 $\pm$ 2.28 for the small FoV setting and 35.14 $\pm$ 2.69 for the large FoV setting; U-Net baseline achieves PSNR of 33.08 $\pm$ 1.75 and 34.29 $\pm$ 2.71 respectively. On the head \& neck CT set, our method achieves PSNR of 39.35 $\pm$ 1.75 for the small FoV setting and 41.21 $\pm$ 1.41 for the large FoV setting; U-Net baseline achieves PSNR of 33.08 $\pm$ 1.75 and 34.29 $\pm$ 2.71 respectively. Additionally, we demonstrate that LIRE can be finetuned to reconstruct high-resolution CBCT data with the same geometry but 1mm voxel spacing and higher detector panel resolution, where it outperforms the U-Net baseline as well

Tussen data en theorie:Het venijn zit in de aard

Algoritmen helpen om op grote schaal beslissingen te nemen. Het is echter lastig om achteraf toe te zien op de kwaliteit van deze beslissingen. Toezicht zou zich met name moeten richten op het wordingsproces van algoritmes: de stappen die genomen worden om te komen van probleemomschrijving tot een geïmplementeerd algoritme. In dit proces worden immers de principiële keuzes gemaakt die bepalend zijn voor de manier waarop het algoritme zal handelen en de wijze waarop het uitwerking heeft op de maatschappij. Door deze keuzes expliciet en onder de juiste overwegingen te maken verkleint het risico op misdragingen. Toezichthouders en ontwikkelaars van algoritmen tezamen kunnen hier een handreiking voor opstellen