Task adapted reconstruction for inverse problems

The paper considers the problem of performing a task defined on a model parameter that is only observed indirectly through noisy data in an ill-posed inverse problem. A key aspect is to formalize the steps of reconstruction and task as appropriate estimators (non-randomized decision rules) in statistical estimation problems. The implementation makes use of (deep) neural networks to provide a differentiable parametrization of the family of estimators for both steps. These networks are combined and jointly trained against suitable supervised training data in order to minimize a joint differentiable loss function, resulting in an end-to-end task adapted reconstruction method. The suggested framework is generic, yet adaptable, with a plug-and-play structure for adjusting both the inverse problem and the task at hand. More precisely, the data model (forward operator and statistical model of the noise) associated with the inverse problem is exchangeable, e.g., by using neural network architecture given by a learned iterative method. Furthermore, any task that is encodable as a trainable neural network can be used. The approach is demonstrated on joint tomographic image reconstruction, classification and joint tomographic image reconstruction segmentation

Coarse-graining in retrodictive quantum state tomography

Quantum state tomography often operates in the highly idealised scenario of assuming perfect measurements. The errors implied by such an approach are entwined with other imperfections relating to the information processing protocol or application of interest. We consider the problem of retrodicting the quantum state of a system, existing prior to the application of random but known phase errors, allowing those errors to be separated and removed. The continuously random nature of the errors implies that there is only one click per measurement outcome -- a feature having a drastically adverse effect on data-processing times. We provide a thorough analysis of coarse-graining under various reconstruction algorithms, finding dramatic increases in speed for only modest sacrifices in fidelity

Roche tomography of the secondary stars in CVs

The secondary stars in cataclysmic variables (CVs) are key to our understanding of the origin, evolution and behaviour of this class of interacting binary. In seeking a fuller understanding of these objects, the challenge for observers is to obtain images of the secondary star. This goal can be achieved through Roche tomography, an indirect imaging technique that can be used to map the Roche-lobe-filling secondary. The review begins with a description of the basic principles that underpin Roche tomography, including methods for determining the system parameters. Finally, we conclude with a look at the main scientific highlights to date, including the first unambiguous detection of starspots on AE Aqr B, and consider the future prospects of this technique.Comment: 4 pages, 4 figures. Accepted for publication in A