Breast cancer is the most common malignancy in women. Unfortunately, even though screening programs have helped to increase survival rates, the number of false positives and false negatives remains high. Phase-contrast X-ray CT is a promising imaging technique which could improve breast cancer diagnosis by combining the high three-dimensional resolution of conventional CT with higher soft-tissue contrast. Grating Interferometry CT (GI-CT) arguably has the highest chance to make the transition to clinical practice. Unfortunately though, obtaining high-quality images is challenging. Grating fabrication defects and photon starvation lead to high noise amplitudes in the measured data. Moreover, the highly ill-conditioned differential nature of the GI-CT forward operator renders the inversion from corrupted data even more cumbersome. In this article we report on a novel regularized iterative reconstruction algorithm with a powerful data-driven regularization strategy to tackle this challenging inverse problem. In particular, we present an algorithm that combines the L-BFGS optimization scheme with a Plug-and-Play denoiser parameterized by a deep neural network and empirically show that the proposed method achieves high quality images, both on simulated data as well as on real measurements.
In this talk we discuss the idea of data-driven regularisers for inverse imaging problems. We are in particular interested in the combination of model-based and purely data-driven image processing approaches. In this context we will make a journey from “shallow” learning for computing optimal parameters for variational regularisation models by bilevel optimization to the investigation of different approaches that use deep neural networks for solving inverse imaging problems. Alongside all approaches that are being discussed, their numerical solution and available solution guarantees will be stated.
Image reconstruction in positron emission tomography (PET) is computationally challenging due to Poisson noise, constraints and potentially non-smooth priors-let alone the sheer size of the problem. An algorithm that can cope well with the first three of the aforementioned challenges is the primal-dual hybrid gradient algorithm (PDHG) studied by Chambolle and Pock in 2011. However, PDHG updates all variables in parallel and is therefore computationally demanding on the large problem sizes encountered with modern PET scanners where the number of dual variables easily exceeds 100 million. In this work, we numerically study the usage of SPDHG-a stochastic extension of PDHG-but is still guaranteed to converge to a solution of the deterministic optimization problem with similar rates as PDHG. Numerical results on a clinical data set show that by introducing randomization into PDHG, similar results as the deterministic algorithm can be achieved using only around 10 % of operator evaluations. Thus, making significant progress towards the feasibility of sophisticated mathematical models in a clinical setting.
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