arXiv subjects

Alexander Denker

Publications and source records attributed to Alexander Denker.

25 records · Page 2Linked to original sources

arXiv2024

Score-Based Generative Models for PET Image Reconstruction

Score-based generative models have demonstrated highly promising results for medical image reconstruction tasks in magnetic resonance imaging or computed tomography. However, their application to Positron Emission Tomography (PET) is still largely unexplored. PET image reconstruction involves a variety of challenges, including Poisson noise with high variance and a wide dynamic range. To address these challenges, we propose several PET-specific adaptations of score-based generative models. The proposed framework is developed for both 2D and 3D PET. In addition, we provide an extension to guided reconstruction using magnetic resonance images. We validate the approach through extensive 2D and 3D $\textit{in-silico}$ experiments with a model trained on patient-realistic data without lesions, and evaluate on data without lesions as well as out-of-distribution data with lesions. This demonstrates the proposed method's robustness and significant potential for improved PET reconstruction.

eess.IV↗

arXiv2023

Invertible residual networks in the context of regularization theory for linear inverse problems

Learned inverse problem solvers exhibit remarkable performance in applications like image reconstruction tasks. These data-driven reconstruction methods often follow a two-step scheme. First, one trains the often neural network-based reconstruction scheme via a dataset. Second, one applies the scheme to new measurements to obtain reconstructions. We follow these steps but parameterize the reconstruction scheme with invertible residual networks (iResNets). We demonstrate that the invertibility enables investigating the influence of the training and architecture choices on the resulting reconstruction scheme. For example, assuming local approximation properties of the network, we show that these schemes become convergent regularizations. In addition, the investigations reveal a formal link to the linear regularization theory of linear inverse problems and provide a nonlinear spectral regularization for particular architecture classes. On the numerical side, we investigate the local approximation property of selected trained architectures and present a series of experiments on the MNIST dataset that underpin and extend our theoretical findings.

math.NA↗

arXiv2023

An Educated Warm Start For Deep Image Prior-Based Micro CT Reconstruction

Deep image prior (DIP) was recently introduced as an effective unsupervised approach for image restoration tasks. DIP represents the image to be recovered as the output of a deep convolutional neural network, and learns the network's parameters such that the output matches the corrupted observation. Despite its impressive reconstructive properties, the approach is slow when compared to supervisedly learned, or traditional reconstruction techniques. To address the computational challenge, we bestow DIP with a two-stage learning paradigm: (i) perform a supervised pretraining of the network on a simulated dataset; (ii) fine-tune the network's parameters to adapt to the target reconstruction task. We provide a thorough empirical analysis to shed insights into the impacts of pretraining in the context of image reconstruction. We showcase that pretraining considerably speeds up and stabilizes the subsequent reconstruction task from real-measured 2D and 3D micro computed tomography data of biological specimens. The code and additional experimental materials are available at https://educateddip.github.io/docs.educated_deep_image_prior/.

eess.IV↗

arXiv2022

PatchNR: Learning from Very Few Images by Patch Normalizing Flow Regularization

Learning neural networks using only few available information is an important ongoing research topic with tremendous potential for applications. In this paper, we introduce a powerful regularizer for the variational modeling of inverse problems in imaging. Our regularizer, called patch normalizing flow regularizer (patchNR), involves a normalizing flow learned on small patches of very few images. In particular, the training is independent of the considered inverse problem such that the same regularizer can be applied for different forward operators acting on the same class of images. By investigating the distribution of patches versus those of the whole image class, we prove that our model is indeed a MAP approach. Numerical examples for low-dose and limited-angle computed tomography (CT) as well as superresolution of material images demonstrate that our method provides very high quality results. The training set consists of just six images for CT and one image for superresolution. Finally, we combine our patchNR with ideas from internal learning for performing superresolution of natural images directly from the low-resolution observation without knowledge of any high-resolution image.

cs.LG↗

arXiv2021

Conditional Invertible Neural Networks for Medical Imaging

Over the last years, deep learning methods have become an increasingly popular choice to solve tasks from the field of inverse problems. Many of these new data-driven methods have produced impressive results, although most only give point estimates for the reconstruction. However, especially in the analysis of ill-posed inverse problems, the study of uncertainties is essential. In our work, we apply generative flow-based models based on invertible neural networks to two challenging medical imaging tasks, i.e. low-dose computed tomography and accelerated medical resonance imaging. We test different architectures of invertible neural networks and provide extensive ablation studies. In most applications, a standard Gaussian is used as the base distribution for a flow-based model. Our results show that the choice of a radial distribution can improve the quality of reconstructions.

eess.IV↗

arXiv2021

Feature reduction for machine learning on molecular features: The GeneScore

We present the GeneScore, a concept of feature reduction for Machine Learning analysis of biomedical data. Using expert knowledge, the GeneScore integrates different molecular data types into a single score. We show that the GeneScore is superior to a binary matrix in the classification of cancer entities from SNV, Indel, CNV, gene fusion and gene expression data. The GeneScore is a straightforward way to facilitate state-of-the-art analysis, while making use of the available scientific knowledge on the nature of molecular data features used.

q-bio.GN↗

arXiv2020

Conditional Normalizing Flows for Low-Dose Computed Tomography Image Reconstruction

Image reconstruction from computed tomography (CT) measurement is a challenging statistical inverse problem since a high-dimensional conditional distribution needs to be estimated. Based on training data obtained from high-quality reconstructions, we aim to learn a conditional density of images from noisy low-dose CT measurements. To tackle this problem, we propose a hybrid conditional normalizing flow, which integrates the physical model by using the filtered back-projection as conditioner. We evaluate our approach on a low-dose CT benchmark and demonstrate superior performance in terms of structural similarity of our flow-based method compared to other deep learning based approaches.

eess.IV↗