Shedding new light on Gaussian harmonic analysis

This dissertation consists out of two rather disjoint parts. One part concerns some results on Gaussian harmonic analysis and the other on an optimization problem in optics. In the first part we study the Ornstein–Uhlenbeck process with respect to the Gaussian measure. We focus on two areas. One is on “Gaussian” analogues of classical results in harmonic analysis, and in the second area we study the higher time-derivatives of the integral kernels associated to the Ornstein–Uhlenbeck operator. After introducing the necessary preliminaries on Hermite polynomials, we look at the non-tangential maximal function for the Ornstein–Uhlenbeck semigroup and we prove analogues to classical results. An important distinction here with the classical case is that the maximal function result for the Laplacian allows for t > 0, whereas our result only holds for certain 0 < t < 1 where the exact range depends on the position in space. Next, we compute an explicit formula for the higher time-derivatives of the integral kernel related to the Ornstein–Uhlenbeck operator. As an application we show several kernel bounds using our formula. Finally, as far as the mathematical part is concerned, we study off-diagonal estimates related to the Ornstein–Uhlenbeck operator. It is well-known that these hold for the Laplacian with respect to the Lebesgue measure, but do these hold for the Ornstein–Uhlenbeck operator with respect to the Gaussian measure? It is known that we always would have L2-L2 bounds, even for all t > 0, but in applications one often wants L2-L1 bounds. Even though these do hold for the Laplacian, we show that these cannot hold for the Ornstein–Uhlenbeck operator even for small 0 < t < 1. Moreover, our proof shows that letting the maximal t depend on the position in space will not work either. In the final part of this dissertation we study a problem in theoretical optics. Here we study the optimization of the electric field induced by light as a plane wave in a disk with given radius. We study the electric fields in the lens pupil and the focal region for several radii in the orde of magnitude of the wave length of the light used.Het onderzoek beschreven in dit proefschrift is mede gefinancierd door de Nederlandse Organisatie voor Wetenschappelijk Onderzoek (NWO), door de NWO-VICI onder projectnummer 639.033.604. Geen ISBNAnalysi

Gaussian Hardy Spaces

In this thesis we study a preprint by Pierre Portal that introduces Gaussian Hardy Spaces and proves equivalence of norms.AnalyseDIAMElectrical Engineering, Mathematics and Computer Scienc

The Lp boundedness of the Riesz Transform

In this thesis we study theorems that will yield easier expressions for the Sobolev space W2,p.Technische WiskundeMathematicsElectrical Engineering, Mathematics and Computer Scienc

Application of Deep Learning in Breast Cancer Imaging

This review gives an overview of the current state of deep learning research in breast cancer imaging. Breast imaging plays a major role in detecting breast cancer at an earlier stage, as well as monitoring and evaluating breast cancer during treatment. The most commonly used modalities for breast imaging are digital mammography, digital breast tomosynthesis, ultrasound and magnetic resonance imaging. Nuclear medicine imaging techniques are used for detection and classification of axillary lymph nodes and distant staging in breast cancer imaging. All of these techniques are currently digitized, enabling the possibility to implement deep learning (DL), a subset of Artificial intelligence, in breast imaging. DL is nowadays embedded in a plethora of different tasks, such as lesion classification and segmentation, image reconstruction and generation, cancer risk prediction, and prediction and assessment of therapy response. Studies show similar and even better performances of DL algorithms compared to radiologists, although it is clear that large trials are needed, especially for ultrasound and magnetic resonance imaging, to exactly determine the added value of DL in breast cancer imaging. Studies on DL in nuclear medicine techniques are only sparsely available and further research is mandatory. Legal and ethical issues need to be considered before the role of DL can expand to its full potential in clinical breast care practice

Differentiating benign and malignant mass and non-mass lesions in breast DCE-MRI using normalized frequency-based features

Contains fulltext : 217331.pdf (publisher's version ) (Closed access

Exploiting the Dixon Method for a Robust Breast and Fibro-Glandular Tissue Segmentation in Breast MRI

Automatic breast and fibro-glandular tissue (FGT) segmentation in breast MRI allows for the efficient and accurate calculation of breast density. The U-Net architecture, either 2D or 3D, has already been shown to be effective at addressing the segmentation problem in breast MRI. However, the lack of publicly available datasets for this task has forced several authors to rely on internal datasets composed of either acquisitions without fat suppression (WOFS) or with fat suppression (FS), limiting the generalization of the approach. To solve this problem, we propose a data-centric approach, efficiently using the data available. By collecting a dataset of T1-weighted breast MRI acquisitions acquired with the use of the Dixon method, we train a network on both T1 WOFS and FS acquisitions while utilizing the same ground truth segmentation. Using the "plug-and-play" framework nnUNet, we achieve, on our internal test set, a Dice Similarity Coefficient (DSC) of 0.96 and 0.91 for WOFS breast and FGT segmentation and 0.95 and 0.86 for FS breast and FGT segmentation, respectively. On an external, publicly available dataset, a panel of breast radiologists rated the quality of our automatic segmentation with an average of 3.73 on a four-point scale, with an average percentage agreement of 67.5%

DeepSMILE: Contrastive self-supervised pre-training benefits MSI and HRD classification directly from H&E whole-slide images in colorectal and breast cancer

We propose a Deep learning-based weak label learning method for analyzing whole slide images (WSIs) of Hematoxylin and Eosin (H&E) stained tumor tissue not requiring pixel-level or tile-level annotations using Self-supervised pre-training and heterogeneity-aware deep Multiple Instance LEarning (DeepSMILE). We apply DeepSMILE to the task of Homologous recombination deficiency (HRD) and microsatellite instability (MSI) prediction. We utilize contrastive self-supervised learning to pre-train a feature extractor on histopathology tiles of cancer tissue. Additionally, we use variability-aware deep multiple instance learning to learn the tile feature aggregation function while modeling tumor heterogeneity. For MSI prediction in a tumor-annotated and color normalized subset of TCGA-CRC (n=360 patients), contrastive self-supervised learning improves the tile supervision baseline from 0.77 to 0.87 AUROC, on par with our proposed DeepSMILE method. On TCGA-BC (n=1041 patients) without any manual annotations, DeepSMILE improves HRD classification performance from 0.77 to 0.81 AUROC compared to tile supervision with either a self-supervised or ImageNet pre-trained feature extractor. Our proposed methods reach the baseline performance using only 40% of the labeled data on both datasets. These improvements suggest we can use standard self-supervised learning techniques combined with multiple instance learning in the histopathology domain to improve genomic label classification performance with fewer labeled data

Artificial Intelligence-Based Classification of Breast Lesions Imaged With a Multiparametric Breast MRI Protocol With Ultrafast DCE-MRI, T2, and DWI

Item does not contain fulltex

State-of-the-Art Deep Learning in Cardiovascular Image Analysis

Cardiovascular imaging is going to change substantially in the next decade, fueled by the deep learning revolution. For medical professionals, it is important to keep track of these developments to ensure that deep learning can have meaningful impact on clinical practice. This review aims to be a stepping stone in this process. The general concepts underlying most successful deep learning algorithms are explained, and an overview of the state-of-the-art deep learning in cardiovascular imaging is provided. This review discusses >80 papers, covering modalities ranging from cardiac magnetic resonance, computed tomography, and single-photon emission computed tomography, to intravascular optical coherence tomography and echocardiography. Many different machines learning algorithms were used throughout these papers, with the most common being convolutional neural networks. Recent algorithms such as generative adversarial models were also used. The potential implications of deep learning algorithms on clinical practice, now and in the near future, are discussed

A Deep Learning-based correction to EPID dosimetry for attenuation and scatter in the Unity MR-Linac system

Item does not contain fulltex