Encoding-decoding (ED) CNNs have demonstrated state-of-the-art performance for noise reduction over the past years. This has triggered the pursuit of better understanding the inner workings of such architectures, which has led to the theory of deep convolutional framelets (TDCF), revealing important links between signal processing and CNNs. Specifically, the TDCF demonstrates that ReLU CNNs induce low-rankness, since these models often do not satisfy the necessary redundancy to achieve perfect reconstruction (PR). In contrast, this paper explores CNNs that do meet the PR conditions. We demonstrate that in these type of CNNs soft shrinkage and PR can be assumed. Furthermore, based on our explorations we propose the learned wavelet-frame shrinkage network, or LWFSN and its residual counterpart, the rLWFSN. The ED path of the (r)LWFSN complies with the PR conditions, while the shrinkage stage is based on the linear expansion of thresholds proposed Blu and Luisier. In addition, the LWFSN has only a fraction of the training parameters (<1%) of conventional CNNs, very small inference times, low memory footprint, while still achieving performance close to state-of-the-art alternatives, such as the tight frame (TF) U-Net and FBPConvNet, in low-dose CT denoising.

Better understanding of hemodynamics conceivably leads to improved diagnosis and prognosis of cardiovascular diseases. Therefore, an elaborate analysis of the blood-flow in heart and thoracic arteries is essential. Contemporary MRI techniques enable acquisition of quantitative time-resolved flow information, resulting in 4D velocity fields that capture the blood-flow behavior. Visual exploration of these fields provides comprehensive insight into the unsteady blood-flow behavior, and precedes a quantitative analysis of additional blood-flow parameters. The complete inspection requires accurate segmentation of anatomical structures, encompassing a time-consuming and hard-to-automate process, especially for malformed morphologies. We present a way to avoid the laborious segmentation process in case of qualitative inspection, by introducing an interactive virtual probe. This probe is positioned semi-automatically within the blood-flow field, and serves as a navigational object for visual exploration. The difficult task of determining position and orientation along the view-direction is automated by a fitting approach, aligning the probe with the orientations of the velocity field. The aligned probe provides an interactive seeding basis for various flow visualization approaches. We demonstrate illustration-inspired particles, integral lines and integral surfaces, conveying distinct characteristics of the unsteady blood-flow. Lastly, we present the results of an evaluation with domain experts, valuing the practical use of our probe and flow visualization techniques.

Insight into the dynamics of blood-flow considerably improves the understanding of the complex cardiovascular system and its pathologies. Advances in MRI technology enable acquisition of 4D blood-flow data, providing quantitative blood-flow velocities over time. The currently typical slice-by-slice analysis requires a full mental reconstruction of the unsteady blood-flow field, which is a tedious and highly challenging task, even for skilled physicians. We endeavor to alleviate this task by means of comprehensive visualization and interaction techniques. In this paper we present a framework for pre-clinical cardiovascular research, providing tools to both interactively explore the 4D blood-flow data and depict the essential blood-flow characteristics. The framework encompasses a variety of visualization styles, comprising illustrative techniques as well as improved methods from the established field of flow visualization. Each of the incorporated styles, including exploded planar reformats, flow-direction highlights, and arrow-trails, locally captures the blood-flow dynamics and may be initiated by an interactively probed vessel cross-section. Additionally, we present the results of an evaluation with domain experts, measuring the value of each of the visualization styles and related rendering parameters.

Visually assessing the effect of the coronary artery anatomy on the perfusion of the heart muscle in patients with coronary artery disease remains a challenging task. We explore the feasibility of visualizing this effect on perfusion using a numerical approach. We perform a computational simulation of the way blood is perfused throughout the myocardium purely based on information from a three-dimensional anatomical tomographic scan. The results are subsequently visualized using both three-dimensional visualizations and bull's eye plots, partially inspired by approaches currently common in medical practice. Our approach results in a comprehensive visualization of the coronary anatomy that compares well to visualizations commonly used for other scanning technologies. We demonstrate techniques giving detailed insight in blood supply, coronary territories and feeding coronary arteries of a selected region. We demonstrate the advantages of our approach through visualizations that show information which commonly cannot be directly observed in scanning data, such as a separate visualization of the supply from each coronary artery. We thus show that the results of a computational simulation can be effectively visualized and facilitate visually correlating these results to for example perfusion data.

We present novel, comprehensive visualization techniques for the diagnosis of patients with Coronary Artery Disease using segmented cardiac MRI data. We extent an accepted medical visualization technique called the bull's eye plot by removing discontinuities, preserving the volumetric nature of the left ventricular wall and adding anatomical context. The resulting volumetric bull's eye plot can be used for the assessment of transmurality. We link these visualizations to a 3D view that presents viability information in a detailed anatomical context. We combine multiple MRI scans (whole heart anatomical data, late enhancement data) and multiple segmentations (polygonal heart model, late enhancement contours, coronary artery tree). By selectively combining different rendering techniques we obtain comprehensive yet intuitive visualizations of the various data sources.

Computer-aided diagnosis (CAD) is a helpful addition to laborious visual inspection for preselection of suspected colonic polyps in virtual colonoscopy. Most of the previous work on automatic polyp detection makes use of indicators based on the scalar curvature of the colon wall and can result in many false-positive detections. Our work tries to reduce the number of false-positive detections in the preselection of polyp candidates. Polyp surface shape can be characterized and visualized using lines of curvature. In this paper, we describe techniques for generating and rendering lines of curvature on surfaces and we show that these lines can be used as part of a polyp detection approach. We have adapted existing approaches on explicit triangular surface meshes, and developed a new algorithm on implicit surfaces embedded in 3D volume data. The visualization of shaded colonic surfaces can be enhanced by rendering the derived lines of curvature on these surfaces. Features strongly correlated with true-positive detections were calculated on lines of curvature and used for the polyp candidate selection. We studied the performance of these features on 5 data sets that included 331 pre-detected candidates, of which 50 sites were true polyps. The winding angle had a significant discriminating power for true-positive detections, which was demonstrated by a Wilcoxon rank sum test with p < 0.001. The median winding angle and inter-quartile range (IQR) for true polyps were 7.817 and 6.770 - 9.288 compared to 2.954 and 1.995 - 3.749 for false-positive detections.