Quantifying admissible undersampling for sparsity-exploiting iterative image reconstruction in X-ray CT

Iterative image reconstruction (IIR) with sparsity-exploiting methods, such as total variation (TV) minimization, investigated in compressive sensing (CS) claim potentially large reductions in sampling requirements. Quantifying this claim for computed tomography (CT) is non-trivial, because both full sampling in the discrete-to-discrete imaging model and the reduction in sampling admitted by sparsity-exploiting methods are ill-defined. The present article proposes definitions of full sampling by introducing four sufficient-sampling conditions (SSCs). The SSCs are based on the condition number of the system matrix of a linear imaging model and address invertibility and stability. In the example application of breast CT, the SSCs are used as reference points of full sampling for quantifying the undersampling admitted by reconstruction through TV-minimization. In numerical simulations, factors affecting admissible undersampling are studied. Differences between few-view and few-detector bin reconstruction as well as a relation between object sparsity and admitted undersampling are quantified.Comment: Revised version that was submitted to IEEE Transactions on Medical Imaging on 8/16/201

Ensuring convergence in total-variation-based reconstruction for accurate microcalcification imaging in breast X-ray CT

Breast X-ray CT imaging is being considered in screening as an extension to mammography. As a large fraction of the population will be exposed to radiation, low-dose imaging is essential. Iterative image reconstruction based on solving an optimization problem, such as Total-Variation minimization, shows potential for reconstruction from sparse-view data. For iterative methods it is important to ensure convergence to an accurate solution, since important image features, such as presence of microcalcifications indicating breast cancer, may not be visible in a non-converged reconstruction, and this can have clinical significance. To prevent excessively long computational times, which is a practical concern for the large image arrays in CT, it is desirable to keep the number of iterations low, while still ensuring a sufficiently accurate reconstruction for the specific imaging task. This motivates the study of accurate convergence criteria for iterative image reconstruction. In simulation studies with a realistic breast phantom with microcalcifications we compare different convergence criteria for reliable reconstruction. Our results show that it can be challenging to ensure a sufficiently accurate microcalcification reconstruction, when using standard convergence criteria. In particular, the gray level of the small microcalcifications may not have converged long after the background tissue is reconstructed uniformly. We propose the use of the individual objective function gradient components to better monitor possible regions of non-converged variables. For microcalcifications we find empirically a large correlation between nonzero gradient components and non-converged variables, which occur precisely within the microcalcifications. This supports our claim that gradient components can be used to ensure convergence to a sufficiently accurate reconstruction.Comment: 5 pages, 4 figures, extended version of conference paper for 2011 IEEE Nuclear Science Symposium and Medical Imaging Conferenc

Convex optimization problem prototyping for image reconstruction in computed tomography with the Chambolle-Pock algorithm

The primal-dual optimization algorithm developed in Chambolle and Pock (CP), 2011 is applied to various convex optimization problems of interest in computed tomography (CT) image reconstruction. This algorithm allows for rapid prototyping of optimization problems for the purpose of designing iterative image reconstruction algorithms for CT. The primal-dual algorithm is briefly summarized in the article, and its potential for prototyping is demonstrated by explicitly deriving CP algorithm instances for many optimization problems relevant to CT. An example application modeling breast CT with low-intensity X-ray illumination is presented.Comment: Resubmitted to Physics in Medicine and Biology. Text has been modified according to referee comments, and typos in the equations have been correcte

Model-based control algorithms for the quadruple tank system: An experimental comparison

We compare the performance of proportional-integral-derivative (PID) control, linear model predictive control (LMPC), and nonlinear model predictive control (NMPC) for a physical setup of the quadruple tank system (QTS). We estimate the parameters in a continuous-discrete time stochastic nonlinear model for the QTS using a prediction-error-method based on the measured process data and a maximum likelihood (ML) criterion. In the NMPC algorithm, we use this identified continuous-discrete time stochastic nonlinear model. The LMPC algorithm is based on a linearization of this nonlinear model. We tune the PID controller using Skogestad's IMC tuning rules using a transfer function representation of the linearized model. Norms of the observed tracking errors and the rate of change of the manipulated variables are used to compare the performance of the control algorithms. The LMPC and NMPC perform better than the PID controller for a predefined time-varying setpoint trajectory. The LMPC and NMPC algorithms have similar performance.Comment: 6 pages, 5 figures, 3 tables, to be published in Foundations of Computer Aided Process Operations / Chemical Process Control (FOCAPO/CPC 2023). Hilton San Antonio Hill Country, San Antonio, Texa

Self-assembly of ordered graphene nanodot arrays (vol 8, 47, 2017)

Change History: A correction to this article has been published and is linked from the HTML version of this article

Nye regionale banekoncepter

Stikordsreferat fra Trafikdage i Aalborg, 28. august 201

Group size dynamics of the endangered mountain nyala (Tragelaphus buxtoni) in protected areas of the Arsi and Ahmar Mountains, Ethiopia

As an adaptive biological trait, group size may offer a useful metric for monitoring the welfare of wildlife species affected by their environmental surroundings. Here, we examine the drivers that cause variation in group size of the endangered mountain nyala (Tragelaphus buxtoni), including a range of natural ecological factors as well as the density of livestock. For this purpose, we collected data along transect lines during both wet and dry seasons focusing on the hitherto poorly studied populations in the Arsi Mountains National Park, Munessa-Kuke Controlled Hunting Area and Muktar Mountain Forest Reserve, which are managed for multiple use of a variety of natural resources. We found group sizes to be an average of 6.3, 4.4 and 4.1 individuals in the Arsi Mountains, Munessa-Kuke and Muktar Mountain study areas, respectively, and a combination of livestock density and habitat visibility explained as much as 74% of the variation in group size. We propose that whereas group size increases with forage availability (as measured by Normalized Difference Vegetation Index -NDVI) and in open habitats (probably due to a switch in antipredator strategy), the presence of livestock also has an independent, negative impact on group size because of the associated disturbance. The findings contribute to understanding the environmental drivers of variation in group size in social antelopes, particularly highlighting the need to improve livestock management to help conservation of species at risk

Modeling habitat suitability for the lesser-known populations of endangered mountain nyala (<i>Tragelaphus buxtoni</i>) in the Arsi and Ahmar Mountains, Ethiopia.

Habitat suitability models have become a valuable tool for wildlife conservation and management, and are frequently used to better understand the range and habitat requirements of rare and endangered species. In this study, we employed two habitat suitability modeling techniques, namely Boosted Regression Tree (BRT) and Maximum Entropy (Maxent) models, to identify potential suitable habitats for the endangered mountain nyala (Tragelaphus buxtoni) and environmental factors affecting its distribution in the Arsi and Ahmar Mountains of Ethiopia. Presence points, used to develop our habitat suitability models, were recorded from fecal pellet counts (n = 130) encountered along 196 randomly established transects in 2015 and 2016. Predictor variables used in our models included major landcover types, Normalized Difference Vegetation Index (NDVI), greenness and wetness tasseled cap vegetation indices, elevation, and slope. Area Under the Curve model evaluations for BRT and Maxent were 0.96 and 0.95, respectively, demonstrating high performance. Both models were then ensembled into a single binary output highlighting an area of agreement. Our results suggest that 1864 km2 (9.1%) of the 20,567 km2 study area is suitable habitat for the mountain nyala with land cover types, elevation, NDVI, and slope of the terrain being the most important variables for both models. Our results highlight the extent to which habitat loss and fragmentation have disconnected mountain nyala subpopulations. Our models demonstrate the importance of further protecting suitable habitats for mountain nyala to ensure the species' conservation