Median and related local filters for tensor-valued images

We develop a concept for the median filtering of tensor data. The main part of this concept is the definition of median for symmetric matrices. This definition is based on the minimisation of a geometrically motivated objective function which measures the sum of distances of a variable matrix to the given data matrices. This theoretically wellfounded concept fits into a context of similarly defined median filters for other multivariate data. Unlike some other approaches, we do not require by definition that the median has to be one of the given data values. Nevertheless, it happens so in many cases, equipping the matrix-valued median even with root signals similar to the scalar-valued situation. Like their scalar-valued counterparts, matrix-valued median filters show excellent capabilities for structure-preserving denoising. Experiments on diffusion tensor imaging, fluid dynamics and orientation estimation data are shown to demonstrate this. The orientation estimation examples give rise to a new variant of a robust adaptive structure tensor which can be compared to existing concepts. For the efficient computation of matrix medians, we present a convex programming framework. By generalising the idea of the matrix median filters, we design a variety of other local matrix filters. These include matrix-valued mid-range filters and, more generally, M-smoothers but also weighted medians and \alpha-quantiles. Mid-range filters and quantiles allow also interesting cross-links to fundamental concepts of matrix morphology

Hardware acceleration using FPGAs for adaptive radiotherapy

Adaptive radiotherapy (ART) seeks to improve the accuracy of radiotherapy by adapting the treatment based on up-to-date images of the patient's anatomy captured at the time of treatment delivery. The amount of image data, combined with the clinical time requirements for ART, necessitates automatic image analysis to adapt the treatment plan. Currently, the computational effort of the image processing and plan adaptation means they cannot be completed in a clinically acceptable timeframe. This thesis aims to investigate the use of hardware acceleration on Field Programmable Gate Arrays (FPGAs) to accelerate algorithms for segmenting bony anatomy in Computed Tomography (CT) scans, to reduce the plan adaptation time for ART. An assessment was made of the overhead incurred by transferring image data to an FPGA-based hardware accelerator using the industry-standard DICOM protocol over an Ethernet connection. The rate was found to be likely to limit the performanceof hardware accelerators for ART, highlighting the need for an alternative method of integrating hardware accelerators with existing radiotherapy equipment. A clinically-validated segmentation algorithm was adapted for implementation in hardware. This was shown to process three-dimensional CT images up to 13.81 times faster than the original software implementation. The segmentations produced by the two implementations showed strong agreement. Modifications to the hardware implementation were proposed for segmenting fourdimensional CT scans. This was shown to process image volumes 14.96 times faster than the original software implementation, and the segmentations produced by the two implementations showed strong agreement in most cases.A second, novel, method for segmenting four-dimensional CT data was also proposed. The hardware implementation executed 1.95 times faster than the software implementation. However, the algorithm was found to be unsuitable for the global segmentation task examined here, although it may be suitable as a refining segmentation in the context of a larger ART algorithm.Adaptive radiotherapy (ART) seeks to improve the accuracy of radiotherapy by adapting the treatment based on up-to-date images of the patient's anatomy captured at the time of treatment delivery. The amount of image data, combined with the clinical time requirements for ART, necessitates automatic image analysis to adapt the treatment plan. Currently, the computational effort of the image processing and plan adaptation means they cannot be completed in a clinically acceptable timeframe. This thesis aims to investigate the use of hardware acceleration on Field Programmable Gate Arrays (FPGAs) to accelerate algorithms for segmenting bony anatomy in Computed Tomography (CT) scans, to reduce the plan adaptation time for ART. An assessment was made of the overhead incurred by transferring image data to an FPGA-based hardware accelerator using the industry-standard DICOM protocol over an Ethernet connection. The rate was found to be likely to limit the performanceof hardware accelerators for ART, highlighting the need for an alternative method of integrating hardware accelerators with existing radiotherapy equipment. A clinically-validated segmentation algorithm was adapted for implementation in hardware. This was shown to process three-dimensional CT images up to 13.81 times faster than the original software implementation. The segmentations produced by the two implementations showed strong agreement. Modifications to the hardware implementation were proposed for segmenting fourdimensional CT scans. This was shown to process image volumes 14.96 times faster than the original software implementation, and the segmentations produced by the two implementations showed strong agreement in most cases.A second, novel, method for segmenting four-dimensional CT data was also proposed. The hardware implementation executed 1.95 times faster than the software implementation. However, the algorithm was found to be unsuitable for the global segmentation task examined here, although it may be suitable as a refining segmentation in the context of a larger ART algorithm

A 40 sec. of arc radio telescope

This thesis outlines the design, construction and operation of a new type of high resolution radio telescope. In its final form this telescope will 'map' an area of sky of one degree diameter with a pencil—beam resolution of 40 sec. of are at a frequency of 1415 MHz during an observing period of approximately 8 hours. The total area of antenna structure is low, yet it is used extremely efficiently and provides a high sensitivity of 2 or 3.10—28Wm-2Hz—l, sufficient for the telescope to be almost 'confusion' limited