Hermitian curve interpolation for CT-data re-sampling

Purpose: Development of an interpolation algorithm for re‐sampling spatially distributed CT‐data with the following features: global and local integral conservation, avoidance of negative interpolation values for positively defined datasets and the ability to control re‐sampling artifacts. Method and Materials: The interpolation can be separated into two steps: first, the discrete CT‐data has to be continuously distributed by an analytic function considering the boundary conditions. Generally, this function is determined by piecewise interpolation. Instead of using linear or high order polynomialinterpolations, which do not fulfill all the above mentioned features, a special form of Hermitian curve interpolation is used to solve the interpolation problem with respect to the required boundary conditions. A single parameter is determined, by which the behavior of the interpolation function is controlled. Second, the interpolated data have to be re‐distributed with respect to the requested grid. Results: The new algorithm was compared with commonly used interpolation functions based on linear and second order polynomial. It is demonstrated that these interpolation functions may over‐ or underestimate the source data by about 10%–20% while the parameter of the new algorithm can be adjusted in order to significantly reduce these interpolation errors. Finally, the performance and accuracy of the algorithm was tested by re‐gridding a series of X‐ray CT‐images. Conclusion: Inaccurate sampling values may occur due to the lack of integral conservation. Re‐sampling algorithms using high order polynomialinterpolation functions may result in significant artifacts of the re‐sampled data. Such artifacts can be avoided by using the new algorithm based on Hermitian curve interpolation

HIGH PERFORMANCE, LOW COST SUBSPACE DECOMPOSITION AND POLYNOMIAL ROOTING FOR REAL TIME DIRECTION OF ARRIVAL ESTIMATION: ANALYSIS AND IMPLEMENTATION

This thesis develops high performance real-time signal processing modules for direction of arrival (DOA) estimation for localization systems. It proposes highly parallel algorithms for performing subspace decomposition and polynomial rooting, which are otherwise traditionally implemented using sequential algorithms. The proposed algorithms address the emerging need for real-time localization for a wide range of applications. As the antenna array size increases, the complexity of signal processing algorithms increases, making it increasingly difficult to satisfy the real-time constraints. This thesis addresses real-time implementation by proposing parallel algorithms, that maintain considerable improvement over traditional algorithms, especially for systems with larger number of antenna array elements. Singular value decomposition (SVD) and polynomial rooting are two computationally complex steps and act as the bottleneck to achieving real-time performance. The proposed algorithms are suitable for implementation on field programmable gated arrays (FPGAs), single instruction multiple data (SIMD) hardware or application specific integrated chips (ASICs), which offer large number of processing elements that can be exploited for parallel processing. The designs proposed in this thesis are modular, easily expandable and easy to implement. Firstly, this thesis proposes a fast converging SVD algorithm. The proposed method reduces the number of iterations it takes to converge to correct singular values, thus achieving closer to real-time performance. A general algorithm and a modular system design are provided making it easy for designers to replicate and extend the design to larger matrix sizes. Moreover, the method is highly parallel, which can be exploited in various hardware platforms mentioned earlier. A fixed point implementation of proposed SVD algorithm is presented. The FPGA design is pipelined to the maximum extent to increase the maximum achievable frequency of operation. The system was developed with the objective of achieving high throughput. Various modern cores available in FPGAs were used to maximize the performance and details of these modules are presented in detail. Finally, a parallel polynomial rooting technique based on Newton’s method applicable exclusively to root-MUSIC polynomials is proposed. Unique characteristics of root-MUSIC polynomial’s complex dynamics were exploited to derive this polynomial rooting method. The technique exhibits parallelism and converges to the desired root within fixed number of iterations, making this suitable for polynomial rooting of large degree polynomials. We believe this is the first time that complex dynamics of root-MUSIC polynomial were analyzed to propose an algorithm. In all, the thesis addresses two major bottlenecks in a direction of arrival estimation system, by providing simple, high throughput, parallel algorithms.

Linear and Piecewise Functions

This morning Dr. Battle will review basic concepts of linear functions and piecewise functions and how they can be used as models for real-world applications. She will also introduce techniques for using a spreadsheet to analyze data.

OUT-OF-STEP DETECTION BASED ON ZUBOV’S APPROXIMATION BOUNDARY METHOD

Disturbances in power systems may lead to electromagnetic transient oscillations due to mismatch of mechanical input power and electrical output power. Out-of-step conditions in power system are common after the disturbances where the continuous oscillations do not damp out and the system becomes unstable. Existing out-of-step detection methods are system specific as extensive off-line studies are required for setting of relays. Most of the existing algorithms also require network reduction techniques to apply in multi-machine power systems. To overcome these issues, this research applies Phasor Measurement Unit (PMU) data and Zubov’s approximation stability boundary method, which is a modification of Lyapunov’s direct method, to develop a novel out-of-step detection algorithm. The proposed out-of-step detection algorithm is tested in a Single Machine Infinite Bus system, IEEE 3-machine 9-bus, and IEEE 10-machine 39-bus systems. Simulation results show that the proposed algorithm is capable of detecting out-of-step conditions in multi-machine power systems without using network reduction techniques and a comparative study with an existing blinder method demonstrate that the decision times are faster. The simulation case studies also demonstrate that the proposed algorithm does not depend on power system parameters, hence it avoids the need of extensive off-line system studies as needed in other algorithms.