Effective interactive computing methods are needed in a number of specific areas of geophysical interpretation, even though the basic algorithms have been established. One approach to raise the quality of interpretation is to promote better interaction between human and the computer. The thesis is concerned with improving this dialog in three areas: automatic event picking, data visualization and sparse data imaging. Fully automatic seismic event picking methods work well in relatively good conditions. They collapse when the signal-to-noise ratio is low and the structure of the subsurface is complex. The interactive seismic event picking system described here blends the interpreter's guidance and judgment into the computer program, as it can bring the user into the loop to make subjective decisions when the picking problem is complicated. Several interactive approaches for 2-D event picking and 3-D horizon tracking have been developed. Envelope (or amplitude) threshold detection for first break picking is based on the assumption that the power of the signal is larger than that of the noise. Correlation and instantaneous phase pickers are designed for and better suited to picking other arrivals. The former is based on the cross-correlation function, and a model trace (or model traces) selected by the interpreter is needed. The instantaneous phase picker is designed to track spatial variations in the instantaneous phase of the analytic form of the arrival. The picking options implemented into the software package SeisWin were tested on real data drawn from many sources, such as full waveform sonic borehole logs, seismic reflection surveys and borehole radar profiles, as well as seven of the most recent 3-D seismic surveys conducted over Australian coal mines. The results show that the interactive picking system in SeisWin is efficient and tolerant. The 3-D horizon tracking method developed especially attracts industrial users. The visualization of data is also a part of the study, as picking accuracy, and indeed the whole of seismic interpretation depends largely on the quality of the final display. The display is often the only window through which an interpreter can see the earth's substructures. Display is a non-linear operation. Adjustments made to meet display deficiencies such as automatic gain control (AGC) have an important and yet ill-documented effect on the performance of pattern recognition operators, both human and computational. AGC is usually implemented in one dimension. Some of the tools in wide spread use for two dimensional image processing which are of great value in the local gain control of conventional seismic sections such as edge detectors, histogram equalisers, high-pass filters, shaded relief are discussed. Examples are presented to show the relative effectiveness of various display options. Conventional migration requires dense arrays with uniform coverage and uniform illumination of targets. There are, however, many instances in which these ideals can not be approached. Event migration and common tangent plane stacking procedures were developed especially for sparse data sets as a part of the research effort underlying this thesis. Picked-event migration migrates the line between any two points on different traces on the time section to the base map. The interplay between the space and time domain gives the interpreter an immediate view of mapping. Tangent plane migration maps the reflector by accumulating the energy from any two possible reflecting points along the common tangent lines on the space plane. These methods have been applied to both seismic and borehole-radar data and satisfactory results have been achieved.

In previous work (Olshausen & Field 1996), an algorithm was described for learning linear sparse codes which, when trained on natural images, produces a set of basis functions that are spatially localized, oriented, and bandpass (i.e., wavelet-like). This note shows how the algorithm may be interpreted within a maximum-likelihood framework. Several useful insights emerge from this connection: it makes explicit the relation to statistical independence (i.e., factorial coding), it shows a formal relationship to the algorithm of Bell and Sejnowski (1995), and it suggests how to adapt parameters that were previously fixed.

Magnetic Resonance Imaging (MRI) is an essential instrument in clinical diag- nosis; however, it is burdened by a slow data acquisition process due to physical limitations. Compressive Sensing (CS) is a recently developed mathematical framework that o ers signi cant bene ts in MRI image speed by reducing the amount of acquired data without degrading the image quality. The process of image reconstruction involves solving a nonlinear constrained optimization problem. The reduction of reconstruction time in MRI is of signi cant bene t. We reformulate sparse MRI reconstruction as a Second Order Cone Program (SOCP).We also explore two alternative techniques to solving the SOCP prob- lem directly: NESTA and speci cally designed SOCP-LB. / UOIT

Progressive developments in computing and sensor technologies during the past decades have enabled the formulation of increasingly advanced problems in statistical inference and signal processing. The thesis is concerned with statistical estimation methods, and is divided into three parts with focus on two different areas: sensor fusion and sparse signal processing. The first part introduces the well-established Bayesian, Fisherian and least-squares estimation frameworks, and derives new estimators. Specifically, the Bayesian framework is applied in two different classes of estimation problems: scenarios in which (i) the signal covariances themselves are subject to uncertainties, and (ii) distance bounds are used as side information. Applications include localization, tracking and channel estimation. The second part is concerned with the extraction of useful information from multiple sensors by exploiting their joint properties. Two sensor configurations are considered here: (i) a monocular camera and an inertial measurement unit, and (ii) an array of passive receivers. New estimators are developed with applications that include inertial navigation, source localization and multiple waveform estimation. The third part is concerned with signals that have sparse representations. Two problems are considered: (i) spectral estimation of signals with power concentrated to a small number of frequencies,and (ii) estimation of sparse signals that are observed by few samples, including scenarios in which they are linearly underdetermined. New estimators are developed with applications that include spectral analysis, magnetic resonance imaging and array processing. / <p>QC 20130426</p>

Hardware texture mapping is essential for real-time rendering. Unfortunately the memory bandwidth and latency often bounds performance in current graphics architectures. Bandwidth consumption can be reduced by compressing the texture map or by using a cache. However, the way a texture map occupies memory and how it is accessed affects the pattern of memory accesses, which in turn affects cache performance. Thus texture compression schemes and cache architectures must be designed in conjunction with each other. We define a sparse texture to be a texture where a substantial percentage of the texture is constant. Sparse textures are of interest as they occur often, and they are used as parts of more general texture compression schemes. We present a hardware compatible implementation of sparse textures based on B-tree indexing and explore cache designs for it. We demonstrate that it is possible to have the bandwidth consumption and miss rate due to the texture data alone scale with the area of the region of interest. We also show that the additional bandwidth consumption and hideable latency due to the B-tree indices are low. Furthermore, the caches necessary for these textures can be quite small.

Computing A^X mod n or A^XB^Y mod n for large X, Y, and n is very important in many ElGamal-like public key cryptosystems. In this paper, we proposed using block method in sparse form to improve the performance of modular exponentiation and analyzing the computational cost by state transition diagram. We also extended the concept of Block Method and make it more general. This method is suitable for some devices with limited storage space, such as smart card.

Minimally invasive technique (MIS) revolutionized the field of surgery for its shorter hospitalization time, lower complication rates, and ultimately reduced morbidity and mortality. However, one of the critical challenges that prevent it from reaching the full potentials is the restricted visualization from the traditional monocular camera systems at the presence of tissue deformations. This dissertation aims to design a new approach which can provide the surgeons with real time 3D visualization of complete organ deformations during the MIS operation. This new approach even allows the surgeon to see through the wall of an organ rather than just looking at its surface. The proposed design consists of two stages. The first training stage identified the deformation subspaces from a training data set in the transformed spherical harmonic domain, such that each surface can be sparsely represented in the structured dictionary with low dimensionality. This novel idea is based on our experimental discovery that the spherical harmonic coefficients of any organ surface lie in specific low dimensional subspaces. The second reconstruction stage reconstructs the complete deformations in realtime using surface samples obtained with an optical device from a limited field of view while applying the structured dictionary. The sparse surface representation algorithm is also applied to ultrasound image enhancement and efficient surgical simulation. The former is achieved by fusing ultrasound samples 5 with optical data under proper weighting strategies. The high speed of surgical simulation is obtained by decreasing the computational cost based on the high compactness of the surface representation algorithm. In order to verify the proposed approaches, we first use the computer models to demonstrate that the proposed approach matches the accuracy of complex mathematical modeling techniques. Then ex-vivo experiments are conducted on freshly excised porcine kidneys utilizing a 3D MRI machine, a 3D optical device and an ultrasound machine to further test the feasibility under practical settings. / text

We present a fast direct algorithm for the solution of linear systems arising from elliptic equations. We extend the work of Xia et al. (2009) on combining the multifrontal method with hierarchical matrices. We offer a more geometric interpretation of that approach, extend it in two dimensions to the unstructured mesh case, and detail an adaptive decomposition procedure for selectively refined meshes. Linear time complexity is shown for a quasi-uniform grid and demonstrated via numerical results for the adaptive algorithm. We also provide an extension to three dimensions with proven linear complexity but a more practical variant with slightly worse scaling is also described. / text

Doctor of Philosophy(PhD) / This thesis proposes the use of the augmented system form - a generalisation of the information form representing both observations and states. In conjunction with this, this thesis proposes a novel graph representation for the estimation problem together with a graph based linear direct solving algorithm. The augmented system form is a mathematical description of the estimation problem showing the states and observations. The augmented system form allows a more general range of factorisation orders among the observations and states, which is essential for constraints and is beneficial for sparsity and numerical reasons. The proposed graph structure is a novel sparse data structure providing more symmetric access and faster traversal and modification operations than the compressed-sparse-column (CSC) sparse matrix format. The graph structure was developed as a fundamental underlying structure for the formulation of sparse estimation problems. This graph-theoretic representation replaces conventional sparse matrix representations for the estimation states, observations and their interconnections. This thesis contributes a new implementation of the indefinite LDL factorisation algorithm based entirely in the graph structure. This direct solving algorithm was developed in order to exploit the above new approaches of this thesis. The factorisation operations consist of accessing adjacencies and modifying the graph edges. The developed solving algorithm demonstrates the significant differences in the form and approach of the graph-embedded algorithm compared to a conventional matrix implementation. The contributions proposed in this thesis improve estimation methods by providing novel mathematical data structures used to represent states, observations and the sparse links between them. These offer improved flexibility and capabilities which are exploited in the solving algorithm. The contributions constitute a new framework for the development of future online and incremental solving, data association and analysis algorithms for online, large scale localisation and mapping.

Research Doctorate - Doctor of Philosophy (PhD) / In this thesis, a number of new methods for constructing vertex-magic total-labelings of graphs are presented. These represent an advance on existing methods since they are general constructions rather than ad hoc constructions for specific families of graphs. Broadly, five new kinds of construction methods are presented. Firstly, we present a class of methods characterized by adding 2- or 4-factors to a labeled graph, reassigning vertex labels to the edges of these factors and then adding new vertex labels to create a VMTL of the new graph. The major result is a unified method for constructing VMTL of large families of regular graphs, providing strong evidence for MacDougall's conjecture that, apart from a few minor exceptions, all regular graphs possess vertex-magic total-labelings. Secondly, we present methods for obtaining a labeling of a union of two graphs, one of which possesses a strong labeling, and then building on this labeling to create a labeling of an irregular graph. These methods as well as results in the Appendices provide strong evidence against an early conjecture regarding labelings and vertex degrees. Thirdly, constructions are presented for a new kind of magic square, containing some zeroes, which can be used to build labelings of graphs from labeled spanning subgraphs. Next, constructions are presented for a new kind of anti-magic square, containing some zeroes, which is equivalent to a strong labeling of certain kinds of bipartite graphs which can in turn be built upon to produce labelings of graphs with more edges. Finally, we present a method of mutating a graph labeling by reassigning edges in a way that preserves the magic constant to obtain a labeling of a different graph. This method provides a prolific source of new labelings.