The goal of this study is the recovery of functions and finite parametric distributions from their spherical means over spheres and designing a general formula or algorithm for the reconstruction of a function f via its spherical mean transform. The theoretical study is and supported with a numerical implementation based on radar data. In this study, we approach the reconstruction problem in two different way. The first one is to show how the reconstruction problem could be converted to a Prony-type system of equations. After solving this Prony-type system of equations, one can extract the parameters that describe the corresponding functions or distributions efficiently. The second way is to solve this problem via a backprojection procedure.

abstract: Disentangling latent spaces is an important research direction in the interpretability of unsupervised machine learning. Several recent works using deep learning are very effective at producing disentangled representations. However, in the unsupervised setting, there is no way to pre-specify which part of the latent space captures specific factors of variations. While this is generally a hard problem because of the non-existence of analytical expressions to capture these variations, there are certain factors like geometric transforms that can be expressed analytically. Furthermore, in existing frameworks, the disentangled values are also not interpretable. The focus of this work is to disentangle these geometric factors of variations (which turn out to be nuisance factors for many applications) from the semantic content of the signal in an interpretable manner which in turn makes the features more discriminative. Experiments are designed to show the modularity of the approach with other disentangling strategies as well as on multiple one-dimensional (1D) and two-dimensional (2D) datasets, clearly indicating the efficacy of the proposed approach. / Dissertation/Thesis / Masters Thesis Electrical Engineering 2019

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Studies on radiofrequency (RF) ablation are often aimed at accurately predicting tissue temperature distributions by numerical solution of the bioheat equation. This thesis describes the development of an analytical solution to serve as a benchmark for subsequent numerical solutions. The solution, which was obtained using integral transforms, has the form of a surface integral nested within another surface integral. An integration routine capable of evaluating such integrals was developed and a C program was written to implement this routine. The surface integration routine was validated using a surface integral with a known analytical solution. The routine was, then, used to generate temperature profiles at various times and for different convection coefficients. To further validate the numerical methods used to obtain temperature profiles, a numerical model was developed with the same approximations used in obtaining the analytical solution. Results of the analytical and numerical solutions match very closely. In addition, three numerical models were developed to assess the validity of some of the assumptions used in obtaining the analytical solution. For each numerical model, one or two of the assumptions used in the analytical model were relaxed to better assess the degree to which they influence results. The results indicate that (1) conduction of heat into the electrode significantly affects lesion size, (2) temperature distributions can be assumed to be axisymmetric, and (3) lesion size and maximum temperature are strongly influenced by the temperature-dependence of electrical conductivity. These conclusions are consistent with results from previous studies on radiofrequency cardiac ablation.

In recent years, multimedia identification has become important as the volume of digital media has dramatically increased. With music files, one method of identification is audio fingerprinting. The underlying method for most algorithms is the Fourier transform. However, due to a lack of temporal resolution, these algorithms rely on the short-time Fourier transform. We propose an audio fingerprinting algorithm that uses a wavelet transform, which has good temporal resolution. In this thesis, we examine the basics of certain topics that are needed in understanding audio fingerprinting techniques. We also look at a brief history of work done in this field. We introduce a new algorithm, called the Hokua algorithm. We developed Hokua to take advantage of certain properties of the wavelet transform. The algorithm uses coefficient peaks of wavelet transforms to identify a sample query. The various algorithms are compared.

No / Extensive research has been performed to investigate effective techniques, including advanced sensors and new monitoring methods, to develop reliable condition monitoring systems for industrial applications. One promising approach to develop effective monitoring methods is the application of time-frequency analysis techniques to extract the crucial characteristics of the sensor signals. This paper investigates the effectiveness of a new time-frequency analysis method based on Empirical Model Decomposition and Hilbert transform for analyzing the nonstationary cutting force signal of the machining process. The advantage of EMD is its ability to adaptively decompose an arbitrary complicated time series into a set of components, called intrinsic mode functions (IMFs), which has particular physical meaning. By decomposing the time series into IMFs, it is flexible to perform the Hilbert transform to calculate the instantaneous frequencies and to generate effective time-frequency distributions called Hilbert spectra. Two effective approaches have been proposed in this paper for the effective detection of tool breakage. One approach is to identify the tool breakage in the Hilbert spectrum, and the other is to detect the tool breakage by means of the energies of the characteristic IMFs associated with characteristic frequencies of the milling process. The effectiveness of the proposed methods has been demonstrated by considerable experimental results. Experimental results show that (1) the relative significance of the energies associated with the characteristic frequencies of milling process in the Hilbert spectra indicates effectively the occurrence of tool breakage; (2) the IMFs are able to adaptively separate the characteristic frequencies. When tool breakage occurs the energies of the associated characteristic IMFs change in opposite directions, which is different from the effect of changes of the cutting conditions e.g. the depth of cut and spindle speed. Consequently, the proposed approach is not only able to effectively capture the significant information reflecting the tool condition, but also reduces the sensitivity to the effect of various uncertainties, and thus has good potential for industrial applications.

No / At present, almost all digital images are stored and transferred in their compressed format in which discrete cosine transform (DCT)-based compression remains one of the most important data compression techniques due to the efforts from JPEG. In order to save the computation and memory cost, it is desirable to have image processing operations such as feature extraction, image indexing, and pattern classifications implemented directly in the DCT domain. To this end, we present in this paper a generalized analysis of spatial relationships between the DCTs of any block and its sub-blocks. The results reveal that DCT coefficients of any block can be directly obtained from the DCT coefficients of its sub-blocks and that the interblock relationship remains linear. It is useful in extracting global features in compressed domain for general image processing tasks such as those widely used in pyramid algorithms and image indexing. In addition, due to the fact that the corresponding coefficient matrix of the linear combination is sparse, the computational complexity of the proposed algorithms is significantly lower than that of the existing methods.

The aim of this research was to develop a method of system identification that would draw inspiration from the approach taken by human experts for simulation model tuning and validation. Human experts are able to utilize their natural pattern recognition ability to identify the various shape attributes, or signatures, of a time series from simulation model outputs. They can also intelligently and effectively perform tasks ranging from system identification to model validation. However, the feature extraction approach employed by them cannot be readily automated due to the difficulty in measuring shape attributes. In order to bridge the gap between the approach taken by human experts and those employed for traditional iterative approaches, a method to quantify the shape attributes was devised. The method presented in this dissertation, the Parameter Signature Isolation Method (PARSIM), uses continuous wavelet transformation to characterize specific aspects of the time series shape through surfaces in the time-scale domain. A salient characteristic of these surfaces is their enhanced delineation of the model outputs and/or their sensitivities. One benefit of this enhanced delineation is the capacity to isolate regions of the time-scale plane, coined as parameter signatures, wherein individual output sensitivities dominate all the others. The parameter signatures enable the estimation of each model parameter error separately with applicability to parameter estimation. The proposed parameter estimation method has unique features, one of them being the capacity for noise suppression, wherein the feature of relying entirely on the time-scale domain for parameter estimation offers direct noise compensation in this domain. Yet another utility of parameter signatures is in measurement selection, whereby the existence of parameter signatures is attributed to the identifiability of model parameters through various outputs. The effectiveness of PARSIM is demonstrated through an array of theoretical models, such as the Lorenz System and the Van der Pol oscillator, as well as through the real-world simulation models of an injection molding process and a jet engine.

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