Compression of vector-valued datasets is increasingly needed for addressing the significant storage and transmission burdens associated with research activities in large-scale computational fluid dynamics and environmental science. However, vector-valued compression schemes have traditionally received few investigations within the data-compression community. Consequently, this dissertation conducts a systematic study of effective algorithms for the coding of vectorvalued datasets and builds practical embedded compression systems for both static and timevarying vector fields. In generalizing techniques from the relatively mature field of image and video coding to vector data, three critical issues must be addressed: the design of a vector wavelet transform (VWT) that is amenable to vector-valued compression applications, the implementation of vector-valued intraframe coding that enables embedded coding, and the investigation of interframe-compression techniques that are appropriate for the complex temporal evolutions of vector features. In this dissertation, we initially invoke multiwavelets to construct VWTs. However, a balancing problem arises when existing multiwavelets are applied directly to vector data. We analyze extensively this performance failure and develop the omnidirectional balancing (OB) design criterion to rectify it. Employing the OB principle, we derive with a family of biorthogonal multiwavelets possessing desired balancing and symmetry properties and yielding performance far superior to that of VWTs implemented via other multiwavelets. In the second part of the dissertation, quantization schemes for vector-valued data are studied, and a complete embedded coding system for static vector fields is designed by combining a VWT with suitable vector-valued successive-approximation quantization. Finally, we extend several interframecompression techniques from video-coding applications to vector sequences for the compression of time-varying vector fields. Since the complexity of temporal evolutions of vector features limits the efficiency of the simple motion models which have been successful for natural video sources, we develop a novel approach to motion compensation which involves applying temporal decorrelation to only low-resolution information. This reduced-resolution motion-compensation technique results in significant improvement in terms of rate-distortion performance.

Because of the vast data volume of hyperspectral imagery, compression becomes a necessary process for hyperspectral data transmission, storage, and analysis. Three-dimensional discrete wavelet transform (DWT) based algorithms are particularly of interest due to their excellent rate-distortion performance. This thesis investigates several issues surrounding efficient compression using JPEG2000. Firstly, the rate-distortion performance is studied when Principal Component Analysis (PCA) replaces DWT for spectral decorrelation with the focus on the use of a subset of principal components (PCs) rather than all the PCs. Secondly, the algorithms are evaluated in terms of data analysis performance, such as anomaly detection and linear unmixing, which is directly related to the useful information preserved. Thirdly, the performance of compressing radiance and reflectance data with or without bad band removal is compared, and instructive suggestions are provided for practical applications. Finally, low-complexity PCA algorithms are presented to reduce the computational complexity and facilitate the future hardware design.

The ongoing development and increased affordability of hyperspectral sensors are increasing their utilization in a variety of applications, such as agricultural monitoring and decision making. Hyperspectral Automated Target Recognition (ATR) systems typically rely heavily on dimensionality reduction methods, and particularly intelligent reduction methods referred to as feature extraction techniques. This dissertation reports on the development, implementation, and testing of new hyperspectral analysis techniques for ATR systems, including their use in agricultural applications where ground truthed observations available for training the ATR system are typically very limited. This dissertation reports the design of effective methods for grouping and down-selecting Discrete Wavelet Transform (DWT) coefficients and the design of automated Wavelet Packet Decomposition (WPD) filter tree pruning methods for use within the framework of a Multiclassifiers and Decision Fusion (MCDF) ATR system. The efficacy of the DWT MCDF and WPD MCDF systems are compared to existing ATR methods commonly used in hyperspectral remote sensing applications. The newly developed methods’ sensitivity to operating conditions, such as mother wavelet selection, decomposition level, and quantity and quality of available training data are also investigated. The newly developed ATR systems are applied to the problem of hyperspectral remote sensing of agricultural food crop contaminations either by airborne chemical application, specifically Glufosinate herbicide at varying concentrations applied to corn crops, or by biological infestation, specifically soybean rust disease in soybean crops. The DWT MCDF and WPD MCDF methods significantly outperform conventional hyperspectral ATR methods. For example, when detecting and classifying varying levels of soybean rust infestation, stepwise linear discriminant analysis, results in accuracies of approximately 30%-40%, but WPD MCDF methods result in accuracies of approximately 70%-80%.

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<p> An investigation as to the appropriateness of the wavelet transform for surface electromyography (EMG) M-wave pattern recognition is described. The M-waves are obtained by stimulating the median nerve at the wrist to activate the motor units. Surface electrodes and a graded stimulus amplitude are used. The resulting M-waves are classified using both wavelet vectors and the traditional power spectral coefficients as features sets in the pattern recognition scheme. A novel system was developed to obtain M-wave collections from subjects in the laboratory and to perform both real-time and offline analysis.</p> <p> The results obtained from the left and right thenar muscles of 4 healthy females and 2 healthy males are presented. These results are further analyzed offline to determine the effects of a changing discriminatory threshold for both wavelet and power spectral pattern recognition techniques. In addition, intra-class and inter-class Euclidean distances are shown for the set of unique M-waves derived from using the different feature sets. A time-invariant wavelet transform is implemented to improve classification by eliminating errors due to latency shifts.</p> <p> The results show that the number of unique M-waves obtained usmg wavelet features is less sensitive to a variation in discriminatory threshold. It may be concluded that a wavelet based feature set shows slight improvement in M-wave pattern classification. The time-invariant wavelet offers further accuracy.</p> / Thesis / Master of Applied Science (MASc)

Yes / Recent studies suggest that multicarrier systems using wavelets outperform conventional OFDM systems using the FFT, in that they have well-contained side lobes, improved spectral efficiency and BER performance, and they do not require a cyclic prefix. Here we study the wavelet packet and discrete wavelet transforms, comparing the BER performance of wavelet transform-based multicarrier systems and Fourier based OFDM systems, for multipath Rayleigh channels with AWGN. In the proposed system zero-forcing channel estimation in the frequency domain has been used. Results confirm that discrete wavelet-based systems using Daubechies wavelets outperform both wavelet packet transform- based systems and FFT-OFDM systems in terms of BER. Finally, Alamouti coding and maximal ratio combining schemes were employed in MIMO environments, where results show that the effects of multipath fading were greatly reduced by the antenna diversity.

The use of ultra-wideband (UWB) signals holds great promise for remote monitoring of vital-signs which has applications in the medical, for first responder and in security. Previous research has shown the feasibility of a UWB-based radar system for respiratory and heartbeat rate estimation. Some simulation and real experimental results are presented to demonstrate the capability of the respiration rate detection. However, past analysis are mostly based upon the assumption of an ideal experiment environment. The accuracy of the estimation and interference factors of this technology has not been investigated. This thesis establishes an analytical framework for the FFT-based signal processing algorithms to detect periodic bio-signals from a single target. Based on both simulation and experimental data, three basic challenges are identified: (1) Small body movement during the measurement interval results in slow variations in the consecutive received waveforms which mask the signals of interest. (2) The relatively strong respiratory signal with its harmonics greatly impact the detection of heartbeat rate. (3) The non-stationary nature of bio-signals creates challenges for spectral analysis. Having identified these problems, adaptive signal processing techniques have been developed which effectively mitigate these problems. Specifically, an ellipse-fitting algorithm is adopted to track and compensate the aperiodic large-scale body motion, and a wavelet-based filter is applied for attenuating the interference caused by respiratory harmonics to accurately estimate the heartbeat frequency. Additionally, the spectrum estimation of non-stationary signals is examined using a different transform method. Results from simulation and experiments show that substantial improvement is obtained by the use of these techniques. Further, this thesis examines the possibility of multi-target detection based on the same measurement setup. Array processing techniques with subspace-based algorithms are applied to estimate multiple respiration rates from different targets. The combination of array processing and single- target detection techniques are developed to extract the heartbeat rates. The performance is examined via simulation and experimental results and the limitation of the current measurement setup is discussed. / Master of Science

Early detection of rail defects is necessary for preventing derailments and costly damage to the train and railway infrastructure. A rail surface flaw can quickly propagate from a small fracture to a broken rail after only a few train cars have passed over it. Rail defect detection is typically performed by using an instrumented car or a separate railway monitoring vehicle. Rail surface irregularities can be measured using accelerometers mounted to the bogie side frames or wheel axles. Typical signal processing algorithms for detecting defects within a vertical acceleration signal use a simple thresholding routine that considers only the amplitude of the signal. As a result, rail surface defects that produce low amplitude acceleration signatures may not be detected, and special track components that produce high amplitude acceleration signatures may be flagged as defects. The focus of this research is to develop an intelligent signal processing algorithm capable of detecting and classifying various rail surface irregularities, including defects and special track components. Three algorithms are proposed and validated using data collected from an instrumented freight car. For the first two algorithms, one uses a windowed Fourier Transform while the other uses the Wavelet Transform for feature extraction. Both of these algorithms use an artificial neural network for feature classification. The third algorithm uses the Wavelet Transform to perform a regularity analysis on the signal. The algorithms are validated with the collected data and shown to out-perform the threshold-based algorithm for the same data set. Proper training of the defect detection algorithm requires a large data set consisting of operating conditions and physical parameters. To generate this training data, a dynamic wheel-rail interaction model was developed that relates defect geometry to the side frame vertical acceleration signature. The model was generated by using combined systems dynamic modeling, and the system was solved with a developed combined lumped and distributed parameter system numerical approximation. The broken rail model was validated with real data collected from an instrumented freight car. The model was then used to train and validate the defect detection methodologies for various train and rail physical parameters and operating conditions. / Ph. D.