The wavelet transform technique has been frequently used in time-frequency analysis as a relatively new concept. Compared to the traditional technique Short-time Fourier Transform (STFT), which is theoretically based on the Fourier transform, the wavelet transform has its advantage on better locality in time and frequency domain, but not significant as the solutions in spectrum. Wavelet transform has dynamic ‘window functions’ to represent time-frequency positions of raw signals, and can get better resolutions in time-frequency analysis. In this report, we shall first briefly introduce fuzzy sets and related concepts. And then we will evaluate their similarities and differences by not only the theoretic comparisons between STFT and wavelet transform, but also the process of the de-nosing to a noisy recorded signal.

The views expressed in this thesis are those of the author and do not reflect the official policy or position of the Department of Defense or the U.S. Government. / The main objective of this study is to find a wavelet-based, feature extracting algorithm for push-to-talk transmitter identification. A distance-measure algorithm is introduced to classify signals belonging to one of four transmitters. The signals are first preprocessed to put them into a form suitable for wavelet analysis. The preprocessing scheme includes taking the envelopes and differentials. Median filtering is also applied to the outputs of the wavelet transform. The distance algorithm uses local extrema of the wavelet coefficients, and computes the distance between the local extrema of a template and the processed signals. A small distance implies high similarity . A signal from each transmitter is selected as a template. A small distance measure indicates that the signal belongs to the transmitter from which the template originated. The distance algorithm can classify correctly the four different signal sets provided for the research. Even at lower signal-to-noise levels, good identification is achieved.

In this dissertation we address the problem of adapting frequency domain tiling using the curvelet transform as the basis algorithm. The optimal tiling, for a given class of images, is computed using denoising performance as the cost function. The major adaptations considered are: the number of scale decompositions, angular decompositions per scale/quadrant, and scale locations. A global optimization algorithm combining the three adaptations is proposed. Denoising performance of adaptive curvelets is tested on seismic and face data sets. The developed adaptation procedure is applied to a number of different application areas. Adaptive curvelets are used to solve the problem of sparse data recovery from subsampled measurements. Performance comparison with default curvelets demonstrates the effectiveness of the adaptation scheme. Adaptive curvelets are also used in the development of a novel image similarity index. The developed measure succeeds in retrieving correct matches from a variety of textured materials. Furthermore, we present an algorithm for classifying different types of seismic activities.

Modern technologies have eased the way for adversaries to bypass the conventional identity authentication and identification processes; hence security systems have been developed to a great extent for protection of privacy and security of identities in different applications. The focus of this thesis is digital watermarking, security and privacy, as well as the ability to employ electrocardiogram as a method to enhance the security and privacy level. A high capacity reversible multiple watermarking scheme is introduced to mainly target the medical images. Furthermore, the use of ECG biometric signals in the form of the embedded watermark is studied. Experimental results indicate that the reversible data hiding scheme outperforms other approaches in the literature in terms of payload capacity and marked image quality. Results from the ECG mark embedding also show that no major degradation in performance is noticeable compared to the case where no watermarking is needed.

Modern technologies have eased the way for adversaries to bypass the conventional identity authentication and identification processes; hence security systems have been developed to a great extent for protection of privacy and security of identities in different applications. The focus of this thesis is digital watermarking, security and privacy, as well as the ability to employ electrocardiogram as a method to enhance the security and privacy level. A high capacity reversible multiple watermarking scheme is introduced to mainly target the medical images. Furthermore, the use of ECG biometric signals in the form of the embedded watermark is studied. Experimental results indicate that the reversible data hiding scheme outperforms other approaches in the literature in terms of payload capacity and marked image quality. Results from the ECG mark embedding also show that no major degradation in performance is noticeable compared to the case where no watermarking is needed.

Multiresolution analysis (MRA) has fairly recently become important, and even essential, to image processing and signal analysis, and is thus having a growing impact on image and signal related areas. As one of the most famous family members of the MRA, the wavelet transform (WT) has demonstrated itself in numerous successful applications in various fields, and become one of the most powerful tools in the fields of image processing and signal analysis. Due to the fact that only the scale information is supplied in WT, the applications using the wavelet transform may be limited when the absolutely-referenced frequency and phase information are required. The Stockwell transform (ST) is a recently proposed multiresolution transform that supplies the absolutely-referenced frequency and phase information. However, the ST redundantly doubles the dimension of the original data set. Because of this redundancy, use of the ST is computationally expensive and even infeasible on some large size data sets. Thus, I propose the use of the discrete orthonormal Stockwell transform (DOST), a non-redundant version of ST. This thesis will continue to implement the theoretical research on the DOST and elaborate on some of our successful applications using the DOST. We uncover the fast calculation mechanism of the DOST using an equivalent matrix form that we discovered. We also highlight applications of the DOST in image compression and image restoration, and analyze the global and local translation properties. The local nature of the DOST suggests that it could be used in many other local applications.

Image processing applications such as image denoising, image segmentation, object detection, object recognition and texture synthesis often require a multi-scale analysis of images. This is useful because different features in the image become prominent at different scales. Traditional imaging models, which have been used for multi-scale analysis of images, have several limitations such as high sensitivity to noise and structural degradation observed at higher scales. Parametric models make certain assumptions about the image structure which may or may not be valid in several situations. Non-parametric methods, on the other hand, are very flexible and adapt to the underlying image structure more easily. It is highly desirable to have effi cient non-parametric models for image analysis, which can be used to build robust image processing algorithms with little or no prior knowledge of the underlying image content. In this thesis, we propose a non-parametric pixel neighbourhood based framework for multi-scale image analysis and apply the model to build image denoising and saliency detection algorithms for the purpose of illustration. It has been shown that the algorithms based on this framework give competitive results without using any prior information about the image statistics.

The construction of the generalized continuous wavelet transform (GCWT) on Hilbert spaces is a special case of the coherent state transform construction, where the coherent state system arises as an orbit of an admissible vector under a strongly continuous unitary representation of a locally compact group. In this thesis we extend this construction to the setting of Hilbert C*-modules. In particular, we define a coherent state transform and a GCWT on Hilbert modules. This construction gives a reconstruction formula and a resolution of the identity formula analogous to those found in the Hilbert space setting. Moreover, the existing theory of standard normalized tight frames in finite countably generated Hilbert modules can be viewed as a discrete case of this construction We also show that the image space of the coherent state transform on Hilbert module is a reproducing kernel Hilbert module. We discuss the kernel and the intertwining property of the group coherent state transform.

Zugl.: Karlsruhe, Univ., Diss., 2006

Zugl.: Karlsruhe, Univ., Diss., 2006