This thesis is based on the modified JPEG encoding which uses a preprocessing called as Cubic Convolution Spline Interpolation to subsample the original image into lower resolution image, the subsampled image is encoded by JPEG. The modified JPEG can get very high compression ratio, it¡¦s quality is better than the JPEG file which has the same compressing ratio, but it still is not good enough. In this thesis we use the scalable wavelet encoding to encode the residual image, which is the difference between original and compression image. Due to the high compressing ratio and scalablity. We can attach the compressed residual image with modified JPEG compressed image to get the scalable compressed image whose compressing ratio can tun from 125 to 50 and always get better quality than optimal JPEG.

¡§Mura¡¨ is a local lightness variation without a clear contour on a uniform surface image, which imparts an unpleasant sensation to human vision. In this study, a Haar wavelet transform (WT) method is proposed to detect the mura of the polarizer. Because of the WT capability of multi-resolution analysis for digital images, the difference of gray level between neighbor pixels in different scale of an image can be analyzed by the WT high frequency coefficient. As a result, different size muras at different location can be segmented. Because the Haar WT cannot extract all the high frequency coefficient from an image at one time, the original image is decomposed into an main image and a subimage at the beginning. The applying the WT technique to extract all the high frequency coefficients from these two images. There exist three types of mura consisting of line mura, band mura, and area mura. Experiments were extensively conducted on different frequencies and sizes of these muras. Experimental results show that the presented approach is able to detect all the line muras, but some band and area muras. The result of this study can be extended to the future researches regarding mura properties and detection methods.

Wrinkling caused in wearing and laundry procedures is one of the most important performance properties of a fabric. Visual examination performed by trained experts is a routine wrinkle evaluation method in textile industry, however, this subjective evaluation is time-consuming. The need for objective, automatic and efficient methods of wrinkle evaluation has been increasing remarkably in recent years. In the present thesis, a wavelet transform based imaging analysis method was developed to measure the 2D fabric surface data captured by an infrared imaging system. After decomposing the fabric image by the Haar wavelet transform algorithm, five parameters were defined based on modified wavelet coefficients to describe wrinkling features, such as orientation, hardness, density and contrast. The wrinkle parameters provide useful information for textile, appliance, and detergent manufactures who study wrinkling behaviors of fabrics. A Support-Vector-Machine based classification scheme was developed for automatic wrinkle rating. Both linear kernel and radial-basis-function (RBF) kernel functions were used to achieve a higher rating accuracy. The effectiveness of this evaluation method was tested by 300 images of five selected fabric types with different fiber contents, weave structures, colors and laundering cycles. The results show agreement between the proposed wavelet-based automatic assessment and experts’ visual ratings. / text

We present a new method to stabilize the three-term AVO inversion using Curvelet and Wavelet transforms. Curvelets are basis functions that effectively represent otherwise smooth objects having discontinuities along smooth curves. The applied formalism explores them to make the most of the continuity along reflectors in seismic images. Combined with Wavelets, Curvelets are used to denoise the data by penalizing high frequencies and small contributions in the AVO-cube. This approach is based on the idea that rapid amplitude changes along the ray-parameter axis are most likely due to noise. The AVO-inverse problem is linearized, formulated and solved for all (x, z) at once. Using densities and velocities of the Marmousi model to define the fluctuations in the elastic properties, the performance of the proposed method is studied and compared with the smoothing along the ray-parameter direction only. We show that our method better approximates the true data after the denoising step, especially when noise level increases.

Hydraulic systems are complex dynamical systems whose performance can be degraded by certain faults, specifically internal or external leakage. The objective of this research is to develop an appropriate signal processing approach for detection and isolation of these faults. By analyzing the dynamics of the hydraulic actuator, an internal leakage is shown to increase the damping characteristic of the system and change the transient response of the pressure signals. An external leakage, on the other hand, drops the pressure signals without having a significant effect on transient responses. Offline detection of internal leakage in hydraulic actuators is first examined by using fast Fourier, wavelet and Hilbert-Huang transforms. The original pressure signal is decomposed using these transform methods and the frequency component which is sensitive to the internal leakage is identified. The root mean square of the processed pressure signal is used and a comparison of the three transforms is made to assess their ability to detect internal leakage fault, through extensive validation tests. The wavelet transform method is shown to be more suitable for internal leakage detection compared to the other two methods. The wavelet based approach is then extended to an online detection method of internal leakage fault. The online approach considers the more realistic case of an actuator that is driven in a closed-loop mode to track pseudorandom position reference inputs against a load emulated by a spring. Furthermore, the method is shown to remain effective even with control systems which are tolerant to leakage faults. Next, the application of wavelet transform to detect external leakage fault using both offline and online applications in hydraulic actuators is described. The method also examines the isolation of this fault from actuator internal leakage in a multiple-fault environment. The results show that wavelet transform is a fast and easily-implementable method for leakage detection in hydraulic actuators without any need to explicitly incorporate the model of actuator or leakage. Internal leakages as low as 0.124 lit/min, are shown to be detectable, for 80% of the times using structured input signal. For online application, internal leakages in the range of 0.2-0.25 lit/min can be identified. External leakages as low as 0.3 lit/min can be detected in all offline and online applications. Other methods such as observer based and Kalman filter methods, which require the model of the actuator or leakage fault, cannot report leakage detection of magnitudes as low as that reported in this work. The low leak rate detection and not requiring a model of the actuator or leakage make this method very attractive for industrial implementation.

Hydraulic systems are complex dynamical systems whose performance can be degraded by certain faults, specifically internal or external leakage. The objective of this research is to develop an appropriate signal processing approach for detection and isolation of these faults. By analyzing the dynamics of the hydraulic actuator, an internal leakage is shown to increase the damping characteristic of the system and change the transient response of the pressure signals. An external leakage, on the other hand, drops the pressure signals without having a significant effect on transient responses. Offline detection of internal leakage in hydraulic actuators is first examined by using fast Fourier, wavelet and Hilbert-Huang transforms. The original pressure signal is decomposed using these transform methods and the frequency component which is sensitive to the internal leakage is identified. The root mean square of the processed pressure signal is used and a comparison of the three transforms is made to assess their ability to detect internal leakage fault, through extensive validation tests. The wavelet transform method is shown to be more suitable for internal leakage detection compared to the other two methods. The wavelet based approach is then extended to an online detection method of internal leakage fault. The online approach considers the more realistic case of an actuator that is driven in a closed-loop mode to track pseudorandom position reference inputs against a load emulated by a spring. Furthermore, the method is shown to remain effective even with control systems which are tolerant to leakage faults. Next, the application of wavelet transform to detect external leakage fault using both offline and online applications in hydraulic actuators is described. The method also examines the isolation of this fault from actuator internal leakage in a multiple-fault environment. The results show that wavelet transform is a fast and easily-implementable method for leakage detection in hydraulic actuators without any need to explicitly incorporate the model of actuator or leakage. Internal leakages as low as 0.124 lit/min, are shown to be detectable, for 80% of the times using structured input signal. For online application, internal leakages in the range of 0.2-0.25 lit/min can be identified. External leakages as low as 0.3 lit/min can be detected in all offline and online applications. Other methods such as observer based and Kalman filter methods, which require the model of the actuator or leakage fault, cannot report leakage detection of magnitudes as low as that reported in this work. The low leak rate detection and not requiring a model of the actuator or leakage make this method very attractive for industrial implementation.

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.

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.

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.