Low Bit-rate Color Video Compression using Multiwavelets in Three Dimensions

In recent years, wavelet-based video compressions have become a major focus of research because of the advantages that it provides. More recently, a growing thrust of studies explored the use of multiple scaling functions and multiple wavelets with desirable properties in various fields, from image de-noising to compression. In term of data compression, multiple scaling functions and wavelets offer a greater flexibility in coefficient quantization at high compression ratio than a comparable single wavelet. The purpose of this research is to investigate the possible improvement of scalable wavelet-based color video compression at low bit-rates by using three-dimensional multiwavelets. The first part of this work included the development of the spatio-temporal decomposition process for multiwavelets and the implementation of an efficient 3-D SPIHT encoder/decoder as a common platform for performance evaluation of two well-known multiwavelet systems against a comparable single wavelet in low bitrate color video compression. The second part involved the development of a motion-compensated 3-D compression codec and a modified SPIHT algorithm designed specifically for this codec by incorporating an advantage in the design of 2D SPIHT into the 3D SPIHT coder. In an experiment that compared their performances, the 3D motion-compensated codec with unmodified 3D SPIHT had gains of 0.3dB to 4.88dB over regular 2D wavelet-based motion-compensated codec using 2D SPIHT in the coding of 19 endoscopy sequences at 1/40 compression ratio. The effectiveness of the modified SPIHT algorithm was verified by the results of a second experiment in which it was used to re-encode 4 of the 19 sequences with lowest performance gains and improved them by 0.5dB to 1.0dB. The last part of the investigation examined the effect of multiwavelet packet on 3-D video compression as well as the effects of coding multiwavelet packets based on the frequency order and energy content of individual subbands

Adaptive Orthogonal Matrix-Valued Wavelets and Compression of Vector-Valued Signals

Wavelet transforms using matrix-valued wavelets (MVWs) can process the components of vector-valued signals jointly, and thus offer potential advantages over scalar wavelets. For every matrix-valued scaling filter, there are infinitely many matrix-valued wavelet filters corresponding to rotated bases. We show how the arbitrary orthogonal factor in the choice of wavelet filter can be selected adaptively with a modified SIMPLIMAX algorithm. The 3×3 orthogonal matrix-valued scaling filters of length 6 with 3 vanishing moments have one intrinsic free scalar parameter in addition to three scalar rotation parameters. Tests suggest that even when optimising over these parameters, no significant improvement is obtained when compared to the naive scalar-based filter. We have found however in an image compression test that, for the naive scaling filter, adaptive basis rotation can decrease the RMSE by over 20%

An Investigation of Orthogonal Wavelet Division Multiplexing Techniques as an Alternative to Orthogonal Frequency Division Multiplex Transmissions and Comparison of Wavelet Families and Their Children

Recently, issues surrounding wireless communications have risen to prominence because of the increase in the popularity of wireless applications. Bandwidth problems, and the difficulty of modulating signals across carriers, represent significant challenges. Every modulation scheme used to date has had limitations, and the use of the Discrete Fourier Transform in OFDM (Orthogonal Frequency Division Multiplex) is no exception. The restriction on further development of OFDM lies primarily within the type of transform it uses in the heart of its system, Fourier transform. OFDM suffers from sensitivity to Peak to Average Power Ratio, carrier frequency offset and wasting some bandwidth to guard successive OFDM symbols. The discovery of the wavelet transform has opened up a number of potential applications from image compression to watermarking and encryption. Very recently, work has been done to investigate the potential of using wavelet transforms within the communication space. This research will further investigate a recently proposed, innovative, modulation technique, Orthogonal Wavelet Division Multiplex, which utilises the wavelet transform opening a new avenue for an alternative modulation scheme with some interesting potential characteristics. Wavelet transform has many families and each of those families has children which each differ in filter length. This research consider comprehensively investigates the new modulation scheme, and proposes multi-level dynamic sub-banding as a tool to adapt variable signal bandwidths. Furthermore, all compactly supported wavelet families and their associated children of those families are investigated and evaluated against each other and compared with OFDM. The linear computational complexity of wavelet transform is less than the logarithmic complexity of Fourier in OFDM. The more important complexity is the operational complexity which is cost effectiveness, such as the time response of the system, the memory consumption and the number of iterative operations required for data processing. Those complexities are investigated for all available compactly supported wavelet families and their children and compared with OFDM. The evaluation reveals which wavelet families perform more effectively than OFDM, and for each wavelet family identifies which family children perform the best. Based on these results, it is concluded that the wavelet modulation scheme has some interesting advantages over OFDM, such as lower complexity and bandwidth conservation of up to 25%, due to the elimination of guard intervals and dynamic bandwidth allocation, which result in better cost effectiveness

Quaternion Matrices : Statistical Properties and Applications to Signal Processing and Wavelets

Similarly to how complex numbers provide a possible framework for extending scalar signal processing techniques to 2-channel signals, the 4-dimensional hypercomplex algebra of quaternions can be used to represent signals with 3 or 4 components. For a quaternion random vector to be suited for quaternion linear processing, it must be (second-order) proper. We consider the likelihood ratio test (LRT) for propriety, and compute the exact distribution for statistics of Box type, which include this LRT. Various approximate distributions are compared. The Wishart distribution of a quaternion sample covariance matrix is derived from first principles. Quaternions are isomorphic to an algebra of structured 4x4 real matrices. This mapping is our main tool, and suggests considering more general real matrix problems as a way of investigating quaternion linear algorithms. A quaternion vector autoregressive (VAR) time-series model is equivalent to a structured real VAR model. We show that generalised least squares (and Gaussian maximum likelihood) estimation of the parameters reduces to ordinary least squares, but only if the innovations are proper. A LRT is suggested to simultaneously test for quaternion structure in the regression coefficients and innovation covariance. Matrix-valued wavelets (MVWs) are generalised (multi)wavelets for vector-valued signals. Quaternion wavelets are equivalent to structured MVWs. Taking into account orthogonal similarity, all MVWs can be constructed from non-trivial MVWs. We show that there are no non-scalar non-trivial MVWs with short support [0,3]. Through symbolic computation we construct the families of shortest non-trivial 2x2 Daubechies MVWs and quaternion Daubechies wavelets.Open Acces

Wavelet-based image compression for mobile applications.

The transmission of digital colour images is rapidly becoming popular on mobile telephones, Personal Digital Assistant (PDA) technology and other wireless based image services. However, transmitting digital colour images via mobile devices is badly affected by low air bandwidth. Advances in communications Channels (example 3G communication network) go some way to addressing this problem but the rapid increase in traffic and demand for ever better quality images, means that effective data compression techniques are essential for transmitting and storing digital images. The main objective of this thesis is to offer a novel image compression technique that can help to overcome the bandwidth problem. This thesis has investigated and implemented three different wavelet-based compression schemes with a focus on a suitable compression method for mobile applications. The first described algorithm is a dual wavelet compression algorithm, which is a modified conventional wavelet compression method. The algorithm uses different wavelet filters to decompose the luminance and chrominance components separately. In addition, different levels of decomposition can also be applied to each component separately. The second algorithm is segmented wavelet-based, which segments an image into its smooth and nonsmooth parts. Different wavelet filters are then applied to the segmented parts of the image. Finally, the third algorithm is the hybrid wavelet-based compression System (HWCS), where the subject of interest is cropped and is then compressed using a wavelet-based method. The details of the background are reduced by averaging it and sending the background separately from the compressed subject of interest. The final image is reconstructed by replacing the averaged background image pixels with the compressed cropped image. For each algorithm the experimental results presented in this thesis clearly demonstrated that encoder output can be effectively reduced while maintaining an acceptable image visual quality particularly when compared to a conventional wavelet-based compression scheme