Due to the lossy nature of image/video compression and the expensive bandwidth and computation resources in a multimedia system, one of the key design issues for image and video coding/transcoding is to optimize trade-off among distortion, rate, and/or complexity. This thesis studies the application of rate distortion (RD) optimization approaches to image and video coding/transcoding for exploring the best RD performance of a video codec compatible to the newest video coding standard H.264 and for designing computationally efficient down-sampling algorithms with high visual fidelity in the discrete Cosine transform (DCT) domain. RD optimization for video coding in this thesis considers two objectives, i.e., to achieve the best encoding efficiency in terms of minimizing the actual RD cost and to maintain decoding compatibility with the newest video coding standard H.264. By the actual RD cost, we mean a cost based on the final reconstruction error and the entire coding rate. Specifically, an operational RD method is proposed based on a soft decision quantization (SDQ) mechanism, which has its root in a fundamental RD theoretic study on fixed-slope lossy data compression. Using SDQ instead of hard decision quantization, we establish a general framework in which motion prediction, quantization, and entropy coding in a hybrid video coding scheme such as H.264 are jointly designed to minimize the actual RD cost on a frame basis. The proposed framework is applicable to optimize any hybrid video coding scheme, provided that specific algorithms are designed corresponding to coding syntaxes of a given standard codec, so as to maintain compatibility with the standard. Corresponding to the baseline profile syntaxes and the main profile syntaxes of H.264, respectively, we have proposed three RD algorithms---a graph-based algorithm for SDQ given motion prediction and quantization step sizes, an algorithm for residual coding optimization given motion prediction, and an iterative overall algorithm for jointly optimizing motion prediction, quantization, and entropy coding---with them embedded in the indicated order. Among the three algorithms, the SDQ design is the core, which is developed based on a given entropy coding method. Specifically, two SDQ algorithms have been developed based on the context adaptive variable length coding (CAVLC) in H.264 baseline profile and the context adaptive binary arithmetic coding (CABAC) in H.264 main profile, respectively. Experimental results for the H.264 baseline codec optimization show that for a set of typical testing sequences, the proposed RD method for H.264 baseline coding achieves a better trade-off between rate and distortion, i.e., 12\% rate reduction on average at the same distortion (ranging from 30dB to 38dB by PSNR) when compared with the RD optimization method implemented in H.264 baseline reference codec. Experimental results for optimizing H.264 main profile coding with CABAC show 10\% rate reduction over a main profile reference codec using CABAC, which also suggests 20\% rate reduction over the RD optimization method implemented in H.264 baseline reference codec, leading to our claim of having developed the best codec in terms of RD performance, while maintaining the compatibility with H.264. By investigating trade-off between distortion and complexity, we have also proposed a designing framework for image/video transcoding with spatial resolution reduction, i.e., to down-sample compressed images/video with an arbitrary ratio in the DCT domain. First, we derive a set of DCT-domain down-sampling methods, which can be represented by a linear transform with double-sided matrix multiplication (LTDS) in the DCT domain. Then, for a pre-selected pixel-domain down-sampling method, we formulate an optimization problem for finding an LTDS to approximate the given pixel-domain method to achieve the best trade-off between visual quality and computational complexity. The problem is then solved by modeling an LTDS with a multi-layer perceptron network and using a structural learning with forgetting algorithm for training the network. Finally, by selecting a pixel-domain reference method with the popular Butterworth lowpass filtering and cubic B-spline interpolation, the proposed framework discovers an LTDS with better visual quality and lower computational complexity when compared with state-of-the-art methods in the literature.

Due to the lossy nature of image/video compression and the expensive bandwidth and computation resources in a multimedia system, one of the key design issues for image and video coding/transcoding is to optimize trade-off among distortion, rate, and/or complexity. This thesis studies the application of rate distortion (RD) optimization approaches to image and video coding/transcoding for exploring the best RD performance of a video codec compatible to the newest video coding standard H.264 and for designing computationally efficient down-sampling algorithms with high visual fidelity in the discrete Cosine transform (DCT) domain. RD optimization for video coding in this thesis considers two objectives, i.e., to achieve the best encoding efficiency in terms of minimizing the actual RD cost and to maintain decoding compatibility with the newest video coding standard H.264. By the actual RD cost, we mean a cost based on the final reconstruction error and the entire coding rate. Specifically, an operational RD method is proposed based on a soft decision quantization (SDQ) mechanism, which has its root in a fundamental RD theoretic study on fixed-slope lossy data compression. Using SDQ instead of hard decision quantization, we establish a general framework in which motion prediction, quantization, and entropy coding in a hybrid video coding scheme such as H.264 are jointly designed to minimize the actual RD cost on a frame basis. The proposed framework is applicable to optimize any hybrid video coding scheme, provided that specific algorithms are designed corresponding to coding syntaxes of a given standard codec, so as to maintain compatibility with the standard. Corresponding to the baseline profile syntaxes and the main profile syntaxes of H.264, respectively, we have proposed three RD algorithms---a graph-based algorithm for SDQ given motion prediction and quantization step sizes, an algorithm for residual coding optimization given motion prediction, and an iterative overall algorithm for jointly optimizing motion prediction, quantization, and entropy coding---with them embedded in the indicated order. Among the three algorithms, the SDQ design is the core, which is developed based on a given entropy coding method. Specifically, two SDQ algorithms have been developed based on the context adaptive variable length coding (CAVLC) in H.264 baseline profile and the context adaptive binary arithmetic coding (CABAC) in H.264 main profile, respectively. Experimental results for the H.264 baseline codec optimization show that for a set of typical testing sequences, the proposed RD method for H.264 baseline coding achieves a better trade-off between rate and distortion, i.e., 12\% rate reduction on average at the same distortion (ranging from 30dB to 38dB by PSNR) when compared with the RD optimization method implemented in H.264 baseline reference codec. Experimental results for optimizing H.264 main profile coding with CABAC show 10\% rate reduction over a main profile reference codec using CABAC, which also suggests 20\% rate reduction over the RD optimization method implemented in H.264 baseline reference codec, leading to our claim of having developed the best codec in terms of RD performance, while maintaining the compatibility with H.264. By investigating trade-off between distortion and complexity, we have also proposed a designing framework for image/video transcoding with spatial resolution reduction, i.e., to down-sample compressed images/video with an arbitrary ratio in the DCT domain. First, we derive a set of DCT-domain down-sampling methods, which can be represented by a linear transform with double-sided matrix multiplication (LTDS) in the DCT domain. Then, for a pre-selected pixel-domain down-sampling method, we formulate an optimization problem for finding an LTDS to approximate the given pixel-domain method to achieve the best trade-off between visual quality and computational complexity. The problem is then solved by modeling an LTDS with a multi-layer perceptron network and using a structural learning with forgetting algorithm for training the network. Finally, by selecting a pixel-domain reference method with the popular Butterworth lowpass filtering and cubic B-spline interpolation, the proposed framework discovers an LTDS with better visual quality and lower computational complexity when compared with state-of-the-art methods in the literature.

We studied the pressure effect of polycrystal BiMnO3 (type-I multiferroic) and single crystal Co3TeO6 (type-II multiferroic) with different magnetic fields and pressures. With the primary objective of understanding the pressure effect on BiMnO3, complex multiple magnetic transitions (kink I, II and III) are observed under the maximum applied pressure of 15.94 kbar (~1.6 GPa). Kink I, a long-range soft ferromagnetic transition at TcI ~ 100 K under ambient pressure, is suppressed completely at 11.74 kbar. Kink II emerges at 8.66 kbar along with TcII ~ 93 K. Kink II is a long-range soft ferromagnetic the same as kink I but canted in nature. Kink III, a canted antiferromagnetic transition at TcIII ~ 72.5 K appears along with kink II also at 8.66 kbar. These results indicate the complicated correlation between the lattice distortion and the spin configuration under pressures and magnetic fields in multiferroic system. Whereas, two distinct anomalies (T1 ~ 26 K and T2 ~ 18 K) are observed on single crystal Co3TeO6 in magnetic susceptibility, specific heat, and neutron diffraction measurements. Interestingly, the strong anisotropic magnetic variations are also noticed in high-magnetic-field hysteresis measurements with applied magnetic field parallel to a- and c- axes. Dielectric studies were also carried out in different magnetic fields at the temperature range 5 ¡V 300 K. Concomitantly, frequency-independent step-like dielectric anomaly is observed around 18 K, coinciding with the transition of magnetic susceptibility, specific heat, and neutron diffraction. The dielectric constant is also modified by external magnetic fields. These experimental results strongly suggest the multiferroicity of Co3TeO6. From temperature-dependent X-ray diffraction studies, it is evident that a structural distortion appears around 18 K, responsible of dielectric and/or magnetic ordering. The transition at 18 K is disappeared under pressure above 9.82 kbar, indicative of suppressing structural distortion. Similarly, the lattice distortion and the spin configuration under pressures are important factors for multiferroic property. Through the specific heat and pressure-dependent susceptibility, the structural distortion probably results from the magnetic ordering, indication the dielectric anomaly at 18 K.

Rapid distortion theory (RDT) is applied to compressible ideal-gas turbulence subjected to homogeneous shear flow. The study examines the linear or rapid processes present in turbulence evolution. Specific areas of investigation include:(i) characterization of the multi-stage flow behavior,(ii) changing role of pressure in the three-regime evolution and (iii) influence of thermodynamic fluctuations on the different regimes. Preliminary investigations utilizing the more accurate Favre-averaged RDT approach show promise however, this approach requires careful validation and testing. In this study the Favre-averaged RDT approach is validated against Direct Numerical Simulation (DNS) and Reynolds-averaged RDT results. The three-stage growth of the flow field statistics is first confirmed. The three regime evolution of turbulence is then examined in three different timescales and the physics associated with each regime is discussed in depth. The changing role of pressure in compressible turbulence evolution shows three distinct stages. The physics of each stage is clearly explained. Next, the influence of initial velocity and thermodynamic fluctuations on the flow field are investigated. The evolution of turbulence is shown to be strongly dependent on the initial gradient Mach number and initial temperature fluctuations which tend to delay the onset of the second regime of evolution. The initial turbulent Mach number, which quantifies velocity fluctuations in the flow, influences turbulence evolution only weakly. Comparison of Reynolds-averaged RDT against Favre-averaged RDT for simulations of nonzero initial flow field fluctuations shows the higher fidelity of the latter approach.

The primary advantage of Class D amplifier is high power efficiency (typically >90%). However, there are two problems in open-loop Class D design: Total Harmonic Distortion (THD) and output dc static current (the power efficiency will be degraded). The THD is rising from non-ideal sample carrier in Pulse Width Modulation circuit, and output dc static current is due to the non-match transfer characteristic in output stage. For designer to have such problems will be a large load. To improve these two problems, we proposed a Class D power amplifier with passive feedback design. Simulation and Measurement results show that the power efficiency is higher than 90% at 250Hz ~ 4KHz. Furthermore, the THD is less than 0.24% at 4 KHz in both simulation and experimental results.

The objective of the thesis is to characterize the linear and nonlinear aspects of inertial and pressure effects in turbulent flows. In the first part of the study, computations of Navier-Stokes and 3D Burgers equations are performed in the rapid distortion (RD) limit to analyze the inviscid linear processes in homogeneous turbulence. By contrasting the results of Navier- Stokes RD equations and Burgers RD equations, the effect of pressure can be isolated. The evolution of turbulent kinetic energy and anisotropy components and invariants are examined. In the second part of the thesis, the velocity gradient dynamics in turbulent flows are studied with the help of inviscid 3D Burgers equations and restricted Euler equations. The analytical asymptotic solutions of velocity gradient tensor are obtained for both Burgers and restricted Euler equations. Numerical computations are also performed to identify the stable solutions. The results are compared and contrasted to identify the effect of pressure on nonlinear velocity gradient dynamics. Of particular interest are the sign of the intermediate principle strain-rate and tendency of vorticity to align with the intermediate principle strain-rate. These aspects of velocity gradients provide valuable insight into the role of pressure in the energy cascade process.

Compressible ideal-gas turbulence subjected to homogeneous shear is investigated at the rapid distortion limit. Specific issues addressed are (i) the interaction between kinetic and internal energies and role of pressure-dilatation; (ii) the modifications to pressure-strain correlation and Reynolds stress anisotropy and (iii) the effect of the composition of velocity fluctuations (solenoidal vs. dilatational). Turbulence evolution is found to be strongly influenced by gradient Mach number, the initial solenoidal-to-dilatational ratio of the velocity field and the initial intensity of the thermodynamic fluctuations. The balance between the initial fluctuations in velocity and thermodynamic variables is also found to be very important. Any imbalance in the two fluctuating fields leads to high levels of pressure-dilatation and intense exchange. For a given initial condition, it is found that the interaction via the pressuredilatation term between the momentum and energy equations reaches a peak at an intermediate gradient Mach number. The energy exchange between internal and kinetic modes is negligible at very high or very low Mach number values due to lack of pressure dilatation. When present, the exchange exhibits oscillations even as the sum of the two energies evolves smoothly. The interaction between shear and solenoidal initial velocity field generates dilatational fluctuations; for some intermediate levels of shear Mach number dilatational fluctuations account for 20% of the total fluctuations. Similarly, the interaction between shear and initial dilatation produces solenoidal oscillations. Somewhat surprisingly, the generation of solenoidal fluctuations increases with gradient Mach number. Larger levels of pressure-strain correlation are seen with dilatational rather than solenoidal initial conditions. Anisotropies of solenoidal and dilatational components are investigated individually. The most interesting observation is that solenoidal and dilatational turbulence tend toward a one componential state but the energetic component is different in each case. As in incompressible shear flows, with solenoidal fluctuations, the streamwise (1,1) component of Reynolds stress is dominant. With dilatational fluctuations, the stream-normal (2,2) component is the strongest. Overall, the study yields valuable insight into the linear processes in high Mach number shear flows and identifies important closure modeling issues.

We study the problem of communicating a discrete time analog source over a channel such that the resulting distortion is minimized. For ergodic channels, Shannon showed that separate source and channel coding is optimal. In this work we study this problem for non-ergodic channels. Although not much can be said about the general problem of transmitting any analog sources over any non-ergodic channels with any distortion metric, for many practical problems like video broadcast and voice transmission, we can gain insights by studying the transmission of a Gaussian source over a wireless channel with mean square error as the distortion measure. Motivated by different applications, we consider three different non-ergodic channel models - (1) Additive white Gaussian noise (AWGN) channel whose signal-to-noise ratio (SNR) is unknown at the transmitter; (2) Rayleigh fading multiple-input multiple-output MIMO channel whose SNR is known at the transmitter; and (3) Rayleigh fading MIMO channel whose SNR is unknown at the transmitter. The traditional approach to study these problems has been to fix certain SNRs of interest and study the corresponding achievable distortion regions. However, the problems formulated this way have not been solved even for simple setups like 2 SNRs for the AWGN channel. We are interested in performance over a wide range of SNR and hence we use the distortion SNR exponent metric to study this problem. Distortion SNR exponent is defined as the rate of decay of distortion with SNR in the high SNR limit. We study several layered transmissions schemes where the source is first compressed in layers and then the layers are transmitted using channel codes that provide variable error protection. Results show that in several cases such layered transmission schemes are optimal in terms of the distortion SNR exponent. Specifically, if the band- width expansion (number of channel uses per source sample) is b, we show that the optimal distortion SNR exponent for the AWGN channel is b and it is achievable using a superposition based layered scheme. For the L-block Rayleigh fading M x N MIMO channel the optimal exponent is characterized for b < (|N - M|+1)= min(M;N) and b > MNL2. This corresponds to the entire range of b when min(M;N) = 1 and L = 1. The results also show that the exponents obtained using layered schemes which are a small subclass of joint source channel coding (JSCC) schemes are, surprisingly, as good as and better in some cases than achievable exponent of all other JSCC schemes reported so far.

Zugl.: Erlangen, Nürnberg, University, Diss., 2009.

Thesis (Ph. D.)--University of Missouri-Columbia, 2000. / Typescript. Vita. Includes bibliographical references (leaves 106-111). Also available on the Internet.