<p>Signal expansions using frames may be considered as generalizations of signal representations based on transforms and filter banks. Frames for sparse signal representations may be designed using an iterative method with two main steps: (1) Frame vector selection and expansion coefficient determination for signals in a training set, – selected to be representative of the signals for which compact representations are desired, using the frame designed in the previous iteration. (2) Update of frame vectors with the objective of improving the representation of step (1). In this thesis we solve step (2) of the general frame design problem using the compact notation of linear algebra.</p><p>This makes the solution both conceptually and computationally easy, especially for the non-block-oriented frames, – for short overlapping frames, that may be viewed as generalizations of critically sampled filter banks. Also, the solution is more general than those presented earlier, facilitating the imposition of constraints, such as symmetry, on the designed frame vectors. We also take a closer look at step (1) in the design method. Some of the available vector selection algorithms are reviewed, and adaptations to some of these are given. These adaptations make the algorithms better suited for both the frame design method and the sparse representation of signals problem, both for block-oriented and overlapping frames.</p><p>The performances of the improved frame design method are shown in extensive experiments. The sparse representation capabilities are illustrated both for one-dimensional and two-dimensional signals, and in both cases the new possibilities in frame design give better results.</p><p>Also a new method for texture classification, denoted Frame Texture Classification Method (FTCM), is presented. The main idea is that a frame trained for making sparse representations of a certain class of signals is a model for this signal class. The FTCM is applied to nine test images, yielding excellent overall performance, for many test images the number of wrongly classified pixels is more than halved, in comparison to state of the art texture classification methods presented in [59].</p><p>Finally, frames are analyzed from a practical viewpoint, rather than in a mathematical theoretic perspective. As a result of this, some new frame properties are suggested. So far, the new insight this has given has been moderate, but we think that this approach may be useful in frame analysis in the future.</p>

Signal expansions using frames may be considered as generalizations of signal representations based on transforms and filter banks. Frames for sparse signal representations may be designed using an iterative method with two main steps: (1) Frame vector selection and expansion coefficient determination for signals in a training set, – selected to be representative of the signals for which compact representations are desired, using the frame designed in the previous iteration. (2) Update of frame vectors with the objective of improving the representation of step (1). In this thesis we solve step (2) of the general frame design problem using the compact notation of linear algebra. This makes the solution both conceptually and computationally easy, especially for the non-block-oriented frames, – for short overlapping frames, that may be viewed as generalizations of critically sampled filter banks. Also, the solution is more general than those presented earlier, facilitating the imposition of constraints, such as symmetry, on the designed frame vectors. We also take a closer look at step (1) in the design method. Some of the available vector selection algorithms are reviewed, and adaptations to some of these are given. These adaptations make the algorithms better suited for both the frame design method and the sparse representation of signals problem, both for block-oriented and overlapping frames. The performances of the improved frame design method are shown in extensive experiments. The sparse representation capabilities are illustrated both for one-dimensional and two-dimensional signals, and in both cases the new possibilities in frame design give better results. Also a new method for texture classification, denoted Frame Texture Classification Method (FTCM), is presented. The main idea is that a frame trained for making sparse representations of a certain class of signals is a model for this signal class. The FTCM is applied to nine test images, yielding excellent overall performance, for many test images the number of wrongly classified pixels is more than halved, in comparison to state of the art texture classification methods presented in [59]. Finally, frames are analyzed from a practical viewpoint, rather than in a mathematical theoretic perspective. As a result of this, some new frame properties are suggested. So far, the new insight this has given has been moderate, but we think that this approach may be useful in frame analysis in the future.

Lic.-avh. Luleå : Luleå tekniska universitet, 2005.

Diss. Linköping : Linköpings universitet, 2007.

<p>In recent years, deploying multiple antennas at both transmitter and receiver has appeared as a very promising technology. By exploiting the spatial domain, multiple-input multiple-output (MIMO) systems can support extremely high data rates as long as the environments can provide sufficiently rich scattering. To design high performance MIMO wireless systems and predict system performance under various circumstances, it is of great interest to have accurate MIMO wireless channel models for different scenarios. In this thesis, we characterize and model MIMO radio propagation channels based on indoor MIMO channel measurements.</p><p>The recent development on MIMO radio channel modeling is briefly reviewed in this thesis. The models are categorized into non-physical and physical models, and discussed respectively. The non-physical models primarily rely on the statistical characteristics of MIMO channels obtained from the measured data, while the physical models describe the MIMO channel (or its distribution) via some physical parameters. We also briefly mention the MIMO channel modeling work within the IEEE 802.11n and 3GPP/3GPP2 standardization work.</p><p>For the narrowband case, a non line-of-sight (NLOS) indoor MIMO channel model is presented. The model is based on a Kronecker structure of the channel covariance matrix and the fact that the channel is complex Gaussian. It is extended to line-of-sight (LOS) scenario by estimating and modeling the dominant component separately. For the wideband case, two NLOS MIMO channel models are proposed. The first model uses the average power delay profile and the Kronecker structure of the second order moments of each channel tap to model the wideband MIMO channel, while the second model combines a simple single-input single-output (SISO) model with the same Kronecker structure of the second order moments. Monte-Carlo simulations are used to generate indoor MIMO channel realizations according to the above models. The results are compared with the measured data and good agreement has been observed.</p><p>Under the assumption of spatial wide sense stationary, a lower bound of the maximum Kronecker model errors is obtained by employing a combination of grid search and semidefinite programming to explore the feasible region. Numerical examples show that the bound is tight for moderate number of grid points. By comparing the worst case model errors with the model errors obtained from the measured channels, we find that the channel correlation matrix in these measurements can, indeed, be well approximated by the Kronecker product of the correlation matrix at the transmitter and the receiver.</p><p>To model wideband MIMO channels, it is important to investigate the angular statistics on both the tap and cluster levels. Based on 5~GHz indoor wireless channel measurements, a frequency domain space alternating generalized expectation maximization (FD-SAGE) algorithm is employed to estimate the multipath components from the measured data. We then manually identify the clusters of the multipaths and calculate the tap and cluster angular spreads (ASs) for each identified cluster. It is found that for the 100 MHz channels, the average tap AS is just a few degrees less than the cluster AS and the difference diminishes for small channel bandwidth.</p>

<p>The demand for efficient communication and data storage is continuously increasing and <i>signal representation</i> and <i>compression</i> are important factors in digital communication and storage systems.</p><p>This work deals with <i>Frame based</i> signal representation and compression. The emphasis is on the design of frames suited for efficient representation, or for low bit rate compression, of classes of signals.</p><p>Traditional signal decompositions such as transforms, wavelets, and filter banks, generate expansions using an analysis-synthesis setting. In this thesis we concentrate on the synthesis or <i>reconstruction</i> part of the signal expansion, having a system with no explicit analysis stage. We want to investigate the use of an <i>overcomplete</i> set of vectors, a frame or an overcomplete dictionary, for signal representations and allow sparse representations. Effective signal representations are desirable in many applications, where signal compression is one example. Others can be signal analysis for different purposes, reconstruction of signals from a limited observation set, feature extraction in pattern recognition and so forth.</p><p>The lack of an explicit analysis stage originates some questions on finding the optimal representation. Finding an optimal sparse representation from an overcomplete set of vectors is NP-complete, and suboptimal vector selection methods are more practical. We have used some existing methods like different variations of the Matching Pursuit (MP) [52] algorithm, and we developed a robust regularized FOCUSS to be able to use FOCUSS (FOCal Underdetermined System Solver [29]) under lossy conditions.</p><p>In this work we develop techniques for frame design, the Method of Optimal Directions (MOD), and propose methods by which such frames can successfully be used in frame based signal representation and in compression schemes. A Multi Frame Compression (MFC) scheme is presented and experiments with several signal classes show that the MFC scheme works well at low bit rates using MOD designed frames. Reconstruction experiments provides complimentary evidence of the good properties of the MOD algorithm.</p>

<p>In signal compression we distinguish between lossless and lossy compression. In lossless compression, the encoded signal is more bit efficient than the original signal and is exactly the same as the original one when decoded. In lossy compression, the encoded signal represents an approximation of the original signal, but it has less number of bits. In the latter situation, the major issue is to find the best possible rate-distortion (RD) tradeoff. The rate-distortion function (RDF) represents the theoretical lower bound of the distortion between the original and the reconstructed signal, subject to a given total bit rate for the compressed signal. This is with respect to any compression scheme. If the compression scheme is given, we can find its operational RDF (ORDF).</p><p>The main contribution of this dissertation is the presentation of a method that finds the operational rate-distortion optimal solution for an overcomplete signal decomposition. The idea of using overcomplete dictionaries, or frames, is to get a sparse representation of the signal. Traditionally, suboptimal algorithms, such as Matching Pursuit (MP), are used for this purpose. Given the frame and the Variable Length Codeword (VLC) table embedded in the entropy coder, the solution of the problem of establishing the best RD trade-off has a very high complexity. The proposed method reduces this complexity significantly by structuring the solution approach such that the dependent quantizer allocation problem reduces into an independent one. In addition, the use of a solution tree further reduces the complexity. It is important to note that this large reduction in complexity is achieved without sacrificing optimality. The optimal rate-distortion solution depends on the frame selection and the VLC table embedded in the entropy coder. Thus, frame design and VLC optimization is part of this work.</p><p>Extensive coding experiments are presented, where Gaussian AR(1) processes and various electrocardiogram (ECG) signals are used as input signals. The experiments demonstrate that the new approach outperforms Rate-Distortion Optimized (RDO) Matching Pursuit, previously proposed in [17], in the rate-distortion sense.</p>

This thesis deals with modelling, analysis, and design of interactions between subsystems in chemical process plants and intracellular biochemical processes. In the first part, the focus is on the selection of decentralized feedback control structures for plants in the chemical process industry, with the aim of achieving a desired performance in the presence of interactions. The second part focuses on modelling and analysis of complex biochemical networks, with the aim of unravelling the impact of interactions between genes, proteins, and metabolites on cell functions. Decentralized control is almost the de-facto standard for control of large-scale systems, and in particular for systems in the process industry. An important task in the design of a decentralized control system is the selection of the control configuration, the so-called input-output pairing, which effectively decides the subsystems. Previous research addressing this problem has primarily focused on the effect of interactions on stability. In this thesis, the problem of selecting control configurations that can deliver a desired control performance is addressed. It is shown that existing measures of interactions, such as the relative gain array (RGA), are poor for selecting configurations for performance due to their inherent assumption of perfect control. Furthermore, several model based tools for the selection of control configurations based on performance considerations are proposed. Central functions in the cell are often linked to complex dynamic behaviors, such as sustained oscillations and multistability, in a biochemical reaction network. Determination of the specific interactions underlying such behaviors is important, for example, to determine sensitivity, robustness, and modelling requirements of given cell functions. A method for identifying the feedback connections and involved subsystems, within a biochemical network, that are the main sources of a complex dynamic behavior is proposed. The effectiveness of the method is illustrated on examples involving cell cycle control, circadian rhythms and glycolytic oscillations. Also, a method for identifying structured dynamic models of biochemical networks, based on experimental data, is proposed. The method is based on results from system identification theory, using time-series measurement data of expression profiles and concentrations of the involved biochemical components. Finally, in order to reduce the complexity of obtained network models, a method for decomposing large-scale networks into biologically meaningful subnetworks is proposed.

In recent years, deploying multiple antennas at both transmitter and receiver has appeared as a very promising technology. By exploiting the spatial domain, multiple-input multiple-output (MIMO) systems can support extremely high data rates as long as the environments can provide sufficiently rich scattering. To design high performance MIMO wireless systems and predict system performance under various circumstances, it is of great interest to have accurate MIMO wireless channel models for different scenarios. In this thesis, we characterize and model MIMO radio propagation channels based on indoor MIMO channel measurements. The recent development on MIMO radio channel modeling is briefly reviewed in this thesis. The models are categorized into non-physical and physical models, and discussed respectively. The non-physical models primarily rely on the statistical characteristics of MIMO channels obtained from the measured data, while the physical models describe the MIMO channel (or its distribution) via some physical parameters. We also briefly mention the MIMO channel modeling work within the IEEE 802.11n and 3GPP/3GPP2 standardization work. For the narrowband case, a non line-of-sight (NLOS) indoor MIMO channel model is presented. The model is based on a Kronecker structure of the channel covariance matrix and the fact that the channel is complex Gaussian. It is extended to line-of-sight (LOS) scenario by estimating and modeling the dominant component separately. For the wideband case, two NLOS MIMO channel models are proposed. The first model uses the average power delay profile and the Kronecker structure of the second order moments of each channel tap to model the wideband MIMO channel, while the second model combines a simple single-input single-output (SISO) model with the same Kronecker structure of the second order moments. Monte-Carlo simulations are used to generate indoor MIMO channel realizations according to the above models. The results are compared with the measured data and good agreement has been observed. Under the assumption of spatial wide sense stationary, a lower bound of the maximum Kronecker model errors is obtained by employing a combination of grid search and semidefinite programming to explore the feasible region. Numerical examples show that the bound is tight for moderate number of grid points. By comparing the worst case model errors with the model errors obtained from the measured channels, we find that the channel correlation matrix in these measurements can, indeed, be well approximated by the Kronecker product of the correlation matrix at the transmitter and the receiver. To model wideband MIMO channels, it is important to investigate the angular statistics on both the tap and cluster levels. Based on 5~GHz indoor wireless channel measurements, a frequency domain space alternating generalized expectation maximization (FD-SAGE) algorithm is employed to estimate the multipath components from the measured data. We then manually identify the clusters of the multipaths and calculate the tap and cluster angular spreads (ASs) for each identified cluster. It is found that for the 100 MHz channels, the average tap AS is just a few degrees less than the cluster AS and the difference diminishes for small channel bandwidth. / <p>QC 20121003</p>

The demand for efficient communication and data storage is continuously increasing and signal representation and compression are important factors in digital communication and storage systems. This work deals with Frame based signal representation and compression. The emphasis is on the design of frames suited for efficient representation, or for low bit rate compression, of classes of signals. Traditional signal decompositions such as transforms, wavelets, and filter banks, generate expansions using an analysis-synthesis setting. In this thesis we concentrate on the synthesis or reconstruction part of the signal expansion, having a system with no explicit analysis stage. We want to investigate the use of an overcomplete set of vectors, a frame or an overcomplete dictionary, for signal representations and allow sparse representations. Effective signal representations are desirable in many applications, where signal compression is one example. Others can be signal analysis for different purposes, reconstruction of signals from a limited observation set, feature extraction in pattern recognition and so forth. The lack of an explicit analysis stage originates some questions on finding the optimal representation. Finding an optimal sparse representation from an overcomplete set of vectors is NP-complete, and suboptimal vector selection methods are more practical. We have used some existing methods like different variations of the Matching Pursuit (MP) [52] algorithm, and we developed a robust regularized FOCUSS to be able to use FOCUSS (FOCal Underdetermined System Solver [29]) under lossy conditions. In this work we develop techniques for frame design, the Method of Optimal Directions (MOD), and propose methods by which such frames can successfully be used in frame based signal representation and in compression schemes. A Multi Frame Compression (MFC) scheme is presented and experiments with several signal classes show that the MFC scheme works well at low bit rates using MOD designed frames. Reconstruction experiments provides complimentary evidence of the good properties of the MOD algorithm.