Digital Filters

The new technology advances provide that a great number of system signals can be easily measured with a low cost. The main problem is that usually only a fraction of the signal is useful for different purposes, for example maintenance, DVD-recorders, computers, electric/electronic circuits, econometric, optimization, etc. Digital filters are the most versatile, practical and effective methods for extracting the information necessary from the signal. They can be dynamic, so they can be automatically or manually adjusted to the external and internal conditions. Presented in this book are the most advanced digital filters including different case studies and the most relevant literature

Multiscale system theory

Cover title.Includes bibliographical references (p. 25-27).Partially supported by the Air Force Office of Scientific Research. AFOSR-88-0032 Partially supported by the National Science Foundation. ECS-8700903 Partially supported by the US Army Research Office. DAAL03-86-K-0171Albert Benveniste, Ramine Nikoukhah, Alan S. Willsky

Digital Filters and Signal Processing

Digital filters, together with signal processing, are being employed in the new technologies and information systems, and are implemented in different areas and applications. Digital filters and signal processing are used with no costs and they can be adapted to different cases with great flexibility and reliability. This book presents advanced developments in digital filters and signal process methods covering different cases studies. They present the main essence of the subject, with the principal approaches to the most recent mathematical models that are being employed worldwide

Digital Filter Design Using Improved Teaching-Learning-Based Optimization

Digital filters are an important part of digital signal processing systems. Digital filters are divided into finite impulse response (FIR) digital filters and infinite impulse response (IIR) digital filters according to the length of their impulse responses. An FIR digital filter is easier to implement than an IIR digital filter because of its linear phase and stability properties. In terms of the stability of an IIR digital filter, the poles generated in the denominator are subject to stability constraints. In addition, a digital filter can be categorized as one-dimensional or multi-dimensional digital filters according to the dimensions of the signal to be processed. However, for the design of IIR digital filters, traditional design methods have the disadvantages of easy to fall into a local optimum and slow convergence. The Teaching-Learning-Based optimization (TLBO) algorithm has been proven beneficial in a wide range of engineering applications. To this end, this dissertation focusses on using TLBO and its improved algorithms to design five types of digital filters, which include linear phase FIR digital filters, multiobjective general FIR digital filters, multiobjective IIR digital filters, two-dimensional (2-D) linear phase FIR digital filters, and 2-D nonlinear phase FIR digital filters. Among them, linear phase FIR digital filters, 2-D linear phase FIR digital filters, and 2-D nonlinear phase FIR digital filters use single-objective type of TLBO algorithms to optimize; multiobjective general FIR digital filters use multiobjective non-dominated TLBO (MOTLBO) algorithm to optimize; and multiobjective IIR digital filters use MOTLBO with Euclidean distance to optimize. The design results of the five types of filter designs are compared to those obtained by other state-of-the-art design methods. In this dissertation, two major improvements are proposed to enhance the performance of the standard TLBO algorithm. The first improvement is to apply a gradient-based learning to replace the TLBO learner phase to reduce approximation error(s) and CPU time without sacrificing design accuracy for linear phase FIR digital filter design. The second improvement is to incorporate Manhattan distance to simplify the procedure of the multiobjective non-dominated TLBO (MOTLBO) algorithm for general FIR digital filter design. The design results obtained by the two improvements have demonstrated their efficiency and effectiveness

From spline wavelet to sampling theory on circulant graphs and beyond– conceiving sparsity in graph signal processing

Graph Signal Processing (GSP), as the field concerned with the extension of classical signal processing concepts to the graph domain, is still at the beginning on the path toward providing a generalized theory of signal processing. As such, this thesis aspires to conceive the theory of sparse representations on graphs by traversing the cornerstones of wavelet and sampling theory on graphs. Beginning with the novel topic of graph spline wavelet theory, we introduce families of spline and e-spline wavelets, and associated filterbanks on circulant graphs, which lever- age an inherent vanishing moment property of circulant graph Laplacian matrices (and their parameterized generalizations), for the reproduction and annihilation of (exponen- tial) polynomial signals. Further, these families are shown to provide a stepping stone to generalized graph wavelet designs with adaptive (annihilation) properties. Circulant graphs, which serve as building blocks, facilitate intuitively equivalent signal processing concepts and operations, such that insights can be leveraged for and extended to more complex scenarios, including arbitrary undirected graphs, time-varying graphs, as well as associated signals with space- and time-variant properties, all the while retaining the focus on inducing sparse representations. Further, we shift from sparsity-inducing to sparsity-leveraging theory and present a novel sampling and graph coarsening framework for (wavelet-)sparse graph signals, inspired by Finite Rate of Innovation (FRI) theory and directly building upon (graph) spline wavelet theory. At its core, the introduced Graph-FRI-framework states that any K-sparse signal residing on the vertices of a circulant graph can be sampled and perfectly reconstructed from its dimensionality-reduced graph spectral representation of minimum size 2K, while the structure of an associated coarsened graph is simultaneously inferred. Extensions to arbitrary graphs can be enforced via suitable approximation schemes. Eventually, gained insights are unified in a graph-based image approximation framework which further leverages graph partitioning and re-labelling techniques for a maximally sparse graph wavelet representation.Open Acces

Fast Variance Prediction for Iteratively Reconstructed CT with Applications to Tube Current Modulation.

X-ray computed tomography (CT) is an important, widely-used medical imaging modality. A primary concern with the increasing use of CT is the ionizing radiation dose incurred by the patient. Statistical reconstruction methods are able to improve noise and resolution in CT images compared to traditional filter backprojection (FBP) based reconstruction methods, which allows for a reduced radiation dose. Compared to FBP-based methods, statistical reconstruction requires greater computational time and the statistical properties of resulting images are more difficult to analyze. Statistical reconstruction has parameters that must be correctly chosen to produce high-quality images. The variance of the reconstructed image has been used to choose these parameters, but this has previously been very time-consuming to compute. In this work, we use approximations to the local frequency response (LFR) of CT projection and backprojection to predict the variance of statistically reconstructed CT images. Compared to the empirical variance derived from multiple simulated reconstruction realizations, our method is as accurate as the currently available methods of variance prediction while being computable for thousands of voxels per second, faster than these previous methods by a factor of over ten thousand. We also compare our method to empirical variance maps produced from an ensemble of reconstructions from real sinogram data. The LFR can also be used to predict the power spectrum of the noise and the local frequency response of the reconstruction. Tube current modulation (TCM), the redistribution of X-ray dose in CT between different views of a patient, has been demonstrated to reduce dose when the modulation is well-designed. TCM methods currently in use were designed assuming FBP-based image reconstruction. We use our LFR approximation to derive fast methods for predicting the SNR of linear observers of a statistically reconstructed CT image. Using these fast observability and variance prediction methods, we derive TCM methods specific to statistical reconstruction that, in theory, potentially reduce radiation dose by 20% compared to FBP-specific TCM methods.PhDElectrical Engineering: SystemsUniversity of Michigan, Horace H. Rackham School of Graduate Studieshttp://deepblue.lib.umich.edu/bitstream/2027.42/111463/1/smschm_1.pd

Diverse applications of the Quantum Walk model in Quantum Information: a theoretical and experimental analysis in the optical framework

Quantum Walks have been a very important model in the last thirty years, after their first definition and rigorous description. The analysis of the many possible variations of their behavior has delivered a plethora of solutions and platforms for the many diverse fields of investigation. The applications of the Quantum Walk model spreads from the development of Quantum Algorithm, to the modeling and simulation of systems of the most diverse nature, such as solid state or biological systems. In general, it helped developing a well-established quantum (or coherent) propagation model, which is useful both inside and outside physics. In this thesis, we focus on the study of disordered Quantum Walks, in order to get better understanding of the inuence of Quantum Walk disordered dynamics to non-classical correlations and propagating quantum information. Afterwards, we generalize this dynamical approach to Quantum Information processing, developing a Quantum Receiver for Quantum State Discrimination featuring a time multiplexing structure and we investigate the potentiality of this Quantum Walk inspired framework in the field of Quantum State Discrimination, through the developing and realization of experimental protocols characterized by increasing complexity. We also report on some apparent deviations from this path, although still aimed at the transfer of our expertise, built in previous investigations, to the study of new models and more complex quantum systems

Multidimensional Wavelets and Computer Vision

This report deals with the construction and the mathematical analysis of multidimensional nonseparable wavelets and their efficient application in computer vision. In the first part, the fundamental principles and ideas of multidimensional wavelet filter design such as the question for the existence of good scaling matrices and sensible design criteria are presented and extended in various directions. Afterwards, the analytical properties of these wavelets are investigated in some detail. It will turn out that they are especially well-suited to represent (discretized) data as well as large classes of operators in a sparse form - a property that directly yields efficient numerical algorithms. The final part of this work is dedicated to the application of the developed methods to the typical computer vision problems of nonlinear image regularization and the computation of optical flow in image sequences. It is demonstrated how the wavelet framework leads to stable and reliable results for these problems of generally ill-posed nature. Furthermore, all the algorithms are of order O(n) leading to fast processing

Combined Industry, Space and Earth Science Data Compression Workshop

The sixth annual Space and Earth Science Data Compression Workshop and the third annual Data Compression Industry Workshop were held as a single combined workshop. The workshop was held April 4, 1996 in Snowbird, Utah in conjunction with the 1996 IEEE Data Compression Conference, which was held at the same location March 31 - April 3, 1996. The Space and Earth Science Data Compression sessions seek to explore opportunities for data compression to enhance the collection, analysis, and retrieval of space and earth science data. Of particular interest is data compression research that is integrated into, or has the potential to be integrated into, a particular space or earth science data information system. Preference is given to data compression research that takes into account the scien- tist's data requirements, and the constraints imposed by the data collection, transmission, distribution and archival systems

Modeling and estimation of multiresolution stochastic processes

Includes bibliographical references (p. 47-51).Caption title.Research supported in part by the National Science Foundation. ECS-8700903 Research supported in part by the Air Force Office of Scientific Research. AFOSR-88-0032 Research supported in part by the US Army Research Office. DAAL03-86-K-0171 Research supported in part by INRIA.Michele Basseville ... [et al.]