A System Approach to the Design of Multirate Filter Banks.

This dissertation studies the design of multirate filter banks by adopting a so-called system approach. The design issue of Johnston\u27s method is first investigated in which an explicit expression of the reconstruction error is derived using Lyapunov stability theory, and new convergent iterative algorithms are proposed through non-linear optimization. The results are extended to the two-dimensional filter banks. The design issue of more general multirate filter banks is also investigated through model matching method. Using standard results from modern control theory, new design algorithms are developed which minimize the reconstruction error while completely eliminating the aliasing error. State-space realizations, inner-outer factorizations, and optimal Hankel norm approximation are used to reduce the complexity of computation and improve the accuracy of the proposed design algorithms

A Panorama on Multiscale Geometric Representations, Intertwining Spatial, Directional and Frequency Selectivity

The richness of natural images makes the quest for optimal representations in image processing and computer vision challenging. The latter observation has not prevented the design of image representations, which trade off between efficiency and complexity, while achieving accurate rendering of smooth regions as well as reproducing faithful contours and textures. The most recent ones, proposed in the past decade, share an hybrid heritage highlighting the multiscale and oriented nature of edges and patterns in images. This paper presents a panorama of the aforementioned literature on decompositions in multiscale, multi-orientation bases or dictionaries. They typically exhibit redundancy to improve sparsity in the transformed domain and sometimes its invariance with respect to simple geometric deformations (translation, rotation). Oriented multiscale dictionaries extend traditional wavelet processing and may offer rotation invariance. Highly redundant dictionaries require specific algorithms to simplify the search for an efficient (sparse) representation. We also discuss the extension of multiscale geometric decompositions to non-Euclidean domains such as the sphere or arbitrary meshed surfaces. The etymology of panorama suggests an overview, based on a choice of partially overlapping "pictures". We hope that this paper will contribute to the appreciation and apprehension of a stream of current research directions in image understanding.Comment: 65 pages, 33 figures, 303 reference

Direct Jet Reconstruction in Proton-Proton and Copper-Copper Collisions at √sNN = 200 GeV

Collision of heavy nuclei at the Relativistic Heavy Ion Collider (RHIC) recreates the state of high temperature quark-gluon plasma that existed shortly after the Big Bang. Measurement using single particle spectra and two-particle correlation shows that this medium is largely opaque to the transit of a high energy quark or gluon. Reconstructing the kinematics of these quarks and gluons can provide additional constraints for the property of their interaction with the medium. While the direct reconstruction of quantum chromodynamics jets, the final state showers of quarks and gluons, has become an indispensable tool at hadron and electron accelerator experiments, the application of this technique to heavy ion collisions at the RHIC energy has been considered a hard problem. The relatively low yield of high transverse momentum jets would have to be detected within a large, fluctuating background that can give rise to a false jet signal. At the RHIC PHENIX experiment, jet reconstruction also has to cope with the limited aperture of the central arm spectrometers. To overcome both problems, which can distort the jet signal in the traditional reconstruction algorithms, this thesis develops an algorithm that reconstructs the jets as maxima of the Gaussian filtered event transverse momentum distribution. The Gaussian angular weighting causes the algorithm to become more sensitive to the jet core versus the jet periphery. It is then combined with a fake jet rejection discriminant to remove the background fluctuation from the jet signal. This algorithm is used to obtain the first jet measurement in heavy ion environment at PHENIX, using data from the 2004/2005 RHIC run. The result includes the proton-proton inclusive jet spectrum, the proton-proton fragmentation function, the copper-copper jet nuclear modification factor, the copper-copper jet central-to-peripheral modification factor, and the copper-copper dijet azimuthal correlation. The measured copper-copper jet nuclear modification factor shows that there is a significant initial state effect to the jet suppression. The observation of no broadening in the copper-copper dijet azimuthal correlation indicates that the traditional energy loss picture via multiple soft scattering may not be applicable to the quark-gluon plasma

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

Asynchronous Representation and Processing of Analog Sparse Signals Using a Time-Scale Framework

In this dissertation we investigate the problem of asynchronous representation and processing of analog sparse signals using a time-scale framework. Recently, in the design of signal representations the focus has been on the use of application-driven constraints for optimality purposes. Appearing in many fields such as neuroscience, implantable biomedical diagnostic devices, and sensor network applications, sparse or burst--like signals are of great interest. A common challenge in the representation of such signals is that they exhibit non--stationary behavior with frequency--varying spectra. By ignoring that the maximum frequency of their spectra is changing with time, uniformly sampling sparse signals collects samples in quiescent segments and results in high power dissipation. Also, continuous monitoring of signals challenges data acquisition, storage, and processing; especially if remote monitoring is desired, as this would require that a large number of samples be generated, stored and transmitted. Power consumption and the type of processing imposed by the size of the devices in the aforementioned applications has motivated the use of asynchronous approaches in our research. First, we work on establishing a new paradigm for the representation of analog sparse signals using a time-frequency representation. Second, we develop a scale-based signal decomposition framework which uses filter-bank structures for the representation-analysis-compression scheme of the sparse information. Using an asynchronous signal decomposition scheme leads to reduced computational requirements and lower power consumption; thus it is promising for hardware implementation. In addition, the proposed algorithm does not require prior knowledge of the bandwidth of the signal and the effect of noise can still be alleviated. Finally, we consider the synthesis step, where the target signal is reconstructed from compressed data. We implement a perfect reconstruction filter bank based on Slepian wavelets to use in the reconstruction of sparse signals from non--uniform samples. In this work, experiments on primary biomedical signal applications, such as electrocardiogram (EEG), swallowing signals and heart sound recordings have achieved significant improvements over traditional methods in the sensing and processing of sparse data. The results are also promising in applications including compression and denoising

Spatio-Temporal Reconstruction Techniques for Optical Microscopy

Optical microscopy offers the unique possibility to study living samples under conditions akin to their native state. However, the technique is not void of inherent problems such as optical blur due to light diffraction, contamination with out-of-focus light from adjacent focal planes, and spherical aberrations. Furthermore, with a dearth of techniques that are capable of imaging multiple focal sections in quick succession, the multi-dimensional capture of dynamically changing samples remains a challenge of its own. Computational techniques that use auxiliary knowledge about the imaging system and the sample to mitigate these problems are hence of great interest in optical microscopy.The first part of this thesis deals with the design of a discrete model to characterize light propagation. Following the scalar diffraction theory in optics, we propose a discrete algorithm, based on generalized sampling theory, to reverse the coherent diffraction process via back propagation. The algorithm consists of a wavelet-based model for the spherical waves emanating from the object of interest and an optimized multi-rate filtering protocol for reconstruction from the diffraction data recorded by non-ideal detectors. The second part of this thesis describes a spatial registration tool designed for multi-view microscopy. Here, the imaged sample is rotated about a lateral axis for the acquisition of multiple 3D datasets from different views in order to subsequently alleviate the severe axial blur found in each such dataset. Automatic algorithms that only rely on maximizing pixel-based similarity provide poor results in such applications owing to the anisotropic point-spread-function (PSF) of optical microscopes. We propose a pyramid-based spatial registration algorithm that re-blurs the multi-view datasets with transformed forms of the PSF in order to make them comparable, before maximizing their pixel-based similarity for registration.The third part of this thesis describes a fast converging iterative multi-view deconvolution technique that can be applied to the spatially registered forms of the 3D datasets acquired using multi-view microscopy. Our sparsity based algorithm solves a non-linear objective function to jointly deconvolve and fuse the multi-view datasets to finally produce a single deblurred 3D result that has nearly isotropic spatial resolution.The fourth part of this thesis addresses problems due to spherical aberrations encountered during the imaging of thick samples in optical microscopy. The depth-varying nature of the optical blur found in such cases renders fast and efficient shift-invariant deconvolution techniques to be inapplicable. Here, we propose a fast iterative-shrinkage-thresholding shift-variant 3D deconvolution method that uses depth-dependent PSFs to reconstruct a 3D deblurred form of the imaged thick specimen. The final part of this thesis describes a non-rigid temporal registration tool that aids in the multi-dimensional imaging of quasi-periodic processes such as cardiac cycles. We propose a variant of dynamic time warping that is capable of both temporally warping and wrapping an input sequence by allowing for jump discontinuities in the non-linear temporal alignment function akin to those found in wrapped phase functions. This work provides a new set of tools for spatio-temporal reconstruction in optical microscopy and we anticipate them to be useful for a wide range of problems in practice

International Conference on Continuous Optimization (ICCOPT) 2019 Conference Book

The Sixth International Conference on Continuous Optimization took place on the campus of the Technical University of Berlin, August 3-8, 2019. The ICCOPT is a flagship conference of the Mathematical Optimization Society (MOS), organized every three years. ICCOPT 2019 was hosted by the Weierstrass Institute for Applied Analysis and Stochastics (WIAS) Berlin. It included a Summer School and a Conference with a series of plenary and semi-plenary talks, organized and contributed sessions, and poster sessions. This book comprises the full conference program. It contains, in particular, the scientific program in survey style as well as with all details, and information on the social program, the venue, special meetings, and more

MATLAB

A well-known statement says that the PID controller is the "bread and butter" of the control engineer. This is indeed true, from a scientific standpoint. However, nowadays, in the era of computer science, when the paper and pencil have been replaced by the keyboard and the display of computers, one may equally say that MATLAB is the "bread" in the above statement. MATLAB has became a de facto tool for the modern system engineer. This book is written for both engineering students, as well as for practicing engineers. The wide range of applications in which MATLAB is the working framework, shows that it is a powerful, comprehensive and easy-to-use environment for performing technical computations. The book includes various excellent applications in which MATLAB is employed: from pure algebraic computations to data acquisition in real-life experiments, from control strategies to image processing algorithms, from graphical user interface design for educational purposes to Simulink embedded systems