Signal separation of musical instruments: simulation-based methods for musical signal decomposition and transcription

This thesis presents techniques for the modelling of musical signals, with particular regard to monophonic and polyphonic pitch estimation. Musical signals are modelled as a set of notes, each comprising of a set of harmonically-related sinusoids. An hierarchical model is presented that is very general and applicable to any signal that can be decomposed as the sum of basis functions. Parameter estimation is posed within a Bayesian framework, allowing for the incorporation of prior information about model parameters. The resulting posterior distribution is of variable dimension and so reversible jump MCMC simulation techniques are employed for the parameter estimation task. The extension of the model to time-varying signals with high posterior correlations between model parameters is described. The parameters and hyperparameters of several frames of data are estimated jointly to achieve a more robust detection. A general model for the description of time-varying homogeneous and heterogeneous multiple component signals is developed, and then applied to the analysis of musical signals. The importance of high level musical and perceptual psychological knowledge in the formulation of the model is highlighted, and attention is drawn to the limitation of pure signal processing techniques for dealing with musical signals. Gestalt psychological grouping principles motivate the hierarchical signal model, and component identifiability is considered in terms of perceptual streaming where each component establishes its own context. A major emphasis of this thesis is the practical application of MCMC techniques, which are generally deemed to be too slow for many applications. Through the design of efficient transition kernels highly optimised for harmonic models, and by careful choice of assumptions and approximations, implementations approaching the order of realtime are viable.Engineering and Physical Sciences Research Counci

Perceptual data mining : bootstrapping visual intelligence from tracking behavior

Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Electrical Engineering and Computer Science, 2002.Includes bibliographical references (p. 161-166).One common characteristic of all intelligent life is continuous perceptual input. A decade ago, simply recording and storing a a few minutes of full frame-rate NTSC video required special hardware. Today, an inexpensive personal computer can process video in real-time tracking and recording information about multiple objects for extended periods of time, which fundamentally enables this research. This thesis is about Perceptual Data Mining (PDM), the primary goal of which is to create a real-time, autonomous perception system that can be introduced into a wide variety of environments and, through experience, learn to model the activity in that environment. The PDM framework infers as much as possible about the presence, type, identity, location, appearance, and activity of each active object in an environment from multiple video sources, without explicit supervision. PDM is a bottom-up, data-driven approach that is built on a novel, robust attention mechanism that reliably detects moving objects in a wide variety of environments. A correspondence system tracks objects through time and across multiple sensors producing sets of observations of objects that correspond to the same object in extended environments. Using a co-occurrence modeling technique that exploits the variation exhibited by objects as they move through the environment, the types of objects, the activities that objects perform, and the appearance of specific classes of objects are modeled. Different applications of this technique are demonstrated along with a discussion of the corresponding issues.(cont.) Given the resulting rich description of the active objects in the environment, it is possible to model temporal patterns. An effective method for modeling periodic cycles of activity is demonstrated in multiple environments. This framework can learn to concisely describe regularities of the activity in an environment as well as determine atypical observations. Though this is accomplished without any supervision, the introduction of a minimal amount of user interaction could be used to produce complex, task-specific perception systems.by Christopher P. Stauffer.Ph.D

Design and Optimization of a 3-D Plasmonic Huygens Metasurface for Highly-Efficient Flat Optics

For miniaturization of future USAF unmanned aerial and space systems to become feasible, accompanying sensor components of these systems must also be reduced in size, weight and power (SWaP). Metasurfaces can act as planar equivalents to bulk optics, and thus possess a high potential to meet these low-SWaP requirements. However, functional efficiencies of plasmonic metasurface architectures have been too low for practical application in the infrared (IR) regime. Huygens-like forward-scattering inclusions may provide a solution to this deficiency, but there is no academic consensus on an optimal plasmonic architecture for obtaining efficient phase control at high frequencies. This dissertation asks the question: what are the ideal topologies for generating Huygens-like metasurface building blocks across a full 2π phase space? Instead of employing any a priori assumption of fundamental scattering topologies, a genetic algorithm (GA) routine was developed to optimize a “blank slate” grid of binary voxels inside a 3D cavity, evolving the voxel bits until a near-globally optimal transmittance (T) was attained at a targeted phase. All resulting designs produced a normalized T≥80 across the entire 2π range, which is the highest metasurface efficiency reported to-date for a plasmonic solution in the IR regime

Directional multiresolution image representations

Efficient representation of visual information lies at the foundation of many image processing tasks, including compression, filtering, and feature extraction. Efficiency of a representation refers to the ability to capture significant information of an object of interest in a small description. For practical applications, this representation has to be realized by structured transforms and fast algorithms. Recently, it has become evident that commonly used separable transforms (such as wavelets) are not necessarily best suited for images. Thus, there is a strong motivation to search for more powerful schemes that can capture the intrinsic geometrical structure of pictorial information. This thesis focuses on the development of new "true" two-dimensional representations for images. The emphasis is on the discrete framework that can lead to algorithmic implementations. The first method constructs multiresolution, local and directional image expansions by using non-separable filter banks. This discrete transform is developed in connection with the continuous-space curvelet construction in harmonic analysis. As a result, the proposed transform provides an efficient representation for two-dimensional piecewise smooth signals that resemble images. The link between the developed filter banks and the continuous-space constructions is set up in a newly defined directional multiresolution analysis. The second method constructs a new family of block directional and orthonormal transforms based on the ridgelet idea, and thus offers an efficient representation for images that are smooth away from straight edges. Finally, directional multiresolution image representations are employed together with statistical modeling, leading to powerful texture models and successful image retrieval systems

Angles and devices for quantum approximate optimization

A potential application of emerging Noisy Intermediate-Scale Quantum (NISQ) devices is that of approximately solving combinatorial optimization problems. This thesis investigates a gate-based algorithm for this purpose, the Quantum Approximate Optimization Algorithm (QAOA), in two major themes. First, we examine how the QAOA resolves the problems it is designed to solve. We take a statistical view of the algorithm applied to ensembles of problems, first, considering a highly symmetric version of the algorithm, using Grover drivers. In this highly symmetric context, we find a simple dependence of the QAOA state’s expected value on how values of the cost function are distributed. Furthering this theme, we demonstrate that, generally, QAOA performance depends on problem statistics with respect to a metric induced by a chosen driver Hamiltonian. We obtain a method for evaluating QAOA performance on worst-case problems, those of random costs, for differing driver choices. Second, we investigate a QAOA context with device control occurring only via single-qubit gates, rather than using individually programmable one- and two-qubit gates. In this reduced control overhead scheme---the digital-analog scheme---the complexity of devices running QAOA circuits is decreased at the cost of errors which are shown to be non-harmful in certain regimes. We then explore hypothetical device designs one could use for this purpose.Eine mögliche Anwendung für “Noisy Intermediate-Scale Quantum devices” (NISQ devices) ist die näherungsweise Lösung von kombinatorischen Optimierungsproblemen. Die vorliegende Arbeit untersucht anhand zweier Hauptthemen einen gatterbasierten Algorithmus, den sogenannten “Quantum Approximate Optimization Algorithm” (QAOA). Zuerst prüfen wir, wie der QAOA jene Probleme löst, für die er entwickelt wurde. Wir betrachten den Algorithmus in einer Kombination mit hochsymmetrischen Grover-Treibern für statistische Ensembles von Probleminstanzen. In diesem Kontext finden wir eine einfache Abhängigkeit von der Verteilung der Kostenfunktionswerte. Weiterführend zeigen wir, dass die QAOA-Leistung generell von der Problemstatistik in Bezug auf eine durch den gewählten Treiber-Hamiltonian induzierte Metrik abhängt. Wir erhalten eine Methode zur Bewertung der QAOA-Leistung bei schwersten Problemen (solche zufälliger Kosten) für unterschiedliche Treiberauswahlen. Zweitens untersuchen wir eine QAOA-Variante, bei der sich die Hardware- Kontrolle nur auf Ein-Qubit-Gatter anstatt individuell programmierbare Ein- und Zwei-Qubit-Gatter erstreckt. In diesem reduzierten Kontrollaufwandsschema—dem digital-analogen Schema—sinkt die Komplexität der Hardware, welche die QAOASchaltungen ausführt, auf Kosten von Fehlern, die in bestimmten Bereichen als ungefährlich nachgewiesen werden. Danach erkunden wir hypothetische Hardware- Konzepte, die für diesen Zweck genutzt werden könnten

Computational micromodel for epigenetic mechanisms

Definition and characterization of the role of Epigenetic mechanisms have gained immense momentum since the completion of the Human Genome Project. The human epigenetic layer, made up of DNA methylation and multiple histone protein modifications, (the key elements of epigenetic mechanisms), is known to act as a switchboard that regulates the occurrence of most cellular events. In multicellular organisms such as humans, all cells have identical genomic contents but vary in DNA Methylation (DM) profile with the result that different types of cells perform a spectrum of functions. DM within the genome is associated with tight control of gene expression, parental imprinting, X-chromosome inactivation, long-term silencing of repetitive elements and chromatin condensation. Recently, considerable evidence has been put forward to demonstrate that environmental stress implicitly alters normal interactions among key epigenetic elements inside the genome. Aberrations in the spread of DM especially hypo/hyper methylation supported by an abnormal landscape of histone modifications have been strongly associated with Cancer initiation and development. While new findings on the impact of these key elements are reported regularly, precise information on how DM is controlled and its relation to networks of histone modifications is lacking. This has motivated modelling of DNA methylation and histone modifications and their interdependence. We describe initial computational methods used to investigate these key elements of epigenetic change, and to assess related information contained in DNA sequence patterns. We then describe attempts to develop a phenomenological epigenetic "micromodel", based on Markov-Chain Monte Carlo principles. This theoretical micromodel ("EpiGMP") aims to explore the effect of histome modifications and gene expression for defined levels of DNA methylation. We apply this micromodel to (i) test networks of genes in colon cancer (extracted from an in-house database, StatEpigen), and (ii) to help define an agent-based modelling framework to explore chromatin remodelling (or the dynamics of physical rearrangements), inside the human genome. Parallelization techniques to address issues of scale during the application of this micromodel have been adopted as well. A generic tool of this kind can potentially be applied to predict molecular events that affect the state of expression of any gene during the onset or progress of cancer. Ultimately, the goal is to provide additional information on ways in which these low level molecular changes determine physical traits for mormal and disease conditions in an organism

Optimal aeroelastic trim for rotorcraft with constrained, non-unique trim solutions

New rotorcraft configurations are emerging, such as the optimal speed helicopter and slowed-rotor compound helicopter which, due to variable rotor speed and redundant lifting components, have non-unique trim solution spaces. The combination of controls and rotor speed that produce the best steady-flight condition is sought among all the possible solutions. This work develops the concept of optimal rotorcraft trim and explores its application to advanced rotorcraft configurations with non-unique, constrained trim solutions. The optimal trim work is based on the nonlinear programming method of the generalized reduced gradient (GRG) and is integrated into a multi-body, comprehensive aeroelastic rotorcraft code. In addition to the concept of optimal trim, two further developments are presented that allow the extension of optimal trim to rotorcraft with rotors that operate over a wide range of rotor speeds. The first is the concept of variable rotor speed trim with special application to rotors operating in steady autorotation. The technique developed herein treats rotor speed as a trim variable and uses a Newton-Raphson iterative method to drive the rotor speed to zero average torque simultaneously with other dependent trim variables. The second additional contribution of this thesis is a novel way to rapidly approximate elastic rotor blade stresses and strains in the aeroelastic trim analysis for structural constraints. For rotors that operate over large angular velocity ranges, rotor resonance and increased flapping conditions are encountered that can drive the maximum cross-sectional stress and strain to levels beyond endurance limits; such conditions must be avoided. The method developed herein captures the maximum cross-sectional stress/strain based on the trained response of an artificial neural network (ANN) surrogate as a function of 1-D beam forces and moments. The stresses/strains are computed simultaneously with the optimal trim and are used as constraints in the optimal trim solution. Finally, an optimal trim analysis is applied to a high-speed compound gyroplane configuration, which has two distinct rotor speed control methods, with the purpose of maximizing the vehicle cruise efficiency while maintaining rotor blade strain below endurance limit values.Ph.D.Committee Chair: Dimitri N. Mavris; Committee Co-Chair: Daniel P Schrage; Committee Member: David A. Peters; Committee Member: Dewey H. Hodges; Committee Member: J.V.R. Prasa

Space programs summary no. 37-49, volume 3 for the period December 1, 1967 to January 30, 1968. Supporting research and advanced development

Space program research projects on systems analysis and engineering, telecommunications, guidance and control, propulsion, and data system

Signal processing with Fourier analysis, novel algorithms and applications

Fourier analysis is the study of the way general functions may be represented or approximated by sums of simpler trigonometric functions, also analogously known as sinusoidal modeling. The original idea of Fourier had a profound impact on mathematical analysis, physics and engineering because it diagonalizes time-invariant convolution operators. In the past signal processing was a topic that stayed almost exclusively in electrical engineering, where only the experts could cancel noise, compress and reconstruct signals. Nowadays it is almost ubiquitous, as everyone now deals with modern digital signals. Medical imaging, wireless communications and power systems of the future will experience more data processing conditions and wider range of applications requirements than the systems of today. Such systems will require more powerful, efficient and flexible signal processing algorithms that are well designed to handle such needs. No matter how advanced our hardware technology becomes we will still need intelligent and efficient algorithms to address the growing demands in signal processing. In this thesis, we investigate novel techniques to solve a suite of four fundamental problems in signal processing that have a wide range of applications. The relevant equations, literature of signal processing applications, analysis and final numerical algorithms/methods to solve them using Fourier analysis are discussed for different applications in the electrical engineering/computer science. The first four chapters cover the following topics of central importance in the field of signal processing: • Fast Phasor Estimation using Adaptive Signal Processing (Chapter 2) • Frequency Estimation from Nonuniform Samples (Chapter 3) • 2D Polar and 3D Spherical Polar Nonuniform Discrete Fourier Transform (Chapter 4) • Robust 3D registration using Spherical Polar Discrete Fourier Transform and Spherical Harmonics (Chapter 5) Even though each of these four methods discussed may seem completely disparate, the underlying motivation for more efficient processing by exploiting the Fourier domain signal structure remains the same. The main contribution of this thesis is the innovation in the analysis, synthesis, discretization of certain well known problems like phasor estimation, frequency estimation, computations of a particular non-uniform Fourier transform and signal registration on the transformed domain. We conduct propositions and evaluations of certain applications relevant algorithms such as, frequency estimation algorithm using non-uniform sampling, polar and spherical polar Fourier transform. The techniques proposed are also useful in the field of computer vision and medical imaging. From a practical perspective, the proposed algorithms are shown to improve the existing solutions in the respective fields where they are applied/evaluated. The formulation and final proposition is shown to have a variety of benefits. Future work with potentials in medical imaging, directional wavelets, volume rendering, video/3D object classifications, high dimensional registration are also discussed in the final chapter. Finally, in the spirit of reproducible research we release the implementation of these algorithms to the public using Github