70 research outputs found
Algebraic Signal Processing Theory: Cooley-Tukey Type Algorithms for DCTs and DSTs
This paper presents a systematic methodology based on the algebraic theory of
signal processing to classify and derive fast algorithms for linear transforms.
Instead of manipulating the entries of transform matrices, our approach derives
the algorithms by stepwise decomposition of the associated signal models, or
polynomial algebras. This decomposition is based on two generic methods or
algebraic principles that generalize the well-known Cooley-Tukey FFT and make
the algorithms' derivations concise and transparent. Application to the 16
discrete cosine and sine transforms yields a large class of fast algorithms,
many of which have not been found before.Comment: 31 pages, more information at http://www.ece.cmu.edu/~smar
Signal processing algorithms for enhanced image fusion performance and assessment
The dissertation presents several signal processing algorithms for image fusion in noisy multimodal
conditions. It introduces a novel image fusion method which performs well for image
sets heavily corrupted by noise. As opposed to current image fusion schemes, the method has
no requirements for a priori knowledge of the noise component. The image is decomposed with
Chebyshev polynomials (CP) being used as basis functions to perform fusion at feature level. The
properties of CP, namely fast convergence and smooth approximation, renders it ideal for heuristic
and indiscriminate denoising fusion tasks. Quantitative evaluation using objective fusion assessment
methods show favourable performance of the proposed scheme compared to previous efforts
on image fusion, notably in heavily corrupted images.
The approach is further improved by incorporating the advantages of CP with a state-of-the-art
fusion technique named independent component analysis (ICA), for joint-fusion processing
based on region saliency. Whilst CP fusion is robust under severe noise conditions, it is prone to
eliminating high frequency information of the images involved, thereby limiting image sharpness.
Fusion using ICA, on the other hand, performs well in transferring edges and other salient features
of the input images into the composite output. The combination of both methods, coupled with
several mathematical morphological operations in an algorithm fusion framework, is considered a
viable solution. Again, according to the quantitative metrics the results of our proposed approach
are very encouraging as far as joint fusion and denoising are concerned.
Another focus of this dissertation is on a novel metric for image fusion evaluation that is based
on texture. The conservation of background textural details is considered important in many fusion
applications as they help define the image depth and structure, which may prove crucial in
many surveillance and remote sensing applications. Our work aims to evaluate the performance of image fusion algorithms based on their ability to retain textural details from the fusion process.
This is done by utilising the gray-level co-occurrence matrix (GLCM) model to extract second-order
statistical features for the derivation of an image textural measure, which is then used to
replace the edge-based calculations in an objective-based fusion metric. Performance evaluation
on established fusion methods verifies that the proposed metric is viable, especially for multimodal
scenarios
Speech enhancement Algorithm based on super-Gaussian modeling and orthogonal polynomials
© 2020 Lippincott Williams and Wilkins. All rights reserved. Different types of noise from the surrounding always interfere with speech and produce annoying signals for the human auditory system. To exchange speech information in a noisy environment, speech quality and intelligibility must be maintained, which is a challenging task. In most speech enhancement algorithms, the speech signal is characterized by Gaussian or super-Gaussian models, and noise is characterized by a Gaussian prior. However, these assumptions do not always hold in real-life situations, thereby negatively affecting the estimation, and eventually, the performance of the enhancement algorithm. Accordingly, this paper focuses on deriving an optimum low-distortion estimator with models that fit well with speech and noise data signals. This estimator provides minimum levels of speech distortion and residual noise with additional improvements in speech perceptual aspects via four key steps. First, a recent transform based on an orthogonal polynomial is used to transform the observation signal into a transform domain. Second, the noise classification based on feature extraction is adopted to find accurate and mutable models for noise signals. Third, two stages of nonlinear and linear estimators based on the minimum mean square error (MMSE) and new models for speech and noise are derived to estimate a clean speech signal. Finally, the estimated speech signal in the time domain is determined by considering the inverse of the orthogonal transform. The results show that the average classification accuracy of the proposed approach is 99.43%. In addition, the proposed algorithm significantly outperforms existing speech estimators in terms of quality and intelligibility measures
Exponential families on resource-constrained systems
This work is about the estimation of exponential family models on resource-constrained
systems. Our main goal is learning probabilistic models on devices with highly restricted
storage, arithmetic, and computational capabilities—so called, ultra-low-power
devices. Enhancing the learning capabilities of such devices opens up opportunities for
intelligent ubiquitous systems in all areas of life, from medicine, over robotics, to home
automation—to mention just a few. We investigate the inherent resource consumption of
exponential families, review existing techniques, and devise new methods to reduce the
resource consumption. The resource consumption, however, must not be reduced at all
cost. Exponential families possess several desirable properties that must be preserved:
Any probabilistic model encodes a conditional independence structure—our methods
keep this structure intact. Exponential family models are theoretically well-founded.
Instead of merely finding new algorithms based on intuition, our models are formalized
within the framework of exponential families and derived from first principles. We do
not introduce new assumptions which are incompatible with the formal derivation of the
base model, and our methods do not rely on properties of particular high-level applications.
To reduce the memory consumption, we combine and adapt reparametrization
and regularization in an innovative way that facilitates the sparse parametrization of
high-dimensional non-stationary time-series. The procedure allows us to load models in
memory constrained systems, which would otherwise not fit. We provide new theoretical
insights and prove that the uniform distance between the data generating process
and our reparametrized solution is bounded. To reduce the arithmetic complexity of
the learning problem, we derive the integer exponential family, based on the very definition
of sufficient statistics and maximum entropy estimation. New integer-valued
inference and learning algorithms are proposed, based on variational inference, proximal
optimization, and regularization. The benefit of this technique is larger, the weaker
the underlying system is, e.g., the probabilistic inference on a state-of-the-art ultra-lowpower
microcontroller can be accelerated by a factor of 250. While our integer inference
is fast, the underlying message passing relies on the variational principle, which is inexact
and has unbounded error on general graphs. Since exact inference and other existing
methods with bounded error exhibit exponential computational complexity, we employ
near minimax optimal polynomial approximations to yield new stochastic algorithms
for approximating the partition function and the marginal probabilities. Changing the
polynomial degree allows us to control the complexity and the error of our new stochastic
method. We provide an error bound that is parametrized by the number of samples, the
polynomial degree, and the norm of the model’s parameter vector. Moreover, important
intermediate quantities can be precomputed and shared with the weak computational device
to reduce the resource requirement of our method even further. All new techniques
are empirically evaluated on synthetic and real-world data, and the results confirm the
properties which are predicted by our theoretical derivation. Our novel techniques allow
a broader range of models to be learned on resource-constrained systems and imply
several new research possibilities
Speech Enhancement Algorithm Based on Super-Gaussian Modeling and Orthogonal Polynomials
Different types of noise from the surrounding always interfere with speech and produce annoying signals for the human auditory system. To exchange speech information in a noisy environment, speech quality and intelligibility must be maintained, which is a challenging task. In most speech enhancement algorithms, the speech signal is characterized by Gaussian or super-Gaussian models, and noise is characterized by a Gaussian prior. However, these assumptions do not always hold in real-life situations, thereby negatively affecting the estimation, and eventually, the performance of the enhancement algorithm. Accordingly, this paper focuses on deriving an optimum low-distortion estimator with models that fit well with speech and noise data signals. This estimator provides minimum levels of speech distortion and residual noise with additional improvements in speech perceptual aspects via four key steps. First, a recent transform based on an orthogonal polynomial is used to transform the observation signal into a transform domain. Second, noise classification based on feature extraction is adopted to find accurate and mutable models for noise signals. Third, two stages of nonlinear and linear estimators based on the minimum mean square error (MMSE) and new models for speech and noise are derived to estimate a clean speech signal. Finally, the estimated speech signal in the time domain is determined by considering the inverse of the orthogonal transform. The results show that the average classification accuracy of the proposed approach is 99.43%. In addition, the proposed algorithm significantly outperforms existing speech estimators in terms of quality and intelligibility measures
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Analytical and numerical techniques for wave scattering
In this thesis, we study the mathematical solution of wave scattering problems which describe the behaviour of waves incident on obstacles and are highly relevant to a raft of applications in the aerospace industry. The techniques considered in the present work can be broadly classed into two categories: analytically based methods which use special transforms and functions to provide a near-complete mathematical description of the scattering process, and numerical techniques which select an approximate solution from a general finite-dimensional space of possible candidates.
The first part of this thesis addresses an analytical approach to the scattering of acoustic and vortical waves on an infinite periodic arrangement of finite-length flat blades in parallel mean flow. This geometry serves as an unwrapped model of the fan components in turbo-machinery. Our contributions include a novel semi-analytical solution based on the Wiener–Hopf technique that extends previous work by lifting the restriction that adjacent blades overlap, and a comprehensive study of the composition of the outgoing energy flux for acoustic wave scattering on this array of blades. These results provide an insight into the importance of energy conversion between the unsteady vorticity shed from the trailing edges of the cascade blades and the acoustic field. Furthermore, we show that the balance of incoming and outgoing energy fluxes of the unsteady field provides a convenient tool for understanding several interesting scattering symmetries on this geometry.
In the second part of the thesis, we focus on numerical techniques based on the boundary integral method which allows us to write the governing equations for zero mean flow in the form of Fredholm integral equations. We study the solution of these integral equations using collocation methods for two-dimensional scatterers with smooth and Lipschitz boundaries. Our contributions are as follows: Firstly, we explore the extent to which least-squares oversampling can improve collocation. We provide rigorous analysis that proves guaranteed convergence for small amounts of oversampling and shows that superlinear oversampling can ensure faster asymptotic convergence rates of the method. Secondly, we examine the computation of the entries in the discrete linear system representing the continuous integral equation in collocation methods for hybrid numerical-asymptotic basis spaces on simple geometric shapes in the context of high-frequency wave scattering. This requires the computation of singular highly-oscillatory integrals and we develop efficient numerical methods that can compute these integrals at frequency-independent cost. Finally, we provide a general result that allows the construction of recurrences for the efficient computation of quadrature moments in a broad class of Filon quadrature methods, and we show how this framework can also be used to accelerate certain Levin quadrature methods.Supported by EPSRC grant EP/L016516/
Visual Servoing
The goal of this book is to introduce the visional application by excellent researchers in the world currently and offer the knowledge that can also be applied to another field widely. This book collects the main studies about machine vision currently in the world, and has a powerful persuasion in the applications employed in the machine vision. The contents, which demonstrate that the machine vision theory, are realized in different field. For the beginner, it is easy to understand the development in the vision servoing. For engineer, professor and researcher, they can study and learn the chapters, and then employ another application method
Structures and Algorithms for Two-Dimensional Adaptive Signal Processing
Coordinated Science Laboratory was formerly known as Control Systems LaboratoryOpe
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