Sparse Semi-Parametric Estimation of Harmonic Chirp Signals

In this work, we present a method for estimating the parameters detailing an unknown number of linear, possibly harmonically related, chirp signals, using an iterative sparse reconstruction framework. The proposed method is initiated by a re-weighted group-sparsity approach, followed by an iterative relaxation-based refining step, to allow for high resolution estimates. Numerical simulations illustrate the achievable performance, offering a notable improvement as compared to other recent approaches. The resulting estimates are found to be statistically efficient, achieving the corresponding Cram´er-Rao lower bound

Sparse Semi-Parametric Chirp Estimator

In this work, we present a method for estimating the parameters detailing an unknown number of linear chirp signals, using an iterative sparse reconstruction framework. The proposed method is initiated by a re-weighted Lasso approach, and then use an iterative relaxation-based refining step to allow for high resolution estimates. The resulting estimates are found to be statistically efficient, achieving the Cramér-Rao lower bound. Numerical simulations illustrate the achievable performance, offering a notable improvement as compared to other recent approaches

An optimally concentrated Gabor transform for localized time-frequency components

Gabor analysis is one of the most common instances of time-frequency signal analysis. Choosing a suitable window for the Gabor transform of a signal is often a challenge for practical applications, in particular in audio signal processing. Many time-frequency (TF) patterns of different shapes may be present in a signal and they can not all be sparsely represented in the same spectrogram. We propose several algorithms, which provide optimal windows for a user-selected TF pattern with respect to different concentration criteria. We base our optimization algorithm on $l^p$-norms as measure of TF spreading. For a given number of sampling points in the TF plane we also propose optimal lattices to be used with the obtained windows. We illustrate the potentiality of the method on selected numerical examples

Generalized Sparse Covariance-based Estimation

In this work, we extend the sparse iterative covariance-based estimator (SPICE), by generalizing the formulation to allow for different norm constraints on the signal and noise parameters in the covariance model. For a given norm, the resulting extended SPICE method enjoys the same benefits as the regular SPICE method, including being hyper-parameter free, although the choice of norms are shown to govern the sparsity in the resulting solution. Furthermore, we show that solving the extended SPICE method is equivalent to solving a penalized regression problem, which provides an alternative interpretation of the proposed method and a deeper insight on the differences in sparsity between the extended and the original SPICE formulation. We examine the performance of the method for different choices of norms, and compare the results to the original SPICE method, showing the benefits of using the extended formulation. We also provide two ways of solving the extended SPICE method; one grid-based method, for which an efficient implementation is given, and a gridless method for the sinusoidal case, which results in a semi-definite programming problem

Probabilistic Estimation of Chirp Instantaneous Frequency Using Gaussian Processes

We present a probabilistic approach for estimating chirp signal and its instantaneous frequency function when the true forms of the chirp and instantaneous frequency are unknown. To do so, we represent them by joint cascading Gaussian processes governed by a non-linear stochastic differential equation, and estimate their posterior distribution by using stochastic filters and smoothers. The model parameters are determined via maximum likelihood estimation. Theoretical results show that the estimation method has a bounded mean squared error. Experiments show that the method outperforms a number of baseline methods on a synthetic model, and we also apply the method to analyse a gravitational wave data.Comment: Submitted to IEEE Transactions on Signal Processin

Image formation in synthetic aperture radio telescopes

Next generation radio telescopes will be much larger, more sensitive, have much larger observation bandwidth and will be capable of pointing multiple beams simultaneously. Obtaining the sensitivity, resolution and dynamic range supported by the receivers requires the development of new signal processing techniques for array and atmospheric calibration as well as new imaging techniques that are both more accurate and computationally efficient since data volumes will be much larger. This paper provides a tutorial overview of existing image formation techniques and outlines some of the future directions needed for information extraction from future radio telescopes. We describe the imaging process from measurement equation until deconvolution, both as a Fourier inversion problem and as an array processing estimation problem. The latter formulation enables the development of more advanced techniques based on state of the art array processing. We demonstrate the techniques on simulated and measured radio telescope data.Comment: 12 page

Comparing Semi-Parametric Model Learning Algorithms for Dynamic Model Estimation in Robotics

Physical modeling of robotic system behavior is the foundation for controlling many robotic mechanisms to a satisfactory degree. Mechanisms are also typically designed in a way that good model accuracy can be achieved with relatively simple models and model identification strategies. If the modeling accuracy using physically based models is not enough or too complex, model-free methods based on machine learning techniques can help. Of particular interest to us was therefore the question to what degree semi-parametric modeling techniques, meaning combinations of physical models with machine learning, increase the modeling accuracy of inverse dynamics models which are typically used in robot control. To this end, we evaluated semi-parametric Gaussian process regression and a novel model-based neural network architecture, and compared their modeling accuracy to a series of naive semi-parametric, parametric-only and non-parametric-only regression methods. The comparison has been carried out on three test scenarios, one involving a real test-bed and two involving simulated scenarios, with the most complex scenario targeting the modeling a simulated robot's inverse dynamics model. We found that in all but one case, semi-parametric Gaussian process regression yields the most accurate models, also with little tuning required for the training procedure

A Compressed Sampling and Dictionary Learning Framework for WDM-Based Distributed Fiber Sensing

We propose a compressed sampling and dictionary learning framework for fiber-optic sensing using wavelength-tunable lasers. A redundant dictionary is generated from a model for the reflected sensor signal. Imperfect prior knowledge is considered in terms of uncertain local and global parameters. To estimate a sparse representation and the dictionary parameters, we present an alternating minimization algorithm that is equipped with a pre-processing routine to handle dictionary coherence. The support of the obtained sparse signal indicates the reflection delays, which can be used to measure impairments along the sensing fiber. The performance is evaluated by simulations and experimental data for a fiber sensor system with common core architecture.Comment: Accepted for publication in Journal of the Optical Society of America A [ \copyright\ 2017 Optical Society of America.]. One print or electronic copy may be made for personal use only. Systematic reproduction and distribution, duplication of any material in this paper for a fee or for commercial purposes, or modifications of the content of this paper are prohibite

Sparse multivariate Gaussian mixture regression

Fitting a multivariate Gaussian mixture to data represents an attractive, as well as challenging problem, in especial when sparsity in the solution is demanded. Achieving this objective requires the concurrent update of all parameters (weight, centers, and precisions) of all multivariate Gaussian functions during the learning process. Such is the focus of this paper, which presents a novel method founded on the minimization of the error of the generalized logarithmic utility function (GLUF). This choice, which allows us to move smoothly from the mean square error (MSE) criterion to the one based on the logarithmic error, yields an optimization problem that resembles a locally convex problem and can be solved with a quasi-Newton method. The GLUF framework also facilitates the comparative study between both extremes, concluding that the classical MSE optimization is not the most adequate for the task. The performance of the proposed novel technique is demonstrated on simulated as well as realistic scenarios