arXiv subjects

Andreas Jakobsson

Publications and source records attributed to Andreas Jakobsson.

25 records · Page 2Linked to original sources

arXiv2019

Interpolation and Extrapolation of Toeplitz Matrices via Optimal Mass Transport

In this work, we propose a novel method for quantifying distances between Toeplitz structured covariance matrices. By exploiting the spectral representation of Toeplitz matrices, the proposed distance measure is defined based on an optimal mass transport problem in the spectral domain. This may then be interpreted in the covariance domain, suggesting a natural way of interpolating and extrapolating Toeplitz matrices, such that the positive semi-definiteness and the Toeplitz structure of these matrices are preserved. The proposed distance measure is also shown to be contractive with respect to both additive and multiplicative noise, and thereby allows for a quantification of the decreased distance between signals when these are corrupted by noise. Finally, we illustrate how this approach can be used for several applications in signal processing. In particular, we consider interpolation and extrapolation of Toeplitz matrices, as well as clustering problems and tracking of slowly varying stochastic processes.

eess.SP↗

arXiv2019

Multi-Marginal Optimal Mass Transport with Partial Information

During recent decades, there has been a substantial development in optimal mass transport theory and methods. In this work, we consider multi-marginal problems wherein only partial information of each marginal is available, which is a setup common in many inverse problems in, e.g., imaging and spectral estimation. By considering an entropy regularized approximation of the original transport problem, we propose an algorithm corresponding to a block-coordinate ascent of the dual problem, where Newton's algorithm is used to solve the sub-problems. In order to make this computationally tractable for large-scale settings, we utilize the tensor structure that arises in practical problems, allowing for computing projections of the multi-marginal transport plan using only matrix-vector operations of relatively small matrices. As illustrating examples, we apply the resulting method to tracking and barycenter problems in spatial spectral estimation. In particular, we show that the optimal mass transport framework allows for fusing information from different time steps, as well as from different sensor arrays, also when the sensor arrays are not jointly calibrated. Furthermore, we show that by incorporating knowledge of underlying dynamics in tracking scenarios, one may arrive at accurate spectral estimates, as well as faithful reconstructions of spectra corresponding to unobserved time points.

eess.SP↗

arXiv2018

Non-Coherent Sensor Fusion via Entropy Regularized Optimal Mass Transport

This work presents a method for information fusion in source localization applications. The method utilizes the concept of optimal mass transport in order to construct estimates of the spatial spectrum using a convex barycenter formulation. We introduce an entropy regularization term to the convex objective, which allows for low-complexity iterations of the solution algorithm and thus makes the proposed method applicable also to higher-dimensional problems. We illustrate the proposed method's inherent robustness to misalignment and miscalibration of the sensor arrays using numerical examples of localization in two dimensions.

eess.SP↗

arXiv2017

Estimating Sparse Signals Using Integrated Wideband Dictionaries

In this paper, we introduce a wideband dictionary framework for estimating sparse signals. By formulating integrated dictionary elements spanning bands of the considered parameter space, one may efficiently find and discard large parts of the parameter space not active in the signal. After each iteration, the zero-valued parts of the dictionary may be discarded to allow a refined dictionary to be formed around the active elements, resulting in a zoomed dictionary to be used in the following iterations. Implementing this scheme allows for more accurate estimates, at a much lower computational cost, as compared to directly forming a larger dictionary spanning the whole parameter space or performing a zooming procedure using standard dictionary elements. Different from traditional dictionaries, the wideband dictionary allows for the use of dictionaries with fewer elements than the number of available samples without loss of resolution. The technique may be used on both one- and multi-dimensional signals, and may be exploited to refine several traditional sparse estimators, here illustrated with the LASSO and the SPICE estimators. Numerical examples illustrate the improved performance.

stat.ME↗

arXiv2017

Designing Sampling Schemes for Multi-Dimensional Data

In this work, we propose a method for determining a non-uniform sampling scheme for multi-dimensional signals by solving a convex optimization problem reminiscent of the sensor selection problem. The resulting sampling scheme minimizes the sum of the Cramér-Rao lower bound for the parameters of interest, given a desired number of sampling points. The proposed framework allows for selecting an arbitrary subset of the parameters detailing the model, as well as weighing the importance of the different parameters. Also presented is a scheme for incorporating any imprecise a priori knowledge of the locations of the parameters, as well as defining estimation performance bounds for the parameters of interest. Numerical examples illustrate the efficiency of the proposed scheme.

stat.ME↗

arXiv2017

CFAR Adaptive Matched Detector for Target Detection in Non-Gaussian Noise With Inverse Gamma Texture

In this paper, we propose an adaptive matched detector of a signal corrupted by a non-Gaussian noise with an inverse gamma texture. The detector is formed using a set of secondary data measurements, and is analytically shown to have a constant false alarm rate. The analytic performance is validated using Monte Carlo simulations, and the proposed detector is shown to offer preferable performance as compared to the related one-step generalized likelihood ratio test (1S-GLRT) and the adaptive subspace detector (ASD).

stat.AP↗

arXiv2017

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.

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