| 1. |
- Babu, Prabhu, et al.
(författare)
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Multiple-hypothesis testing rules for high-dimensional model selection and sparse-parameter estimation
- 2023
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Ingår i: Signal Processing. - : Elsevier BV. - 0165-1684 .- 1872-7557. ; 213
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Tidskriftsartikel (refereegranskat)abstract
- We consider the problem of model selection for high-dimensional sparse linear regression models. We pose the model selection problem as a multiple-hypothesis testing problem and employ the methods of false discovery rate (FDR) and familywise error rate (FER) to solve it. We also present the reformulation of the FDR/FER-based approaches as criterion-based model selection rules and establish their relation to the extended Bayesian Information Criterion (EBIC), which is a state-of-the-art high-dimensional model selection rule. We use numerical simulations to show that the proposed FDR/FER method is well suited for high-dimensional model selection and performs better than EBIC.
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| 2. |
- Bastianello, Nicola, et al.
(författare)
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Extrapolation-Based Prediction-Correction Methods for Time-varying Convex Optimization
- 2023
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Ingår i: Signal Processing. - : Elsevier BV. - 0165-1684 .- 1872-7557. ; 210
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Tidskriftsartikel (refereegranskat)abstract
- In this paper, we focus on the solution of online optimization problems that arise often in signal processing and machine learning, in which we have access to streaming sources of data. We discuss algorithms for online optimization based on the prediction-correction paradigm, both in the primal and dual space. In particular, we leverage the typical regularized least-squares structure appearing in many signal processing problems to propose a novel and tailored prediction strategy, which we call extrapolation-based. By using tools from operator theory, we then analyze the convergence of the proposed methods as applied both to primal and dual problems, deriving an explicit bound for the tracking error, that is, the distance from the time-varying optimal solution. We further discuss the empirical performance of the algorithm when applied to signal processing, machine learning, and robotics problems.
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| 3. |
- Bokaei, Mohammad, et al.
(författare)
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Harmonic retrieval using weighted lifted-structure low-rank matrix completion
- 2024
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Ingår i: Signal Processing. - : Elsevier BV. - 0165-1684 .- 1872-7557. ; 216
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Tidskriftsartikel (refereegranskat)abstract
- In this paper, we investigate the problem of recovering the frequency components of a mixture of K complex sinusoids from a random subset of N equally-spaced time-domain samples. Because of the random subset, the samples are effectively non-uniform. Besides, the frequency values of each of the K complex sinusoids are assumed to vary continuously within a given range. For this problem, we propose a two-step strategy: (i) we first lift the incomplete set of uniform samples (unavailable samples are treated as missing data) into a structured matrix with missing entries, which is potentially low-rank; then (ii) we complete the matrix using a weighted nuclear minimization problem. We call the method a weighted lifted-structured (WLi) low-rank matrix recovery. Our approach can be applied to a range of matrix structures such as Hankel and double-Hankel, among others, and provides improvement over the unweighted existing schemes such as EMaC and DEMaC. We provide theoretical guarantees for the proposed method, as well as numerical simulations in both noiseless and noisy settings. Both the theoretical and the numerical results confirm the superiority of the proposed approach.
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| 4. |
- Borpatra Gohain, Prakash, et al.
(författare)
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Scale-Invariant and consistent Bayesian information criterion for order selection in linear regression models
- 2022
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Ingår i: Signal Processing. - : Elsevier BV. - 0165-1684 .- 1872-7557. ; 196
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Tidskriftsartikel (refereegranskat)abstract
- The Bayesian information criterion (BIC) is one of the most well-known criterion used for model order estimation in linear regression models. However, in its popular form, BIC is inconsistent as the noise variance tends to zero given that the sample size is small and fixed. Several modifications of the original BIC have been proposed that takes into account the high-SNR consistency, but it has been recently observed that the performance of the high-SNR forms of BIC highly depends on the scaling of the data. This scaling problem is a byproduct of the data dependent penalty design, which generates irregular penalties when the data is scaled and often leads to greater underfitting or overfitting losses in some scenarios when the noise variance is too small or large. In this paper, we present a new form of the BIC for order selection in linear regression models where the parameter vector dimension is small compared to the sample size. The proposed criterion eliminates the scaling problem and at the same time is consistent for both large sample sizes and high-SNR scenarios.
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| 5. |
- Brynolfsson, Johan, et al.
(författare)
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A time-frequency-shift invariant parameter estimator for oscillating transient functions using the matched window reassignment
- 2021
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Ingår i: Signal Processing. - : Elsevier BV. - 0165-1684. ; 183
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Tidskriftsartikel (refereegranskat)abstract
- In this paper we present the matched window reassignment method, generalizing the results to complex valued signals in multiple dimensions. For an oscillating transient signal with an envelope shape described by an arbitrary twice differentiable function, the reassigned spectrogram, with a matched window, concentrates all energy into one single time-frequency point. An estimator for the parameters of the envelope, in multiple dimensions, is constructed using the above property where the concentration is measured using the Rényi entropy. Furthermore, we present a classification scheme, where an observation is classified based on the concentration when reassigning with a set of model functions. Finally, two examples of parameter estimation from real-world measurements are shown, a one-dimensional time series of a single dolphin click and a two-dimensional time-series of seismic data.
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| 6. |
- Cang, Siyuan, et al.
(författare)
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Toeplitz-based blind deconvolution of underwater acoustic channels using wideband integrated dictionaries
- 2021
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Ingår i: Signal Processing. - : Elsevier BV. - 0165-1684. ; 179
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Tidskriftsartikel (refereegranskat)abstract
- In this paper, we propose a blind channel deconvolution method based on a sparse reconstruction framework exploiting a wideband dictionary under the (relatively weak) assumption that the transmitted signal may be assumed to be well modelled as a sum of sinusoids. Using a Toeplitz structured formulation of the received signal, we form an iterative blind deconvolution scheme, alternatively estimating the underwater impulse response and the transmitted waveform. The resulting optimization problems are convex, and we formulate a computationally efficient solver using the Alternating Direction Method of Multipliers (ADMM). We illustrate the performance of the resulting estimator using both simulated and measured underwater signals.
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| 7. |
- Ding, Xinghao, et al.
(författare)
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High-resolution source localization exploiting the sparsity of the beamforming map
- 2022
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Ingår i: Signal Processing. - : Elsevier BV. - 0165-1684. ; 192
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Tidskriftsartikel (refereegranskat)abstract
- Beamforming technology plays a significant role in source localization and quantification. As traditional delay-and-sum beamformers generally yield low spatial resolution, as well as suffer from the occurrence of spurious sources, different forms of deconvolution methods have been proposed in the literature. In this work, we propose two approaches based on a sparse reconstruction framework combined with the use of the Fourier-based efficient implementation techniques. Numerical simulations and experimental data analysis show the effectiveness and advantages of the proposed methods.
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| 8. |
- Elvander, Filip, et al.
(författare)
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Multi-marginal optimal transport using partial information with applications in robust localization and sensor fusion
- 2020
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Ingår i: Signal Processing. - : Elsevier BV. - 0165-1684 .- 1872-7557. ; 171
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Tidskriftsartikel (refereegranskat)abstract
- 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, a common setup in many inverse problems in, e.g., remote sensing and imaging. 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.
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| 9. |
- Emzir, Muhammad Fuady, et al.
(författare)
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Multidimensional projection filters via automatic differentiation and sparse-grid integration
- 2023
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Ingår i: Signal Processing. - : Elsevier. - 0165-1684 .- 1872-7557. ; 204
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Tidskriftsartikel (refereegranskat)abstract
- The projection filter is a technique for approximating the solutions of optimal filtering problems. In projection filters, the Kushner–Stratonovich stochastic partial differential equation that governs the propagation of the optimal filtering density is projected to a manifold of parametric densities, resulting in a finite-dimensional stochastic differential equation. Despite the fact that projection filters are capable of representing complicated probability densities, their current implementations are limited to Gaussian family or unidimensional filtering applications. This work considers a combination of numerical integration and automatic differentiation to construct projection filter algorithms for more generic problems. Specifically, we provide a detailed exposition of this combination for the manifold of the exponential family, and show how to apply the projection filter to multidimensional cases. We demonstrate numerically that based on comparison to a finite-difference solution to the Kushner–Stratonovich equation and a bootstrap particle filter with systematic resampling, the proposed algorithm retains an accurate approximation of the filtering density while requiring a comparatively low number of quadrature points. Due to the sparse-grid integration and automatic differentiation used to calculate the expected values of the natural statistics and the Fisher metric, the proposed filtering algorithms are highly scalable. They therefore are suitable to many applications in which the number of dimensions exceeds the practical limit of particle filters, but where the Gaussian-approximations are deemed unsatisfactory.
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| 10. |
- Gogic, Ivan, et al.
(författare)
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Regression-based methods for face alignment: A survey
- 2021
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Ingår i: Signal Processing. - : ELSEVIER. - 0165-1684 .- 1872-7557. ; 178
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Forskningsöversikt (refereegranskat)abstract
- Face alignment is the process of determining a face shape given its location and size in an image. It is used as a basis for other facial analysis tasks and for human-machine interaction and augmented reality applications. It is a challenging problem due to the extremely high variability in facial appearance affected by many external (illumination, occlusion, head pose) and internal factors (race, facial expression). However, advances in deep learning combined with domain-related knowledge from previous research recently demonstrated impressive results nearly saturating the unconstrained benchmark data sets. The focus is shifting towards reducing the computational burden of the face alignment models since real-time performance is required for such a highly dynamic task. Furthermore, many applications target devices on the edge with limited computational power which puts even greater emphasis on computational efficiency. We present the latest development in regression-based approaches that have led towards nearly solving the face alignment problem in an unconstrained scenario. Various regression architectures are systematically explored and recent training techniques discussed in the context of face alignment. Finally, a benchmark comparison of the most successful methods is presented, taking into account execution time as well, to provide a comprehensive overview of this dynamic research field. (C) 2020 Elsevier B.V. All rights reserved.
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