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This paper focuses on a linear model with noisy inputs in which the performance of the conventional Total Least Squares (TLS) approach is (maybe surprisingly) far from satisfactory. Under the typical Gaussian assumption, we obtain the maximum likelihood (ML) estimator of the system response. This estimator promotes a reasonable balance between the empirical and theoretical variances of the residual...
In this paper, we propose to use cross recurrence plot analysis (CRPA) to estimate the time-difference of arrival (TDOA) of underwater acoustic signals arriving on an array of hydrophones. Instead of considering the signal as a whole to estimate the TDOA, like classical methods do, we first detected the series of samples that look alike on each pair of hydrophones of the array by using cross-recurrence...
We provide an overview of recent advances that have come about in the area of cognitive radar over the past decade. The area of cognitive radar involves closed loop radar operation to overcome the challenges imposed by harsh environments, difficult targets, and a rapidly shrinking spectrum. In particular this construct is devised to bring to bear all available resources on transmit and receive as...
We consider a two-way relay network consisting of two single-antenna transceivers and multiple multi-antenna relays. Assuming a multiple access broadcast (MABC) relaying scheme, we aim to jointly obtain the optimal relay beamforming matrices as well as the optimal transceiver transmit powers which minimize the total transmit power under given signal-to-noise-ratio (SNR) constraints at the transceivers...
Maximal monotone operators are set-valued mappings which extend (but are not limited to) the notion of subdifferential of a convex function. The proximal point algorithm is a method for finding a zero of a maximal monotone operator. The algorithm consists in fixed point iterations of a mapping called the resolvent which depends on the maximal monotone operator of interest. The paper investigates a...
This note considers the problem of blind identification of a linear, time-invariant (LTI) system when the input signals are unknown, but belong to sufficiently diverse, known subspaces. This problem can be recast as the recovery of a rank-1 matrix, and is effectively relaxed using a semidefinite program (SDP). We show that exact recovery of both the unknown impulse response, and the unknown inputs,...
This note studies the problem of nonsymmetric rank-one matrix completion. We show that in every instance where the problem has a unique solution, one can recover the original matrix through the second round of the sum-of-squares/Lasserre hierarchy with minimization of the trace of the moments matrix. Our proof system is based on iteratively building a sum of N − 1 linearly independent squares, where...
We study the design of minimum variance portfolio when asset returns follow a low rank factor model. Using results from random matrix theory, an optimal shrinkage approach for the isolated eigenvalues of the covariance matrix is developed. The proposed portfolio optimization strategy is shown to have good performance on synthetic data but not always on real data sets. This leads us to refine the data...
This paper presents a new approach to solving the rank constrained beamforming problem. Instead of relaxing the problem to a feasible set of the positive semidefinite matrices, we restrict the problem to a space of polynomials whose dimension is equal to the desired rank. The solution to the resulting optimization is then required to be full rank, allowing a simple matrix decomposition to recover...
Hierarchical alternating least squares (HALS) algorithms are efficient computational methods for nonnegative matrix factorization (NMF). Given an initial solution, HALS algorithms update the solution block by block iteratively so that the error decreases monotonically. However, update rules in HALS algorithms are not well-defined. In addition, due to this problem, the convergence of the sequence of...
Recently a selection of sequential matrix diagonalisation (SMD) algorithms have been introduced which approximate polynomial eigenvalue decomposition of parahermitian matrices. These variants differ only in the search methods that are used to bring energy onto the zero-lag. Here we analyse the search methods in terms of their computational complexities for different sizes of parahermitian matrices...
This article introduces an original approach to understand the behavior of standard kernel spectral clustering algorithms (such as the Ng-Jordan-Weiss method) for large dimensional datasets. Precisely, using advanced methods from the field of random matrix theory and assuming Gaussian data vectors, we show that the Laplacian of the kernel matrix can asymptotically be well approximated by an analytically...
We propose an algorithm for blind calibration of multi-channel samplers in the presence of unknown gains and offsets, which is useful in many applications such as multi-channel analog-to-digital converters, image super-resolution, and sensor networks. Using a subspace-based rank condition developed by Vandewalle et al., we obtain a set of linear equations with respect to complex harmonics whose frequencies...
Motivated by applications in recommendation systems and bioinformatics, we consider the problem of completing a low rank, partially observed binary matrix with graph information. We show that the corresponding problem can be set up in a positive and unlabeled data learning (referred to as PU learning in literature) framework. We make connections to convex optimization and show that existing greedy...
Recent work has shown that convex programming allows to recover a superposition of point sources exactly from low-resolution data as long as the sources are separated by 2/fc, where fc is the cut-off frequency of the sensing process. The proof relies on the construction of a certificate whose existence implies exact recovery. This certificate has since been used to establish that the approach is robust...
This paper provides a theoretical analysis of diffraction-limited superresolution, demonstrating that arbitrarily close point sources can be resolved in ideal situations. Precisely, we assume that the incoming signal is a linear combination of M shifted copies of a known waveform with unknown shifts and amplitudes, and one only observes a finite collection of evaluations of this signal. We characterize...
In this paper, we study discrete and continuous versions of the LASSO in order to solve the deconvolution problem. We shed light on the Non Degenerate Source Condition, a property which yields support robustness for both the continuous and discrete problems. More precisely, we show that this property yields exact support recovery in the continuous case and the estimation of twice the number of spikes...
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