Céline Aubel

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While spike trains are obviously not band-limited, the theory of super-resolution tells us that perfect recovery of unknown spike locations and weights from low-pass Fourier transform measurements is possible provided that the minimum spacing, &#x0394;, between spikes is not too small. Specifically, for a cutoff frequency of f<sub>c</sub>, the work of(More)
In this paper, we present a novel algorithm to learn phase-invariant dictionaries, which can be used to efficiently approximate a variety of signals, such as audio signals or images. Our approach relies on finding a small number of generating atoms that can be used-along with their phase-shifts-to sparsely approximate a given signal. Our method is inspired(More)
We formulate a unified framework for the separation of signals that are sparse in &#x201C;morphologically&#x201D; different redundant dictionaries. This formulation incorporates the so-called &#x201C;analysis&#x201D; and &#x201C;synthesis&#x201D; approaches as special cases and contains novel hybrid setups. We find corresponding coherence-based recovery(More)
Performance analyses of subspace algorithms for cisoid parameter estimation available in the literature are predominantly of statistical nature with a focus on asymptotic-either in the sample size or the SNR-statements. This paper presents a deterministic, finite sample size, and finite-SNR performance analysis of the ESPRIT algorithm and the matrix pencil(More)
We derive bounds on the extremal singular values and the condition number of N × K, with N > K, Vandermonde matrices with nodes in the unit disk. Such matrices arise in many fields of applied mathematics and engineering, e.g., in interpolation and approximation theory, sampling theory, compressed sensing, differential equations, control theory, and line(More)
This paper addresses the problem of identifying a linear time-varying (LTV) system characterized by a (possibly infinite) discrete set of delays and Doppler shifts. We prove that stable identifiability is possible if the upper uniform Beurling density of the delay-Doppler support set is strictly smaller than 1/2 and stable identifiability is impossible for(More)
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