International audienceThe estimation of directions of arrival is formulated as the decomposition of a 3-way array into a sum of rank-one terms, which is possible when the receive array enjoys some geometrical structure. The main advantage is that this decomposition is essentially unique under mild assumptions, if computed exactly. The drawback is that a low-rank approximation does not always exist. Therefore, a constraint is first introduced that ensures the existence of the latter best approximate. Then Cramér-Rao bounds are derived for localization parameters and source signals, assuming the others are nuisance parameters; some inaccuracies found in the literature are pointed out. Performances are eventually compared with reference algorithms such as ESPRIT, in the presence of additive Gaussian noise, with possibly non circular distribution

International audienceIn this paper, we present and analyze the performance of multidimensional ESPRIT (N-D ESPRIT) method for estimating parameters of N-D superimposed damped and/or undamped exponentials. N-D ESPRIT algorithm is based on low-rank decomposition of multilevel Hankel matrices formed by the N-D data. In order to reduce the computational complexity for large signals, we propose a fast N-D ESPRIT using truncated singular value decomposition (SVD). Then, through a first-order perturbation analysis, we derive simple expressions of the variance of the estimates in N-D multiple-tones case. These expressions do not involve the factors of the SVD. We also derive closed-form expressions of the variances of the complex modes, frequencies, and damping factors estimates in the N-D single-tone case. Computer results are presented to show effectiveness of the fast version of N-D ESPRIT and verify theoretical expressions

We address the problem of multidimensional modal estimation using sparse estimation techniques coupled with an efficient multigrid approach. Modal dictionaries are obtained by discretizing modal functions (damped complex exponentials). To get a good resolution, it is necessary to choose a fine discretization grid resulting in intractable computational problems due to the huge size of the dictionaries. The idea behind the multigrid approach amounts to refine the dictionary over several levels of resolution. The algorithm starts from a coarse grid and adaptively improves the resolution in dependence of the active set provided by sparse approximation methods. The proposed method is quite general in the sense that it allows one to process in the same way mono-and multidimensional signals. We show through simulations that, as compared to high-resolution modal estimation methods, the proposed sparse modal method can greatly enhance the estimation accuracy for noisy signals and shows good robustness with respect to the choice of the number of components.

Structured illumination microscopy is a recent imaging technique that aims at going beyond the classical optical resolution limits by reconstructing a high-resolution image from several low-resolution images acquired through modulation of the transfer function of the microscope. A precise knowledge of the sinusoidal modulation parameters is necessary to enable the super-resolution effect expected after reconstruction. In this work, we investigate the retrieval of these parameters directly from the acquired data, using a novel 2-D spectral estimation method.

The problem of direction of arrival (DoA) estimation of seismic plane waves impinging on an array of sensors is considered from a new deterministic perspective using tensor decomposition techniques. In addition to temporal and spatial sampling, further information is taken into account, based on the different propagation speed of body waves (P and S) through solid media. Performances are evaluated through simulated data in terms of the Cramér-Rao bounds and compared to other reference methods such as ESPRIT and MUSIC, in the presence of additive Gaussian circular noise. The proposed approach is then applied to real seismic data recorded at the Argentière glacier, occurring at the interface between the ice mass and the underlying bedrock. MUSIC and ESPRIT rely on the estimation of the covariance matrix of received data, thus requiring a large number of time samples. Moreover, information about propagation speed diversity is not taken into account by existing models in array processing. The discovered advantage in terms of the average error in estimating the direction of arrival of body waves is noteworthy, especially for a low number of sensors, and in separating closely located sources. Additionally, an improvement of precision in processing real seismic data is observed.

Index Terms-Multidimensional modal retrieval, frequency estimation, simultaneous sparse approximation, multigrid dictionary refinement, Cramér-Rao lower bound, harmonic retrieval

In this paper we analyse the performance of 2-D ESPRIT method for estimating parameters of 2-D superimposed damped exponentials. 2-D ESPRIT algorithm is based on lowrank decomposition of a Hankel-block-Hankel matrix that is formed by the 2-D data. Through a first-order perturbation analysis, we derive closed-form expressions for the variances of the complex modes, frequencies and damping factors estimates in the 2-D single-tone case. This analysis allows to define the optimal parameters used in the construction of the Hankel-block-Hankel matrix. A fast algorithm for calculating the SVD of Hankelblock-Hankel matrices is also used to enhance the computational complexity of the 2-D ESPRIT algorithm.

We propose a sparse modal estimation approach for analyzing 2-D NMR signals. It consists in decomposing the 2-D problem into two 1-D modal estimations. Each 1-D problem is formulated in terms of simultaneous sparse approximation which is efficiently solved using the Simultaneous Orthogonal Matching Pursuit method associated with a multi-grid dictionary refinement. Then, we propose a new criterion for mode pairing which comes down to solve a sparse approximation problem involving a low dimensional dictionary. The effectiveness of the method is demonstrated on real NMR data.