Super-Resolution of Positive Sources: the Discrete Setup

In single-molecule microscopy it is necessary to locate with high precision point sources from noisy observations of the spectrum of the signal at frequencies capped by $f_c$, which is just about the frequency of natural light. This paper rigorously establishes that this super-resolution problem can be solved via linear programming in a stable manner. We prove that the quality of the reconstruction crucially depends on the Rayleigh regularity of the support of the signal; that is, on the maximum number of sources that can occur within a square of side length about $1/f_c$. The theoretical performance guarantee is complemented with a converse result showing that our simple convex program convex is nearly optimal. Finally, numerical experiments illustrate our methods.Comment: 31 page, 7 figure

Advanced interferometric techniques for high resolution bathymetry

International audienceCurrent high-resolution side scan and multibeam sonars produce very large data sets. However, conventional interferometry-based bathymetry algorithms underestimate the potential information of such soundings, generally because they use small baselines to avoid phase ambiguity. Moreover, these algorithms limit the triangulation capabilities of multibeam echosounders to the detection of one sample per beam, i.e., the zero-phase instant. In this paper we argue that the correlation between signals plays a very important role in the exploration of a remotely observed scene. In the case of multibeam sonars, capabilities can be improved by using the interferometric signal as a continuous quantity. This allows consideration of many more useful soundings per beam and enriches understanding of the environment. To this end, continuous interferometry detection is compared here, from a statistical perspective, first with conventional interferometry-based algorithms and then with high-resolution methods, such as the Multiple Signal Classification (MUSIC) algorithm. We demonstrate that a well-designed interferometry algorithm based on a coherence error model and an optimal array configuration permits a reduction in the number of beam formings (and therefore the computational cost) and an improvement in target detection (such as ship mooring cables or masts). A possible interferometry processing algorithm based on the complex correlation between received signals is tested on both sidescan sonars and multibeam echosounders and shows promising results for detection of small in-water targets

A comparative study of signal processing methods for structural health monitoring

In this paper four non-parametric and five parametric signal processing techniques are reviewed and their performances are compared through application to a sample exponentially damped synthetic signal with closely-spaced frequencies representing the ambient response of structures. The non-parametric methods are Fourier transform, periodogram estimate of power spectral density, wavelet transform, and empirical mode decomposition with Hilbert spectral analysis (Hilbert-Huang transform). The parametric methods are pseudospectrum estimate using the multiple signal categorization (MUSIC), empirical wavelet transform, approximate Prony method, matrix pencil method, and the estimation of signal parameters by rotational invariance technique (ESPRIT) method. The performances of different methods are studied statistically using the Monte Carlo simulation and the results are presented in terms of average errors of multiple sample analyses