Salvatore Caporale

Salvatore Caporale, Yvan Petillot

Synthetic aperture imaging systems achieve constant azimuth resolution by coherently summating the observations acquired along the aperture path. At this aim, their locations have to be known with subwavelength accuracy. In underwater Synthetic Aperture Sonar (SAS), the nature of propagation and navigation in water makes the retrieval of this information challenging. Inertial sensors have to be employed in combination with signal processing techniques, which are usually referred to as micronavigation. In this paper we propose a novel micronavigation approach based on the minimization of an error function between two contiguous pings having some mutual information. This error is obtained by comparing the vector space intersections between the pings orthogonal projectors. The effectiveness and generality of the proposed approach is demonstrated by means of simulations and by means of an experiment performed in a controlled environment.

Salvatore Caporale, Yvan Petillot

A warping operator consists of an invertible axis deformation applied either in the signal domain or in the corresponding Fourier domain. Additionally, a warping transformation is usually required to preserve the signal energy, thus preserving orthogonality and being invertible by its adjoint. Initially, the design of such operators has been motivated by the idea of suitably generalizing the properties of orthogonal time-frequency decompositions such as wavelets and filter banks, hence the energy preservation property was essential. Recently, warping operators have been employed for frequency dispersion compensation in the Fourier domain or the identification of waveforms similarity in the time domain. For such applications, the energy preservation requirement can be given up, thus making warping a special case of interpolation. In this context, the purpose of this work is to provide analytical models and efficient computational algorithms for time warping with respect to piecewise smooth warping maps by transposing and extending a theoretical framework which has been previously introduced for frequency warping. Moreover, the same approach is generalized to the case of warping without energy preservation, thus obtaining a fast interpolation operator with analytically defined and fast inverse operator.