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We present a formulation of the linear sampling method (LSM) for imaging conducting targets using a spatially sparse set of receive locations. The technique mitigates the lack of spatial channels by disciplining the LSM solution to achieve the correct electric field boundary conditions on an estimate of the target boundary. As the true target boundary is unknown, we use an iterative procedure to jointly optimize the LSM solution and the target boundary estimate by minimizing both the LSM residual as well as the deviation from the desired boundary conditions. We show that the proposed technique significantly improves imaging fidelity from sparse receivers using both simulated and experimental target data. [ABSTRACT FROM AUTHOR]

We present a formulation of the linear sampling method (LSM) for reconstructing target shape from spatially sparse data sets. The technique compensates for a lack of spatial data by incorporating $a$ priori propagation information into the LSM inversion. A constraint is placed on the LSM solution that enforces a phase relationship across frequency that is determined by the electrical path length between the array transmitters and the imaging scene pixels. The effect of the constraint is that image artifacts that do not evince the expected phase relationship according to their position relative to the array are suppressed. We apply the proposed technique to simulated and experimental sparse-aperture data sets and show that the resulting imagery is significantly more faithful to the true target shape as compared to the imagery created with the standard LSM. [ABSTRACT FROM AUTHOR]

We propose an approach to characterize the AC underwater radiation produced by a ship over a shallow water medium using dipole sources distributed over an interior surface to the ship. The proposed approach relies on the accurate and efficient representation of dipole sources over the shallow water medium that characterizes the behavior of the electric or magnetic field. The approach is reduced to the solution of the resultant matrix system from the dipole representation. These systems are ill-posed, i.e., if the matrix systems are not solved by special regularization methods, the resultant solution will amplify the measurement noise. The regularization method applied is the least squares QR iterations combined with a new stopping rule that uses a numerical estimate of the measurement noise. Numerically generated data is used to study the validity of the different dipole representations. Finally, we validate our methodology using magnetic measurements that result from degaussing coils of a mid-size vessel. [ABSTRACT FROM AUTHOR]

This paper investigates the use of a qualitative inverse scattering method known as the linear sampling method (LSM) for imaging underwater scenes using limited aperture receiver configurations. The LSM is based on solving a set of unstable integral equations known as the far-field equations and whose stability breaks down even further for under-sampled observation aperture data. Based on the results of a recent study concerning multi-frequency LSM imaging, we propose an iterative inversion method that is founded upon a compressive sensing framework. In particular, we leverage multi-frequency diversity in the data by imposing a partial frequency variation prior on the solution which we show is justified when the frequency bandwidth is sampled finely enough. We formulate an alternating direction method of multiplier approach to minimize the proposed cost function. Proof of concept is established through numerically generated data as well as experimental acoustic measurements taken in a shallow pool facility at the U.S Naval Research Laboratory. [ABSTRACT FROM AUTHOR]

This paper investigates the source reconstruction problem in underwater mediums using a compressive Near-Field Electromagnetic Holography (NEH) approach. More specifically we investigate the use of ℓ1 regularization for the purpose of decomposing near-field magnetic and/or electric surface measurements into electric and magnetic dipole sources. Our study indicates that not only do ℓ1 decompositions enable much higher resolution of sources than traditional ℓ2 approaches, but important features of the dipoles are preserved in the reconstruction. Our hypothesis are supported by numerical experiments as well as underwater physical measurements obtained in an earth field simulator facility. [ABSTRACT FROM AUTHOR]

In this work, we study the problem of characterizing electromagnetic radiation from given near-field electromagnetic measurements on an arbitrarily shaped surface. Due to the evanescent waves present in the near-field data the inversion procedure requires special treatment in order to recover a stable physical solution. Our proposed approach to this challenging inverse problem is to seek a sparse decomposition of the fields into elementary electric and/or magnetic dipole on an equivalent source surface. As we show in this paper the incorporation of a sparsity constraint during the inversion process yields impressive stability and accuracy. Additionally the method exhibits a remarkable ability to image and identify point like dipole sources even when spaced closer than a fraction of the wavelength from each other. The proposed inversion procedure is very simple to implement, is easily adaptable to arbitrary surfaces, and is relatively fast even with dense grids. These features make the proposed method suitable for a complete on-the-spot electromagnetic radiation analysis; a capability in which many applications rely on. Proof of concept for this work is established through simple numerical experiments, and from physical measurements taken for a slotted radiating cylinder. [ABSTRACT FROM PUBLISHER]

The linear sampling method (LSM) offers a qualitative image reconstruction approach, which is known as a viable alternative for obstacle support identification to the well-studied filtered backprojection (FBP), which depends on a linearized forward scattering model. Of practical interest is the imaging of obstacles from sparse aperture far-field data under a fixed single frequency mode of operation. Under this scenario, the Tikhonov regularization typically applied to LSM produces poor images that fail to capture the obstacle boundary. In this paper, we employ an alternative regularization strategy based on constraining the sparsity of the solution's spatial gradient. Two regularization approaches based on the spatial gradient are developed. A numerical comparison to the FBP demonstrates that the new method's ability to account for aspect-dependent scattering permits more accurate reconstruction of concave obstacles, whereas a comparison to Tikhonov-regularized LSM demonstrates that the proposed approach significantly improves obstacle recovery with sparse-aperture data. [ABSTRACT FROM AUTHOR]