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We study the problem of actively imaging a range-limited far-field scene using an antenna array. We describe how the range limit imposes structure in the measurements across multiple wavelengths. This structure allows us to introduce a novel trade-off: the number of spatial array measurements (i.e., beams that have to be formed) can be reduced to be significantly lower than the number array elements if the scene is illuminated with a broadband source. To take advantage of this trade-off, we use a small number of "generic" linear combinations of the array outputs, instead of the phase offsets used in conventional beamforming. We provide theoretical justification for the proposed trade-off without making any strong structural assumptions on the target scene (such as sparsity) except that it is range-limited. In proving our theoretical results, we take inspiration from the sketching literature. We also provide simulation results to establish the merit of the proposed signal acquisition strategy. Our proposed method results in a reduction in the number of required spatial measurements in an array imaging system and hence can directly impact their speed and cost of operation. [ABSTRACT FROM AUTHOR]

We consider the problem of imaging extended reflectors in terminating waveguides. We form the image by back-propagating the array response matrix projected on the waveguide's nonevanescent modes. The projection is adequately defined for any array aperture size covering fully or partially the waveguide's vertical cross-section. We perform a resolution analysis of the imaging method and show that the resolution is determined by the central frequency, while the image's signal-to-noise ratio improves as the bandwidth increases. The robustness of the imaging method is assessed with fully nonlinear scattering data in terminating waveguides with complex geometries. [ABSTRACT FROM AUTHOR]

We propose an illumination strategy for interferometric imaging that allows for robust depth recovery from intensity-only measurements. For an array with colocated sources and receivers, we show that all the possible interferometric data for multiple sources, receivers, and frequencies can be recovered from intensity-only measurements provided that we have sufficient source location and frequency illumination diversity. There is no need for phase reconstruction in this approach. Using interferometric imaging methods we show that in homogeneous media there is no loss of resolution when imaging with intensities only. If in these imaging methods we reduce incoherence by restricting the multifrequency interferometric data to nearby array elements and nearby frequencies we obtain robust images in weakly inhomogeneous background media with a somewhat reduced resolution. [ABSTRACT FROM AUTHOR]

In this paper we consider narrow band, active array imaging of weak localized scatterers when only the intensities are recorded at an array with N transducers. We assume that the medium is homogeneous and, hence, wave propagation is fully coherent. This work is an extension of our previous paper [A. Novikov, M. Moscoso, and G. Papanicolaou, SIAM J. Imaging Sci., 8 (2015), pp. 1547{1573], where we showed that using linear combinations of intensity-only measurements, obtained from N² illuminations, imaging of localized scatterers can be carried out efficiently using imaging methods based on the singular value decomposition of the time-reversal matrix. Here we show that the same strategy can be accomplished with only 3N - 2 illuminations, therefore enormously reducing the data acquisition process. Furthermore, we show that in the paraxial regime one can form the images by using six illuminations only. In particular, this paraxial regime includes Fresnel and Fraunhofer diffraction. The key point of this work is that if one controls the illuminations, imaging with intensity only can be easily reduced to an imaging with phases and, therefore, one can apply standard imaging techniques. Detailed numerical simulations illustrate the performance of the proposed imaging strategy with and without data noise. [ABSTRACT FROM AUTHOR]

We study array imaging of a sparse scene of point-like sources or scatterers in a homogeneous medium. For source imaging, the sensors in the array are receivers that collect measurements of the wave field. For imaging scatterers, the array probes the medium with waves and records the echoes. In either case the image formation is stated as a sparsity promoting l1 optimization problem, and the goal of the paper is to quantify the resolution. We consider both narrow-band and broad-band imaging, and a geometric setup with a small array. We take first the case of the unknowns lying on the imaging grid and derive resolution limits that depend on the sparsity of the scene. Then we consider the general case with the unknowns at arbitrary locations. The analysis is based on estimates of the cumulative mutual coherence and a related concept, which we call the interaction coefficient. The latter complements recent results in compressed sensing by deriving deterministic resolution limits that account for worst-case scenarios in terms of locations of the unknowns in the imaging region, and also by interpreting the results in some cases where uniqueness of the solution does not hold. We demonstrate the theoretical predictions with numerical simulations. [ABSTRACT FROM AUTHOR]

We study active array imaging of small but strong scatterers in homogeneous media when multiple scattering between them is important. We use the Foldy-Lax equations to model wave propagation with multiple scattering when the scatterers are small relative to the wavelength. In active array imaging we seek to locate the positions and reflectivities of the scatterers, that is, to determine the support of the reflectivity vector and the values of its nonzero elements from echoes recorded on the array. This is a nonlinear inverse problem because of the multiple scattering. In this paper, we show how to avoid the nonlinearity and form images noniteratively through a two-step process which involves ℓ1 norm minimization. However, under certain illuminations imaging may be affected by screening, where some scatterers are obscured by multiple scattering. This problem can be mitigated by using multiple and diverse illuminations. In this case, we determine solution vectors that have a common support. The uniqueness and stability of the support of the reflectivity vector obtained with single or multiple illuminations are analyzed, showing that the errors are proportional to the amount of noise in the data with a proportionality factor dependent on the sparsity of the solution and the mutual coherence of the sensing matrix, which is determined by the geometry of the imaging array. Finally, to filter out noise and improve the resolution of the images, we propose an approach that combines optimal illuminations using the singular value decomposition of the response matrix together with sparsity promoting optimization jointly for all illuminations. In this work, an extension of our previous paper [A. Chai, M. Moscoso, and G. Papanicolaou, Inverse Problems, 29 (2013), 025016] on imaging using optimization techniques, we now account for multiple scattering effects. [ABSTRACT FROM AUTHOR]

We consider the problem of selective imaging extended reflectors in waveguides using the response matrix of the scattered field obtained with an active array. Selective imaging amounts to being able to focus at the edges of a reflector, which typically give rise to weaker echoes than those coming from its main body. To this end, we propose a selective imaging method that uses projections on low-rank subspaces of a weighted modal projection of the array response matrix, P(w). We analyze theoretically our imaging method for a simplified model problem where the scatterer is a vertical one-dimensional perfect reflector. In this case, we show that the rank of ... equals the size of the reflector divided by the cross-range array resolution. We also derive analytic expressions for the singular vectors of ... and carry out a detailed theoretical analysis of our selective imaging functional. Our numerical simulations are in very good agreement with the theory and illustrate the robustness of our imaging functional for reflectors of various shapes. [ABSTRACT FROM AUTHOR]

We introduce an adaptive approach for the detection of a reflector in a strongly scattering medium using a time-frequency representation of the array response matrix followed by a singular value decomposition (SVD). We use the local cosine transform (LCT) for the time-frequency representation and introduce a detection criterion that identifies anomalies in the top singular values, across frequencies and in different time windows, that are due to the reflector. The detection is adaptive because the time windows that contain the primary echoes from the reflector are not determined in advance. Their location and width are identified by searching through the time-frequency binary tree of the LCT. After detecting the presence of the reflector we filter the array response matrix to retain information only in the time windows that have been selected. We also project the filtered array response matrix to the subspace associated with the top singular value and then image using travel time migration. We show with extensive numerical simulations that this approach to detection and imaging works well in heavy clutter that is calibrated using random matrix theory so as to simulate regimes close to the experiments in [A. Aubry and A. Derode, J. Appl. Phys., 106 (2009), 044903]. While the detection and filtering algorithm presented here works well in general clutter, it has been analyzed theoretically only for the case of randomly layered media [ABSTRACT FROM AUTHOR]