We consider imaging of fast moving small objects in space, such as low Earth orbit satellites, which are also rotating around a fixed axis. The imaging system consists of ground based, asynchronous sources of radiation and several passive receivers above the dense atmosphere. We use the cross-correlation of the received signals to reduce distortions from ambient medium fluctuations. Imaging with correlations also has the advantage of not requiring any knowledge about the probing pulse, and it depends weakly on the emitter positions. We account for the target s orbital velocity by introducing the necessary Doppler compensation. In particular, we show that over limited imaging regions, a constant Doppler factor can be used, resulting in an efficient data structure for the correlations of the recorded signals. To image a fast rotating object we also need to compensate for the rotation. We show that the rotation parameters can be extracted directly from the autocorrelation of the data before the formation of the image. We then investigate and analyze an imaging method that relies on backpropagating the cross-correlation data structure to two points rather than one and thus forms an interference matrix. The proposed imaging method consists of estimating the reflectivity as the top eigenvector of the migrated cross-correlation data interference matrix. We call this the rank-1 image and show that it provides superior image resolution compared to the usual single-point migration scheme for fast moving and rotating objects. Moreover, we observe a significant improvement in resolution due to the rotation leading to a diffraction limited resolution. We carry out a theoretical analysis that illustrates the role of the two-point migration method as well as that of the inverse aperture and rotation in improving resolution. Extensive numerical simulations support the theoretical results.

The numerical solution of the elastodynamic problem with kinematic boundary conditions is considered using mixed finite elements for the space discretization and a staggered leap-frog scheme for the discretization in time. The stability of the numerical scheme is shown under the usual CFL condition. Using the general form of Robin-type boundary conditions some cases of debonding and the resulting acoustic emission are studied. The methodology presented finds applications to geophysics such as in seismic waves simulation with dynamic rupture and energy release. In this paper, we focus on problems of fracture occurring at the interface of composite materials. Our goal is to study both the mechanism of crack initiation and propagation, as well as the acoustic emission of the released structure-borne energy which may be used in structural health monitoring and prognosis applications.

We develop and analyze a quantitative signal subspace imaging method for single-frequency array imaging. This method is an extension to multiple signal classification which uses (i) the noise subspace to determine the location and support of targets, and (ii) the signal subspace to recover quantitative information about the targets. For point targets, we are able to recover the complex reflectivity and for an extended target under the Born approximation, we are able to recover a scalar quantity that is related to the product of the volume and relative dielectric permittivity of the target. Our resolution analysis for a point target demonstrates this method is capable of achieving exact recovery of the complex reflectivity at subwavelength resolution. Additionally, this resolution analysis shows that noise in the data effectively acts as a regularization to the imaging functional resulting in a method that is surprisingly more robust and effective with noise than without noise.