Illumination strategies for intensity-only imaging

We propose a new strategy for narrow band, active array imaging of localized scat- terers when only the intensities are recorded and measured at the array. We consider a homogeneous medium so that wave propagation is fully coherent. We show that imaging with intensity-only measurements can be carried out using the time reversal operator of the imaging system, which can be obtained from intensity measurements using an appropriate illumination strategy and the polarization identity. Once the time reversal operator has been obtained, we show that the images can be formed using its singular value decomposition (SVD). We use two SVD-based methods to image the scatterers. The proposed approach is simple and efficient. It does not need prior information about the sought image, and guarantees exact recovery in the noise-free case. Furthermore, it is robust with respect to additive noise. Detailed numerical simulations illustrate the performance of the proposed imaging strategy when only the intensities are captured

Array imaging of localized objects in homogeneous and heterogeneous media

We present a comprehensive study of the resolution and stability properties of sparse promoting optimization theories applied to narrow band array imaging of localized scatterers. We consider homogeneous and heterogeneous media, and multiple and single scattering situations. When the media is homogeneous with strong multiple scattering between scatterers, we give a non-iterative formulation to find the locations and reflectivities of the scatterers from a nonlinear inverse problem in two steps, using either single or multiple illuminations. We further introduce an approach that uses the top singular vectors of the response matrix as optimal illuminations, which improves the robustness of sparse promoting optimization with respect to additive noise. When multiple scattering is negligible, the optimization problem becomes linear and can be reduced to a hybrid-$\ell_1$ method when optimal illuminations are used. When the media is random, and the interaction with the unknown inhomogeneities can be primarily modeled by wavefront distortions, we address the statistical stability of these methods. We analyze the fluctuations of the images obtained with the hybrid-$\ell_1$ method, and we show that it is stable with respect to different realizations of the random medium provided the imaging array is large enough. We compare the performance of the hybrid-$\ell_1$ method in random media to the widely used Kirchhoff migration and the multiple signal classification methods

Synthetic aperture imaging with intensity-only data

We consider imaging the reflectivity of scatterers from intensity-only data recorded by a single moving transducer that both emits and receives signals, forming a synthetic aperture. By exploiting frequency illumination diversity, we obtain multiple intensity measurements at each location, from which we determine field cross-correlations using an appropriate phase controlled illumination strategy and the inner product polarization identity. The field cross-correlations obtained this way do not, however, provide all the missing phase information because they are determined up to a phase that depends on the receiver's location. The main result of this paper is an algorithm with which we recover the field cross-correlations up to a single phase that is common to all the data measured over the synthetic aperture, so all the data are synchronized. Thus, we can image coherently with data over all frequencies and measurement locations as if full phase information was recorded

Synthetic Aperture Imaging With Intensity-Only Data.

We consider imaging the reflectivity of scatterers from intensity-only data recorded by a single moving transducer that both emits and receives signals, forming a synthetic aperture. By exploiting frequency illumination diversity, we obtain multiple intensity measurements at each location, from which we determine field cross-correlations using an appropriate phase controlled illumination strategy and the inner product polarization identity. The field cross-correlations obtained this way do not, however, provide all the missing phase information because they are determined up to a phase that depends on the receiver's location. The main result of this paper is an algorithm with which we recover the field cross-correlations up to a single phase that is common to all the data measured over the synthetic aperture, so all the data are synchronized. Thus, we can image coherently with data over all frequencies and measurement locations as if full phase information was recorded

Current self-oscillations, spikes and crossover between charge monopole and dipole waves in semiconductor superlattices

Self-sustained current oscillations in weakly-coupled superlattices are studied by means of a self-consistent microscopic model of sequential tunneling including boundary conditions naturally. Well-to-well hopping and recycling of charge monopole domain walls produce current spikes (high frequency modulation) superimposed on the oscillation. For highly doped injecting contacts, the self-oscillations are due to dynamics of monopoles. As the contact doping decreases, a lower-frequency oscillatory mode due to recycling and motion of charge dipoles is predicted. For low contact doping, this mode dominates and monopole oscillations disappear. At intermediate doping, both oscillation modes coexist as stable solutions and hysteresis between them is possible.Comment: 4 pages, 4 figure

Microscopic Model for Sequential Tunneling in Semiconductor Multiple Quantum Wells

We propose a selfconsistent microscopic model of vertical sequential tunneling through a multi-quantum well.The model includes a detailed description of the contacts,uses the Transfer Hamiltonian for expressions of the current and it treats the Coulomb interaction within a mean field approximation. We analyze the current density through a double well and a superlattice and study the formation of electric field domains and multistability coming from the Coulomb interaction. Phase diagrams of parameter regions (bias, doping in the heterostructure and in the contacts,etc) where the different solutions exist are given.Comment: 4 pages, 8 Postscript Figure

Accelerated 4D Flow MRI Using a Shared Subspace Constraint

Cardiovascular diseases are the leading cause of death in the world, more than the next three leading causes of death combined. Cardiovascular imaging techniques have allowed for the study and understanding of the function and structure of the heart as well as the detection, diagnosis, and monitoring of cardiovascular diseases in patients. One powerful technique for cardiac imaging is 4D phase contrast magnetic resonance imaging (PC-MRI) which allows measurement of blood flow velocity in the heart and vessels. However, 4D PC-MRI is difficult to perform due to low imaging speed and is therefore often carried out using accelerated imaging techniques which reconstruct images from reduced data. One approach for accelerating PC-MRI is explicitsubspace low-rank imaging; this project focuses on further accelerating explicit-subspace low-rank PC-MRI through the use of a shared temporal subspace between PC-MR images with velocity encoded in different directions. We will: a) investigate the subspace structure of the differently encoded images to verify that they indeed live in a shared subspace; b) evaluate the feasibility of estimating this shared subspace from reduced auxiliary data (which has direct implications on the frame rate of the resulting images); and c) demonstrate the utility of exploiting this subspace structure when performing image reconstruction from reduced data.Ope