Ivana Stojanovic

Sparsity-Driven Synthetic Aperture Radar Imaging: Reconstruction, autofocusing, moving targets, and compressed sensing

This article presents a survey of recent research on sparsity-driven synthetic aperture radar (SAR) imaging. In particular, it reviews 1) the analysis and synthesis-based sparse signal representation formulations for SAR image formation together with the associated imaging results, 2) sparsity-based methods for wide-angle SAR imaging and anisotropy characterization, 3) sparsity-based methods for joint imaging and autofocusing from data with phase errors, 4) techniques for exploiting sparsity for SAR imaging of scenes containing moving objects, and 5) recent work on compressed sensing (CS)-based analysis and design of SAR sensing missions.

Imaging of Moving Targets With Multi-Static SAR Using an Overcomplete Dictionary

This paper presents a method for imaging of moving targets using multi-static radar by treating the problem as one of joint spatial reflectivity signal inversion with respect to an overcomplete dictionary of target velocities. Existing approaches to dealing with moving targets in SAR solve the nonlinear problem of target scattering and motion estimation typically through decoupled matched filtering. In contrast, by using an overcomplete dictionary approach we effectively linearize the forward model and solve the moving target problem as a larger, unified regularized inversion problem subject to sparsity constraints. This unified framework allows estimation of scatter motion and reflectivity to be done in an optimal and global way. We show examples of the potential of the new method for sensing configurations with transmitters and receivers randomly dispersed in a multi-static geometry within a narrow forward cone around the scene of interest.

Joint space aspect reconstruction of wide-angle SAR exploiting sparsity

In this paper we present an algorithm for wide-angle synthetic aperture radar (SAR) image formation. Reconstruction of wide-angle SAR holds a promise of higher resolution and better information about a scene, but it also poses a number of challenges when compared to the traditional narrow-angle SAR. Most prominently, the isotropic point scattering model is no longer valid. We present an algorithm capable of producing high resolution reflectivity maps in both space and aspect, thus accounting for the anisotropic scattering behavior of targets. We pose the problem as a non-parametric three-dimensional inversion problem, with two constraints: magnitudes of the backscattered power are highly correlated across closely spaced look angles and the backscattered power originates from a small set of point scatterers. This approach considers jointly all scatterers in the scene across all azimuths, and exploits the sparsity of the underlying scattering field. We implement the algorithm and present reconstruction results on realistic data obtained from the XPatch Backhoe dataset.

Compressed sensing of mono-static and multi-static SAR

In this paper we study the impact of sparse aperture data collection of a SAR sensor on reconstruction quality of a scene of interest. Different mono and multi-static SAR measurement configurations produce different Fourier sampling patterns. These patterns reflect different spectral and spatial diversity trade-offs that must be made during task planning. Compressed sensing theory argues that the mutual coherence of the measurement probes is related to the reconstruction performance of sparse domains. With this motivation we compare the mutual coherence and corresponding reconstruction behavior of various mono-static and ultra-narrow band multi-static configurations, which trade-off frequency for geometric diversity. We investigate if such simple metrics are related to SAR reconstruction quality in an obvious way.

Compressed Sensing of Monostatic and Multistatic SAR

In this letter, we study the impact of compressed data collections from a synthetic aperture radar (SAR) sensor on the reconstruction quality of a scene of interest. Different monostatic and multistatic SAR measurement configurations produce different Fourier sampling patterns. These patterns reflect different spectral and spatial diversity tradeoffs that must be made during task planning. Compressed sensing theory argues that the mutual coherence of the measurement probes is related to the reconstruction performance of sparse domains. With this motivation, we propose a closely related t%-average mutual coherence parameter as a sensing configuration quality parameter and examine its relationship to the reconstruction behavior of various monostatic and ultranarrow-band multistatic configurations. We investigate how this easily computed metric is related to SAR reconstruction quality.

Compressed sensing in optical coherence tomography

Optical coherence tomography (OCT) is a valuable technique for non-invasive imaging in medicine and biology. In some applications, conventional time-domain OCT (TD-OCT) has been supplanted by spectral-domain OCT (SD-OCT); the latter uses an apparatus that contains no moving parts and can achieve orders of magnitude faster imaging. This enhancement comes at a cost, however: the CCD array detectors required for SD-OCT are more expensive than the simple photodiodes used in TD-OCT. We explore the possibility of extending the notion of compressed sensing (CS) to SD-OCT, potentially allowing the use of smaller detector arrays. CS techniques can yield accurate signal reconstructions from highly undersampled measurements, i.e., data sampled significantly below the Nyquist rate. The Fourier relationship between the measurements and the desired signal in SD-OCT makes it a good candidate for compressed sensing. Fourier measurements represent good linear projections for the compressed sensing of sparse point-like signals by random under-sampling of frequency-domain data, and axial scans in OCT are generally sparse in nature. This sparsity property has recently been used for the reduction of speckle in OCT images. We have carried out simulations to demonstrate the usefulness of compressed sensing for simplifying detection schemes in SD-OCT. In particular, we demonstrate the reconstruction of a sparse axial scan by using fewer than 10 percent of the measurements required by standard SD-OCT.

Data dissemination in wireless broadcast channels: Network coding versus cooperation

Network coding and cooperative diversity have each extensively been explored in the literature as a means to substantially improve the performance of wireless networks. Yet, little work has been conducted to compare their performance under a common framework. Our goal in this paper is to fill in this gap. Specifically, we consider a single-hop wireless network consisting of a base station and N receivers. We perform an asymptotic analysis, as N rarr infin, of the expected delay associated with the broadcasting of a file consisting of K packets. We show that if K is fixed, cooperation outperforms network coding, in the sense that the expected delay is proportional to K (and thus within a constant factor of the optimal delay) in the former case while it grows logarithmically with N in the latter case. On the other hand, if K grows with N at a rate at least as fast as (logN)r, for r Gt 1, then we show that the average delay of network coding is also proportional to K and lower than the average delay of cooperation if the packet error probability is smaller than 0.36. Our analytical findings are validated through extensive numerical simulations.

Interrupted SAR persistent surveillance via group sparse reconstruction of multipass data

In this paper we present a new method for synthetic aperture radar (SAR) image formation from interrupted, multipass SAR phase history data, with application to persistent surveillance SAR imaging. We propose a new compressed sensing-motivated approach to reconstruction that jointly processes multipass interrupted data using a sparse recovery technique with a group support constraint and results in improved imagery. We compare our approach, a group sparsity (GS) algorithm, to methods that independently process each data pass, namely the basis pursuit denoising and iterative adaptive approach methods. We find that the joint processing of GS results in coherent change detection gains over the other approaches regardless of interrupt pattern. To illustrate the capabilities of GS, we evaluate coherent change detection performance using images from the Gotcha SAR.

Low-dose X-ray CT reconstruction based on joint sinogram smoothing and learned dictionary-based representation

In this paper we propose two novel image reconstruction methods for low-dose X-ray CT data. Both approaches are based on anisotropic sinogram smoothing coupled with sparse local image representation with respect to a learned over complete dictionary. The redundant dictionary is learned from normal-dose CT training images and encodes artifact-free image behavior. The methods differ in the details of how the redundant dictionary information is included. Efficient solution approaches to the new formulations are provided. Comparative results on simulated low-dose imagery are given. Our approach is new in how it applies learning-based dictionary techniques to low-dose CT reconstruction, in its use of high quality training data in dictionary generation, and in its incorporation of anisotropic sinogram constraints together with the dictionary-based representation.

Data Dissemination in Wireless Broadcast Channels: Network Coding or Cooperation

Network coding and cooperative diversity have each extensively been explored in the literature as a means to substantially improve the performance of wireless networks. Yet, little work has been conducted to compare their performance under a common framework. Our goal in this paper is to fill in this gap. Specifically, we consider a single-hop wireless network consisting of a base station and N receivers. We perform an asymptotic analysis, as N rarr infin, of the expected delay associated with the broadcasting of a file consisting of K packets. We show that if K is fixed, cooperation outperforms network coding, in the sense that the expected delay is proportional to K (and thus within a constant factor of the optimal delay) in the former case while it grows logarithmically with N in the latter case. On the other hand, if K grows with N at a rate at least as fast as (log N)r, for r > 1, then we show that the average delay of network coding is within a factor less than two of the optimal delay, no worse than the average delay of cooperation. Our analytical findings are validated through extensive numerical simulations.