Nikola Subotic

Distributed RADAR waveform design based on compressive sensing considerations

In this paper we describe a joint waveform design methodology for distributed imaging RADARs using the concepts of compressive sensing. Compressive sensing is an active area of research that offers the promise of good object reconstruction with a sparse measurement set. The measurement set of the scene is based on a set of dasiaprobes,psila the radar waveforms. The set of measurements must satisfy the restricted isometry property and the scene being interrogated must be dasiacompressiblepsila meaning that it can be sparsely represented in some basis. We examine waveform and position considerations for a distributed radar system to satisfy these constraints and show their impact on waveform design and image reconstruction.

Parametric reconstruction of internal building structures via canonical scattering mechanisms

In this paper, we describe a model-based, non-linear reconstruction method for mapping internal building structures using through-wall radar data. We based the model on canonical geometry constructs that are commonly used in construction practices. These constructs are then formulated as sets of simple scattering mechanisms, which can be estimated from the data. Our non-linear approach employs an iterative, conditional estimation method as a function of the intervening structures between the sensor and the object under consideration. Specific associations of scattering mechanisms are then used to re-create various building structures such as walls, doors, stairs, etc. We discuss some examples of estimating specific scattering mechanisms and a model-based reasoning approach for assembling them to reconstruct the interior structure of a building.

An analysis of coded aperture acquisition and reconstruction using multi-frame code sequences for relaxed optical design constraints

We present an investigation of the performance of coded aperture optical systems where the elements of a set of binary coded aperture masks are applied over a sequence of acquired images. In particular, we are interested in investigating code sequences and image reconstruction algorithms that reduce the optical fidelity and hardware requirements for the system. Performance is jointly tied to the mask design, the image estimation algorithm, and the inherent optical response of the system. As such, we adopt a simplified reconstruction model and consider generalized optical system aberrations in designing masks used for multi-frame reconstruction of the imagery. We also consider the case of non-Nyquist sampled (aliased) imagery. These investigations have focused on using a regularized least-squares reconstruction model and mean squared error as a performance metric. Masks are found by attempting to minimize a closed form objective that predicts the mean squared error for the reconstruction algorithm. We find that even with suboptimal solutions that binary masks can be used to improve imagery over the case of an uncoded aperture with the same aberration.

Compressive sensing and 3-D radar imaging

Nonstandard image formation methods can enable fully three-dimensional fine resolution radar images of some objects of interest to be constructed from certain types of sparsely sampled three-dimensional apertures, which contain too little collected data to support traditional imaging methods. Such three-dimensional image products provide more target information than traditional SAR and ISAR imagery, and eliminate most of the difficulties associated with interpretation, mensuration, and recognition that result from overlay effects, self shadowing, scaling and viewing angle uncertainties.

Optimization and waveforms for compressive sensing applications in the presence of interference

Compressive sensing concepts have potential applications to multiple RADAR problems, which include Moving Target Indication, and RADAR imaging in two and three spatial dimensions. Currently known sufficient conditions for reliable sparse signal reconstruction do not seem to be directly applicable or practical for some traditional RADAR problems. But experiments and mathematical invariance properties of some reconstruction methods indicate that useful products can often be obtained using these methods for circumstances outside the usual conditions.

Cramèr-Rao lower bounds for radar parameter estimation in noise plus structured interference

This document derives approximate expressions for the Cramèr-Rao lower bounds on the variance of unbiased estimates of the parameters of a narrow-band radar model in the presence of additive white Gaussian noise as well as interference with known structure. We show that the Cramèr-Rao lower bounds with interference are comprised of the bound when the interference is not present and a term that is proportional to the squared normalized-correlation between the radar signal and the interfering signal. Numerical simulations demonstrating these bounds are shown and the threshold effect is observed. The bounds are then used to define an objective function to be used for waveform co-design, and a simple example of this is shown.

Incorporating prior knowledge of urban scene spatial structure in aperture code designs for surveillance systems

Two major missions of Surveillance systems are imaging and ground moving target indication (GMTI). Recent advances in coded aperture electro optical systems have enabled persistent surveillance systems with extremely large fields of regard. The areas of interest for these surveillance systems are typically urban, with spatial topologies having a very definite structure. We incorporate aspects of a priori information on this structure in our aperture code designs to enable optimized dealiasing operations for undersampled focal plane arrays. Our framework enables us to design aperture codes to minimize mean square error for image reconstruction or to maximize signal to clutter ratio for GMTI detection. In this paper we present a technical overview of our code design methodology and show the results of our designed codes on simulated DIRSIG mega-scene data.

Decomposition approaches to separate clutter/background from buried object signatures

Ground penetrating radar measurements are dominated by the strong return from the ground interface and volume scattering from distributed subsurface in-homogeneities. Buried object detection performance can be improved if these clutter sources can be reduced relative to the scattering from the buried objects of interest. This paper applies two recently developed methods of separating a signal into a low-rank component (representing the background) and a sparse component (the buried object), robust principal component analysis (RPCA) and dynamic mode decomposition (DMD), to the problem of separating subsurface scattering anomalies from a slowly varying background. The algorithms are described and an example application to field-collected impulse GPR data is shown. The target-to-clutter ratio is significantly improved in the sparse component compare to that in the original data suggesting that these techniques are viable methods of suppressing surface clutter and distributed volumetric clutter.

Potential application of micro-bolometer coupled antenna-pairs in beam synthesis

The IR antenna-pair coupled micro-bolometers has demonstrated its unique power response features compared to the single antenna coupled micro-bolometers. The response pattern is determined by that of the single antenna and an interference oscillation term of the antenna-pair with respective to the angle of incidence of the radiation field, and can be steered by shifting the location of the bolometer. This paper explores the potential application of antenna-pair coupled detector in beam synthesis. It describes an array configuration based upon these micro-bolometers, and discusses the corresponding coherent data processing method for the purpose of obtaining response pattern narrowing effects from such an array. This directional gain enhancement, together with the beam steering control, could potentially lead to an array capable of providing a novel IR lensless imaging technique.

System models for IR diffractive optical systems based on a coherence theoretic framework

Diffractive optical systems in the Infrared (IR) wavelength regime are being re-examined for remote sensing applications. A pupil-plane adaptive coded aperture can enable a fine resolution, wide field of view sensor system without mechanical scanning. Due to the relatively long wavelengths, coded aperture systems in the IR have unique issues in regards to e.g. X-ray coded apertures. These include diffraction effects, wavelength dependence of optical elements, off axis aberrations due to thick screens, etc. In this paper, we provide a general system model framework based on partial coherence theory that enables us to explore many of the technical challenges in IR diffractive imaging. This paper develops the general theory and shows examples of issues that impact the optical transfer function (OTF) and impulse response of these types of architectures.