Velocity Dealiased Spectral Estimators of Range Migrating Targets using a Single Low-PRF Wideband Waveform

Wideband radars are promising systems that may provide numerous advantages, like simultaneous detection of slow and fast moving targets, high range-velocity resolution classification, and electronic countermeasures. Unfortunately, classical processing algorithms are challenged by the range-migration phenomenon that occurs then for fast moving targets. We propose a new approach where the range migration is used rather as an asset to retrieve information about target velocitiesand, subsequently, to obtain a velocity dealiased mode. More specifically three new complex spectral estimators are devised in case of a single low-PRF (pulse repetition frequency) wideband waveform. The new estimation schemes enable one to decrease the level of sidelobes that arise at ambiguous velocities and, thus, to enhance the discrimination capability of the radar. Synthetic data and experimental data are used to assess the performance of the proposed estimators

Convex Model-Based Synthetic Aperture Radar Processing

The use of radar often conjures up images of small blobs on a screen. But current synthetic aperture radar (SAR) systems are able to generate near-optical quality images with amazing benefits compared to optical sensors. These SAR sensors work in all weather conditions, day or night, and provide many advanced capabilities to detect and identify targets of interest. These amazing abilities have made SAR sensors a work-horse in remote sensing, and military applications. SAR sensors are ranging instruments that operate in a 3D environment, but unfortunately the results and interpretation of SAR images have traditionally been done in 2D. Three-dimensional SAR images could provide improved target detection and identification along with improved scene interpretability. As technology has increased, particularly regarding our ability to solve difficult optimization problems, the 3D SAR reconstruction problem has gathered more interest. This dissertation provides the SAR and mathematical background required to pose a SAR 3D reconstruction problem. The problem is posed in a way that allows prior knowledge about the target of interest to be integrated into the optimization problem when known. The developed model is demonstrated on simulated data initially in order to illustrate critical concepts in the development. Then once comprehension is achieved the processing is applied to actual SAR data. The 3D results are contrasted against the current gold- standard. The results are shown as 3D images demonstrating the improvement regarding scene interpretability that this approach provides

MIMO Radar Waveform Design and Sparse Reconstruction for Extended Target Detection in Clutter

This dissertation explores the detection and false alarm rate performance of a novel transmit-waveform and receiver filter design algorithm as part of a larger Compressed Sensing (CS) based Multiple Input Multiple Output (MIMO) bistatic radar system amidst clutter. Transmit-waveforms and receiver filters were jointly designed using an algorithm that minimizes the mutual coherence of the combined transmit-waveform, target frequency response, and receiver filter matrix product as a design criterion. This work considered the Probability of Detection (P D) and Probability of False Alarm (P FA) curves relative to a detection threshold, τ th, Receiver Operating Characteristic (ROC), reconstruction error and mutual coherence measures for performance characterization of the design algorithm to detect both known and fluctuating targets and amidst realistic clutter and noise. Furthermore, this work paired the joint waveform-receiver filter design algorithm with multiple sparse reconstruction algorithms, including: Regularized Orthogonal Matching Pursuit (ROMP), Compressive Sampling Matching Pursuit (CoSaMP) and Complex Approximate Message Passing (CAMP) algorithms. It was found that the transmit-waveform and receiver filter design algorithm significantly outperforms statically designed, benchmark waveforms for the detection of both known and fluctuating extended targets across all tested sparse reconstruction algorithms. In particular, CoSaMP was specified to minimize the maximum allowable P FA of the CS radar system as compared to the baseline ROMP sparse reconstruction algorithm of previous work. However, while the designed waveforms do provide performance gains and CoSaMP affords a reduced peak false alarm rate as compared to the previous work, fluctuating target impulse responses and clutter severely hampered CS radar performance when either of these sparse reconstruction techniques were implemented. To improve detection rate and, by extension, ROC performance of the CS radar system under non-ideal conditions, this work implemented the CAMP sparse reconstruction algorithm in the CS radar system. It was found that detection rates vastly improve with the implementation of CAMP, especially in the case of fluctuating target impulse responses amidst clutter or at low receive signal to noise ratios (β n). Furthermore, where previous work considered a τ th=0, the implementation of a variable τ th in this work offered novel trade off between P D and P FA in radar design to the CS radar system. In the simulated radar scene it was found that τ th could be moderately increased retaining the same or similar P D while drastically improving P FA. This suggests that the selection and specification of the sparse reconstruction algorithm and corresponding τ th for this radar system is not trivial. Rather, a tradeoff was noted between P D and P FA based on the choice and parameters of the sparse reconstruction technique and detection threshold, highlighting an engineering trade-space in CS radar system design. Thus, in CS radar system design, the radar designer must carefully choose and specify the sparse reconstruction technique and appropriate detection threshold in addition to transmit-waveforms, receiver filters and building the dictionary of target impulse responses for detection in the radar scene

Novel Methods in Computational Imaging with Applications in Remote Sensing

This dissertation is devoted to novel computational imaging methods with applications in remote sensing. Computational imaging methods are applied to three distinct applications including imaging and detection of buried explosive hazards utilizing array radar, high resolution imaging of satellites in geosynchronous orbit utilizing optical hypertelescope arrays, and characterization of atmospheric turbulence through multi-frame blind deconvolution utilizing conventional optical digital sensors. The first application considered utilizes a radar array employed as a forward looking ground penetrating radar system with applications in explosive hazard detection. A penalized least squares technique with sparsity-inducing regularization is applied to produce imagery, which is consistent with the expectation that objects are sparsely populated but extended with respect to the pixel grid. Additionally, a series of pre-processing steps is demonstrated which result in a greatly reduced data size and computational cost. Demonstrations of the approach are provided using experimental data and results are given in terms of signal to background ratio, image resolution, and relative computation time. The second application involves a sparse-aperture telescope array configured as a hypertelescope with applications in long range imaging. The penalized least squares technique with sparsity-inducing regularization is adapted and applied to this very different imaging modality. A comprehensive study of the algorithm tuning parameters is performed and performance is characterized using the Structure Similarity Metric (SSIM) to maximize image quality. Simulated measurements are used to show that imaging performance achieved using the pro- posed algorithm compares favorably in comparison to conventional Richardson-Lucy deconvolution. The third application involves a multi-frame collection from a conventional digital sensor with the primary objective of characterizing the atmospheric turbulence in the medium of propagation. In this application a joint estimate of the image is obtained along with the Zernike coefficients associated with the atmospheric PSF at each frame, and the Fried parameter r0 of the atmosphere. A pair of constraints are applied to a penalized least squares objective function to enforce the theoretical statistics of the set of PSF estimates as a function of r0. Results of the approach are shown with both simulated and experimental data and demonstrate excellent agreement between the estimated r0 values and the known or measured r0 values respectively