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

Time-domain Compressive Beamforming for Medical Ultrasound Imaging

Over the past 10 years, Compressive Sensing has gained a lot of visibility from the medical imaging research community. The most compelling feature for the use of Compressive Sensing is its ability to perform perfect reconstructions of under-sampled signals using l1-minimization. Of course, that counter-intuitive feature has a cost. The lacking information is compensated for by a priori knowledge of the signal under certain mathematical conditions. This technology is currently used in some commercial MRI scanners to increase the acquisition rate hence decreasing discomfort for the patient while increasing patient turnover. For echography, the applications could go from fast 3D echocardiography to simplified, cheaper echography systems. Real-time ultrasound imaging scanners have been available for nearly 50 years. During these 50 years of existence, much has changed in their architecture, electronics, and technologies. However one component remains present: the beamformer. From analog beamformers to software beamformers, the technology has evolved and brought much diversity to the world of beam formation. Currently, most commercial scanners use several focalized ultrasonic pulses to probe tissue. The time between two consecutive focalized pulses is not compressible, limiting the frame rate. Indeed, one must wait for a pulse to propagate back and forth from the probe to the deepest point imaged before firing a new pulse. In this work, we propose to outline the development of a novel software beamforming technique that uses Compressive Sensing. Time-domain Compressive Beamforming (t-CBF) uses computational models and regularization to reconstruct de-cluttered ultrasound images. One of the main features of t-CBF is its use of only one transmit wave to insonify the tissue. Single-wave imaging brings high frame rates to the modality, for example allowing a physician to see precisely the movements of the heart walls or valves during a heart cycle. t-CBF takes into account the geometry of the probe as well as its physical parameters to improve resolution and attenuate artifacts commonly seen in single-wave imaging such as side lobes. In this thesis, we define a mathematical framework for the beamforming of ultrasonic data compatible with Compressive Sensing. Then, we investigate its capabilities on simple simulations in terms of resolution and super-resolution. Finally, we adapt t-CBF to real-life ultrasonic data. In particular, we reconstruct 2D cardiac images at a frame rate 100-fold higher than typical values