Initial Inputs: Adaptive Front-End Signal Processing

1. Initial Inputs:Adaptive Front-End Signal Processing W. Clem Karl Boston University

2. Long term aims • Methods robust to sensor configuration & sparsity of data • “Submissive sensing” matched to backend management • Works with wide range of configurations • No “my way or the highway” signal processing • E.g. Circular SAR, Multistatic SAR, spatial-spectral diversity • Understanding of performance • Presensing impact of sensing choices for management (e.g. frequency versus geometric diversity) • Understanding performance consequences of sensing choices • Postsensing estimates and uncertainties for fusion • Methods for complex scenes, non-conventional uses, and greedy decision makers  expect more, get more • Target motion • 3D scene structure • Anisotropic behavior MURI: Integrated Fusion, Performance Prediction, and Sensor Management for Automatic Target Exploitation

3. New BU signal processing • Multistatic imaging I: • Physical modeling • Sparsity-based reconstruction • Multistatic imaging II: • Understanding performance • Mutual coherence as predictor • Imaging dynamic scenes • Overcomplete dictionary formulation • Recursive assimilation of data MURI: Integrated Fusion, Performance Prediction, and Sensor Management for Automatic Target Exploitation

4. Multistatic Radar • Sensing Model • Different choices for K(t), rx, tx possible Reflectivity Tx frequency Tx/Rx geometry Transmit Freq B = bistatic angle uB = bistatic bisector wtx = transmitted frequency From Wicks et al MURI: Integrated Fusion, Performance Prediction, and Sensor Management for Automatic Target Exploitation

5. Many Sensing Options… Case 2: Stationary Tx, Moving Rx, UNB waveform Case 1: Stationary Tx/Rx, Wideband waveform Case 3: Stationary Tx, Moving Rx, Wideband waveform Case 4: Monostatic Tx/Rx, Wideband waveform MURI: Integrated Fusion, Performance Prediction, and Sensor Management for Automatic Target Exploitation

6. Multistatic Comments • Rich framework to study: • sensor tradeoffs • resource optimization • waveform/sensor planning • Waveform diversity: • UNB  wideband • Many transmitters  few transmitters • Etc… • Need new tools for processing non-conventional datasets MURI: Integrated Fusion, Performance Prediction, and Sensor Management for Automatic Target Exploitation

7. Reconstruction Formulation • Sparsity-based L2-L1 reconstruction using extension of previous SAR work • Leads to a second order cone program, effectively solved by an interior point method MURI: Integrated Fusion, Performance Prediction, and Sensor Management for Automatic Target Exploitation

8. Example: UNB Multistatic SAR • UNB (single frequency) • Ntx=10, Nrx = 55 Sparse coverage • Uniform circular coverage • Fourier support (resolution) µ UNB frequency MURI: Integrated Fusion, Performance Prediction, and Sensor Management for Automatic Target Exploitation

9. Results FBP, cw = 2MHz, SNR = 15dB FBP, cw = 4MHz, SNR = 15dB Extension of FBP Truth LS-L1, cw = 2MHz, SNR = 15dB LS-L1, cw = 4MHz, SNR = 15dB LS-L1 MURI: Integrated Fusion, Performance Prediction, and Sensor Management for Automatic Target Exploitation

10. Understanding Performance • Want to understand performance consequences of different sensor configurations • Guidance for sensor management • Compressed sensing theory says reconstruction performance related to mutual coherence of configurations • # of measurements needed to reconstruct sparse scene µ (mutual coherence)2 MURI: Integrated Fusion, Performance Prediction, and Sensor Management for Automatic Target Exploitation

11. Initial work • Compare different monostatic and UNB multistatic radar configurations • Mutual coherence • Measure of diversity of sensing probes MURI: Integrated Fusion, Performance Prediction, and Sensor Management for Automatic Target Exploitation

12. Different Sampling Strategies Monostatic Multistatic MURI: Integrated Fusion, Performance Prediction, and Sensor Management for Automatic Target Exploitation

13. Results • Mutual coherence lower for multistatic configuration as number of probes are reduced Monostatic Multistatic MURI: Integrated Fusion, Performance Prediction, and Sensor Management for Automatic Target Exploitation

14. Results (Cont) • Example reconstruction for Ntx/Nq=10 case • Reconstructions confirm prediction Ground Truth Monostatic Multistatic MURI: Integrated Fusion, Performance Prediction, and Sensor Management for Automatic Target Exploitation

15. Dynamic Scenes: Moving Targets • Augment model to include velocity • Discrete form of forward model: Static targets at a reference time Phase shift due to motion A depends on unknown scatterer velocity v in pixel p, so nonlinear problem! MURI: Integrated Fusion, Performance Prediction, and Sensor Management for Automatic Target Exploitation

16. Overcomplete Dictionary Approach • Modify forward operator to include all velocity hypotheses • Pixel reflectively becomes a vector • New overcomplete observation model • A is now fully specified, so observation is linear…but solution f must be very sparse • We know how to do this! MURI: Integrated Fusion, Performance Prediction, and Sensor Management for Automatic Target Exploitation

17. Overcomplete Problem Solution • Idea: sparest solution should automatically identify correct velocity and scattering • Solution via custom made large-scale interior point method MURI: Integrated Fusion, Performance Prediction, and Sensor Management for Automatic Target Exploitation

18. Example #1: • Multistatic configuration with Ntx= 10, Nrx = 55 • Dictionary does not contain true velocities Truth CW = 4MHz, OD MURI: Integrated Fusion, Performance Prediction, and Sensor Management for Automatic Target Exploitation