Title: Compressive Sensing for Electromagnetic Imaging Using Nesterov-Based Algorithm
Compressive Sensing (CS) is a relatively novel signal processing theory; it states that sparse signals can be recovered using far fewer samples or measurements than the required by the Nyquist sampling criterion. This technique, applied to Electromagnetic Imaging and implemented using the Nesterovs algorithm, has been used in this work to reduce the number of sensors and improve the robustness of several security and biomedical imaging systems.
Nesterovs algorithm is a first order method that provides a framework for minimizing nonsmooth convex functions on any given convex set. The algorithm recasts the original problem as finding a saddle point in the primal-dual feasibility set when the original function is smoothed by using weighted prox-function. The solution to this minimization problem is given by iteratively estimating three sequences: the first sequence is computed using a gradient-descent pathway, the second sequence is computed from an averaged gradientdescent pathway, and the third sequence is computed as a weighted average of the first two in order to lead to the final solution. The first two sequences are obtained by solving the stationary equation from the Karush-Kuhn-Tucker (KKT) optimality conditions, and they can be performed fast without matrix inversion for orthogonal projectors.
In the context of security applications, three different configurations have been studied. In the first case, the CS-Nesterov algorithm has been coupled with a high frequency electromagnetic solver, based on the Modified Equivalent Current Analysis (MECA) method, in order to design the next generation of millimeter-wave portal scanning systems. These techniques, in conjunction with a Simulated Annealing (SA) algorithm, have been proved successful in reducing the number of sensors and enhancing the overall imaging performance of the security sensing system. The second security application is related with the more challenging problem of threat detection at standoff distances. In this case, MECA modeling and CS-Nesterov inversion are combined with the novel use of a set of Passive Reflective Surfaces (PRS) close to the target. The PRS works as a coding aperture that enables high resolution imaging when reconstructing the shape and dielectric properties of targets at 10m away from the radar. Finally, the CS-Nesterov algorithm has been applied to a mid-range, on-the-move threat detection problem. Fast forward and inverse operators, based on a novel multistatic Fourier-based transform formulation, have been implemented and coupled with CS-Nesterov algorithm to perform real time imaging.
In the context of biomedical applications, the CS-Nesterov method has been used in a novel hybrid Digital Breast Tomosynthesis (DBT) / Nearfield Radar Imaging (NRI) system configuration. The non-homogeneous tissue distribution of the breast, described in terms of dielectric constant and conductivity, is extracted from the DBT image; and it is used by a fullwave Finite Difference in the Frequency Domain (FDFD) method to build a linearized model of the non-linear NRI imaging problem. The inversion of the linear problem is solved using CS-Nesterov method, which leads to a reduction on the required number of sensing antennas, dynamic range, and operational bandwidth of the NRI system without loss of performance. The last application presented in this work is the use of the CS-Nesterov approach to reduce the noise of optical photoplethysmography data generated by a non-contact imaging device. This pre-processing algorithm enhances the performance of discriminant classifiers in terms of differentiation of the wound bed from the devitalized burn tissue and healthy skin.
Prof. Jose A. Martinez-Lorenzo (advisor)
Prof. Carey Rappaport
Prof. Edwin Marengo
Prof. Rifat Sipahi