Compressed Sensing Algorithms for Electromagnetic Imaging Applications

Download or read book Compressed Sensing Algorithms for Electromagnetic Imaging Applications written by Richard Obermeier and published by . This book was released on 2016 with total page 78 pages. Available in PDF, EPUB and Kindle. Book excerpt: Compressed Sensing (CS) theory is a novel signal processing paradigm, which states that sparse signals of interest can be accurately recovered from a small set of linear measurements using efficient L1-norm minimization techniques. CS theory has been successfully applied to many sensing applications; such has optical imaging, X-ray CT, and Magnetic Resonance Imaging (MRI). However, there are two critical deficiencies in how CS theory is applied to these practical sensing applications. First, the most common reconstruction algorithms ignore the constraints placed on the recovered variable by the laws of physics. Second, the measurement system must be constructed deterministically, and so it is not possible to utilize random matrix theory to assess the CS reconstruction capabilities of the sensing matrix. In this thesis, we propose solutions to these two deficiencies in the context of electromagnetic imaging applications, in which the unknown variables are related to the dielectric constant and conductivity of the scatterers. First, we introduce a set of novel Physicality Constrained Compressed Sensing (PCCS) optimization programs, which augment the standard CS optimization programs to force the resulting variables to obey the laws of physics. The PCCS problems are investigated from both theoretical and practical stand-points, as well as in the context of a hybrid Digital Breast Tomosynthesis (DBT) / Nearfield Radar Imaging (NRI) system for breast cancer detection. Our analysis shows how the PCCS problems provide enhanced recovery capabilities over the standard CS problems. We also describe three efficient algorithms for solving the PCCS optimization programs. Second, we present a novel numerical optimization method for designing so-called "compressive antennas" with enhanced CS recovery capabilities. In this method, the constitutive parameters of scatterers placed along a traditional antenna are designed in order to maximize the capacity of the sensing matrix. Through a theoretical analysis and a series of numerical examples, we demonstrate the ability of the optimization method to design antenna configurations with enhanced CS recovery capabilities. Finally, we briefly discuss an extension of the design method to Multiple Input Multiple Output (MIMO) communication systems.