Buchbeiträge

This chapter addresses sparse signal reconstruction under various types of structural side constraints with applications in multi-antenna systems. Side constraints may result from prior information on the measurement system and the sparse signal structure. They may involve the structure of the sensing matrix, the structure of the non-zero support values, the temporal structure of the sparse representation vector, and the nonlinear measurement structure. First, we demonstrate how a priori information in the form of structural side constraints influence recovery guarantees (null space properties) using ℓ1-minimization. Furthermore, for constant modulus signals, signals with row, block, and rank sparsity, as well as non-circular signals, we illustrate how structural prior information can be used to devise efficient algorithms with improved recovery performance and reduced computational complexity. Finally, we address the measurement system design for linear and nonlinear measurements of sparse signals. To this end, we derive a new linear mixing matrix design based on coherence minimization. Then, we extend our focus to nonlinear measurement systems where we design parallel optimization algorithms to efficiently compute stationary points in the sparse phase-retrieval problem with and without dictionary learning.

Nondestructive material testing and evaluation is a vast interdisciplinary field as well as a challenge due to the variety of applications. Whereas the focus of nondestructive testing is to identify anomalies within a specimen, the reconstruction of defect properties and their influence on the materials usability is the focus of nondestructive evaluation. In this chapter the technology of motion-induced eddy current testing (MIECT) is introduced. In contrast to traditional eddy current testing (ECT) methods, MIECT makes use of relative motion between the object under test and permanent magnets. The induced eddy currents interact with the applied magnetic field and result in a Lorentz force, depending on the impressed magnetic induction, the electrical conductivity, and the measuring velocity. Because permanent magnets produce considerably stronger magnetic fields than current-carrying ECT coils, even deep internal defects can be detected using the Lorentz force eddy current testing (LET). It is shown how the electromagnetic fields can be described theoretically and simulated numerically, as well as how imperfections/defects in non-ferromagnetic, conducting specimens can be detected using an appropriate laboratory environment. Comparative studies have shown that LET applied to metallic composite material or friction stir welds is a promising and competitive alternative to traditional ECT methods enabling the contactless evaluation of moving electrical conductors.