Recovery under Side Constraints

This paper 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 representationvector, and the nonlinear measurement structure. First, we demonstrate how a priori information in 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. Moreover, we discuss the 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

Compact Formulations for Sparse Reconstruction in Fully and Partly Calibrated Sensor Arrays

Sensor array processing is a classical field of signal processing which offers various applications in practice, such as direction of arrival estimation or signal reconstruction, as well as a rich theory, including numerous estimation methods and statistical bounds on the achievable estimation performance. A comparably new field in signal processing is given by sparse signal reconstruction (SSR), which has attracted remarkable interest in the research community during the last years and similarly offers plentiful fields of application. This thesis considers the application of SSR in fully calibrated sensor arrays as well as in partly calibrated sensor arrays. The main contributions are a novel SSR method for application in partly calibrated arrays as well as compact formulations for the SSR problem, where special emphasis is given on exploiting specific structure in the signals as well as in the array topologies