Low-complexity DCD-based sparse recovery algorithms

Sparse recovery techniques find applications in many areas. Real-time implementation of such techniques has been recently an important area for research. In this paper, we propose computationally efficient techniques based on dichotomous coordinate descent (DCD) iterations for recovery of sparse complex-valued signals. We first consider $\ell_2 \ell_1$ optimization that can incorporate \emph{a priori} information on the solution in the form of a weight vector. We propose a DCD-based algorithm for $\ell_2 \ell_1$ optimization with a fixed $\ell_1$-regularization, and then efficiently incorporate it in reweighting iterations using a \emph{warm start} at each iteration. We then exploit homotopy by sampling the regularization parameter and arrive at an algorithm that, in each homotopy iteration, performs the $\ell_2 \ell_1$ optimization on the current support with a fixed regularization parameter and then updates the support by adding/removing elements. We propose efficient rules for adding and removing the elements. The performance of the homotopy algorithm is further improved with the reweighting. We then propose an algorithm for $\ell_2 \ell_0$ optimization that exploits homotopy for the $\ell_0$ regularization; it alternates between the least-squares (LS) optimization on the support and the support update, for which we also propose an efficient rule. The algorithm complexity is reduced when DCD iterations with a \emph{warm start} are used for the LS optimization, and, as most of the DCD operations are additions and bit-shifts, it is especially suited to real time implementation. The proposed algorithms are investigated in channel estimation scenarios and compared with known sparse recovery techniques such as the matching pursuit (MP) and YALL1 algorithms. The numerical examples show that the proposed techniques achieve a mean-squared error smaller than that of the YALL1 algorithm and complexity comparable to that of the MP algorithm

Sensor Signal and Information Processing II

In the current age of information explosion, newly invented technological sensors and software are now tightly integrated with our everyday lives. Many sensor processing algorithms have incorporated some forms of computational intelligence as part of their core framework in problem solving. These algorithms have the capacity to generalize and discover knowledge for themselves and learn new information whenever unseen data are captured. The primary aim of sensor processing is to develop techniques to interpret, understand, and act on information contained in the data. The interest of this book is in developing intelligent signal processing in order to pave the way for smart sensors. This involves mathematical advancement of nonlinear signal processing theory and its applications that extend far beyond traditional techniques. It bridges the boundary between theory and application, developing novel theoretically inspired methodologies targeting both longstanding and emergent signal processing applications. The topic ranges from phishing detection to integration of terrestrial laser scanning, and from fault diagnosis to bio-inspiring filtering. The book will appeal to established practitioners, along with researchers and students in the emerging field of smart sensors processing