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Part I of this paper reviewed the development of the linear active noise control (ANC) technique in the past decade. However, ANC systems might have to deal with some nonlinear components and the performance of linear ANC techniques may degrade in this scenario. To overcome this limitation, nonlinear ANC (NLANC) algorithms were developed. In Part II, we review the development of NLANC algorithms during the last decade. The contributions of heuristic ANC algorithms are outlined. Moreover, we emphasize recent advances of NLANC algorithms, such as spline ANC algorithms, kernel adaptive filters, and nonlinear distributed ANC algorithms. Then, we present recent applications of ANC technique including linear and nonlinear perspectives. Future research challenges regarding ANC techniques are also discussed. [ABSTRACT FROM AUTHOR]

• A novel diffusion adaptation framework and two simple yet efficient sparsity adaptive diffusion algorithms are proposed for CS reconstruction. • Novel analyses on convergence conditions and improvement of the step size upper bound are proposed. • Experimental results confirm the theoretical analysis, and show that the proposed diffusion algorithms can achieve desirable reconstruction accuracy as well as much faster convergence speed compared with stand-alone l 0 -LMS algorithm. Compressive sensing (CS) has drawn much attention in recent years due to its low sampling rate as well as high recovery accuracy. As an important procedure, reconstructing a sparse signal from a few measurement data has been intensively studied. In this paper, we propose a novel diffusion adaptation framework for CS reconstruction, where the reconstruction is performed in a distributed network. The data of the measurement matrix are partitioned into small parts and are stored in each node, which assigns the storage load in a decentralized manner. Information diffusion provides the reconstruction ability of each node. Then, a simple and efficient sparsity adaptive diffusion algorithm has been proposed to collaboratively recover the sparse signal over the network. The convergence of the proposed algorithm is analyzed. To further increase the convergence speed, a novel mini-batch based diffusion algorithm is also proposed. Simulation results show that the proposed framework and algorithms can achieve good reconstruction accuracy as well as a much faster convergence speed compared with stand-alone l 0 -LMS algorithm for CS. [ABSTRACT FROM AUTHOR]