Dynamics of Damped Approximate Message Passing Algorithms For linear system models, the approximate massage passing (AMP) is one of the effective iterative sparse recovery algorithms. However, depending on a measurement matrix ensemble, AMP may face convergence issues. Some algorithms are proposed so far to avoid the convergence issues, e.g., the orthogonal AMP (OAMP) and the mean removal. One of the simplest ways to avoid the convergence issues is to introduce a damping effect into AMP. In this paper, we derive a simple recursive equations that characterizes the damped OAMP, which is an OAMP in which the damping effect is introduced, and show that the result can be applied to the damped version of the original AMP.

Online Distributed Learning Over Graphs With Multitask GraphFilter Models In this article, we are interested in adaptive and distributed estimation of graph filters from streaming data. We formulate this problem as a consensus estimation problem over graphs, which can be addressed with diffusion LMS strategies. Most popular graphshift operators such as those based on the graph Laplacian matrix, or the adjacency matrix, are not energy preserving. This may result in an illconditioned estimation problem, and reduce the convergence speed of the distributed algorithms. To address this issue and improve the transient performance, we introduce a preconditioned graph diffusion LMS algorithm. We also propose a computationally efficient version of this algorithm by approximating the Hessian matrix with local information. Performance analyses in the mean and meansquare sense are provided. Finally, we consider a more general problem where the filter coefficients to estimate may vary over the graph. To avoid a large estimation bias, we introduce an unsupervised clustering method for splitting the global estimation problem into local ones. Numerical results show the effectiveness of the proposed algorithms and validate the theoretical results.