<![CDATA[ IEEE Transactions on Signal Processing - new TOC ]]>
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TOC Alert for Publication# 78 2018April 19<![CDATA[SILVar: Single Index Latent Variable Models]]>66112790280310053<![CDATA[Fast Low-Rank Bayesian Matrix Completion With Hierarchical Gaussian Prior Models]]>6611280428171810<![CDATA[Phase Retrieval via Reweighted Amplitude Flow]]>$n$ -dimensional solution $boldsymbol {x}$ to a system of quadratic equations of the form $y_i=|langle boldsymbol {a}_i,boldsymbol {x}rangle |^2$ for $1leq i leq m$, which is also known as the generalized phase retrieval problem. For this NP-hard problem, a novel approach is developed for minimizing the amplitude-based least-squares empirical loss, which starts with a weighted maximal correlation initialization obtainable through a few power or Lanczos iterations, followed by successive refinements based on a sequence of iteratively reweighted gradient iterations. The two stages (initialization and gradient flow) distinguish themselves from prior contributions by the inclusion of a fresh (re)weighting regularization procedure. For certain random measurement models, the novel scheme is shown to be able to recover the true solution $boldsymbol {x}$ in time proportional to reading the data $lbrace (boldsymbol {a}_i;y_i)rbrace _{1leq i leq m}$. This holds with high probability and without extra assumption on the signal vector $boldsymbol {x}$ to be recovered, provided that the number $m$ of equations is some constant $c>0$ times the number $n$ of unknowns in the signal vector, namely $m>cn$ . Empirically, the upshots of this contribution are: first, (almost) $text{100}{%}$ perfect signal recovery in the high-dimensional (say $ngeq 2000$) regime given only an information-theoretic limit number of noiseless equations, namely $m=2n-1$, in the real Gaussian case; and second, (nearly) optimal statistical accuracy in the presence of additive noise of bounded support. Finally, substantial numerical tests using both synthetic data and real images corroborate markedly improved recovery performance and computational efficiency of the novel scheme relative to the state-of-the-art approaches.]]>6611281828331077<![CDATA[On Nonconvex Decentralized Gradient Descent]]>nonconvex optimization, our understanding is more limited. When we lose convexity, we cannot hope that our algorithms always return global solutions though they sometimes still do. Somewhat surprisingly, the decentralized consensus algorithms, DGD and Prox-DGD, retain most other properties that are known in the convex setting. In particular, when diminishing (or constant) step sizes are used, we can prove convergence to a (or a neighborhood of) consensus stationary solution under some regular assumptions. It is worth noting that Prox-DGD can handle nonconvex nonsmooth functions if their proximal operators can be computed. Such functions include SCAD, MCP, and $ell _q$ quasi-norms, $qin [0,1)$. Similarly, Prox-DGD can take the constraint to a nonconvex set with an easy projection. To establish these properties, we have to introduce a completely different line of analysis, as well as modify existing proofs that were used in the convex setting.]]>661128342848686<![CDATA[Application of Manifold Separation to Parametric Localization for Incoherently Distributed Sources]]>6611284928601394<![CDATA[Blind Interference Alignment for the <inline-formula><tex-math notation="LaTeX">$K$</tex-math> </inline-formula>-User MISO BC Under Limited Symbol Extension]]>$K$ -user multiple-input single-output broadcast channel (BC) in the absence of channel state information at the transmitter under the finite channel coherent time. For the considered $K$-user BC, a transmitter is equipped with multiple conventional antennas, and receivers are equipped with a reconfigurable antenna that is capable of dynamically modifying the receiving beam radiation pattern. In this system, we propose a blind interference alignment scheme that is able to allocate an asymmetric number of information symbols to each user, which is essentially required to improve DoFs under limited symbol extension. A generalized systematic construction method of transmit beamforming vectors and receiving mode selection patterns to deal with such asymmetric allocation is established. As a consequence, for a broad class of network configurations and symbol extension constraints, the proposed scheme attains an improved sum DoF compared to the previous works, allowing only for the same number of information symbols for all users.]]>661128612875921<![CDATA[Beam Design and User Scheduling for Nonorthogonal Multiple Access With Multiple Antennas Based on Pareto Optimality]]>$M$ -user MISO BCs with SIC is solved.]]>661128762891922<![CDATA[Using Joint Generalized Eigenvectors of a Set of Covariance Matrix Pencils for Deflationary Blind Source Extraction]]>661128922904851<![CDATA[Learning the MMSE Channel Estimator]]>${mathcal O}(Mlog M)$ floating point operations, where $M$ is the channel dimension. While in the absence of structure the complexity is much higher, we obtain a similarly efficient (but suboptimal) estimator by using the MMSE estimator of the structured model as a blueprint for the architecture of a neural network. This network learns the MMSE estimator for the unstructured model, but only within the given class of estimators that contains the MMSE estimator for the structured model. Numerical simulations with typical spatial channel models demonstrate the generalization properties of the chosen class of estimators to realistic channel models.]]>6611290529171074<![CDATA[Low-Rank Matrix Recovery From Noisy, Quantized, and Erroneous Measurements]]>6611291829321370