A Max-Product EM Algorithm for Reconstructing Markov-tree Sparse Signals from Compressive Samples

We propose a Bayesian expectation-maximization (EM) algorithm for reconstructing Markov-tree sparse signals via belief propagation. The measurements follow an underdetermined linear model where the regression-coefficient vector is the sum of an unknown approximately sparse signal and a zero-mean white Gaussian noise with an unknown variance. The signal is composed of large- and small-magnitude components identified by binary state variables whose probabilistic dependence structure is described by a Markov tree. Gaussian priors are assigned to the signal coefficients given their state variables and the Jeffreys' noninformative prior is assigned to the noise variance. Our signal reconstruction scheme is based on an EM iteration that aims at maximizing the posterior distribution of the signal and its state variables given the noise variance. We construct the missing data for the EM iteration so that the complete-data posterior distribution corresponds to a hidden Markov tree (HMT) probabilistic graphical model that contains no loops and implement its maximization (M) step via a max-product algorithm. This EM algorithm estimates the vector of state variables as well as solves iteratively a linear system of equations to obtain the corresponding signal estimate. We select the noise variance so that the corresponding estimated signal and state variables obtained upon convergence of the EM iteration have the largest marginal posterior distribution. We compare the proposed and existing state-of-the-art reconstruction methods via signal and image reconstruction experiments.Comment: To appear in IEEE Transactions on Signal Processin

A geometric morphometric relationship predicts stone flake shape and size variability

The archaeological record represents a window onto the complex relationship between stone artefact variance and hominin behaviour. Differences in the shapes and sizes of stone flakes-the most abundant remains of past behaviours for much of human evolutionary history-may be underpinned by variation in a range of different environmental and behavioural factors. Controlled flake production experiments have drawn inferences between flake platform preparation behaviours, which have thus far been approximated by linear measurements, and different aspects of overall stone flake variability (Dibble and Rezek J Archaeol Sci 36:1945-1954, 2009; Lin et al. Am Antiq 724-745, 2013; Magnani et al. J Archaeol Sci 46:37-49, 2014; Rezek et al. J Archaeol Sci 38:1346-1359, 2011). However, when the results are applied to archaeological assemblages, there remains a substantial amount of unexplained variability. It is unclear whether this disparity between explanatory models and archaeological data is a result of measurement error on certain key variables, whether traditional analyses are somehow a general limiting factor, or whether there are additional flake shape and size drivers that remain unaccounted for. To try and circumvent these issues, here, we describe a shape analysis approach to assessing stone flake variability including a newly developed three-dimensional geometric morphometric method (\u273DGM\u27). We use 3DGM to demonstrate that a relationship between platform and flake body governs flake shape and size variability. Contingently, we show that by using this 3DGM approach, we can use flake platform attributes to both (1) make fairly accurate stone flake size predictions and (2) make relatively detailed predictions of stone flake shape. Whether conscious or instinctive, an understanding of this geometric relationship would have been critical to past knappers effectively controlling the production of desired stone flakes. However, despite being able to holistically and accurately incorporate three-dimensional flake variance into our analyses, the behavioural drivers of this variance remain elusive

Weighted Least Squares Techniques for Improved Received Signal Strength Based Localization

The practical deployment of wireless positioning systems requires minimizing the calibration procedures while improving the location estimation accuracy. Received Signal Strength localization techniques using propagation channel models are the simplest alternative, but they are usually designed under the assumption that the radio propagation model is to be perfectly characterized a priori. In practice, this assumption does not hold and the localization results are affected by the inaccuracies of the theoretical, roughly calibrated or just imperfect channel models used to compute location. In this paper, we propose the use of weighted multilateration techniques to gain robustness with respect to these inaccuracies, reducing the dependency of having an optimal channel model. In particular, we propose two weighted least squares techniques based on the standard hyperbolic and circular positioning algorithms that specifically consider the accuracies of the different measurements to obtain a better estimation of the position. These techniques are compared to the standard hyperbolic and circular positioning techniques through both numerical simulations and an exhaustive set of real experiments on different types of wireless networks (a wireless sensor network, a WiFi network and a Bluetooth network). The algorithms not only produce better localization results with a very limited overhead in terms of computational cost but also achieve a greater robustness to inaccuracies in channel modeling

Extended Target Recognition in Cognitive Radar Networks

We address the problem of adaptive waveform design for extended target recognition in cognitive radar networks. A closed-loop active target recognition radar system is extended to the case of a centralized cognitive radar network, in which a generalized likelihood ratio (GLR) based sequential hypothesis testing (SHT) framework is employed. Using Doppler velocities measured by multiple radars, the target aspect angle for each radar is calculated. The joint probability of each target hypothesis is then updated using observations from different radar line of sights (LOS). Based on these probabilities, a minimum correlation algorithm is proposed to adaptively design the transmit waveform for each radar in an amplitude fluctuation situation. Simulation results demonstrate performance improvements due to the cognitive radar network and adaptive waveform design. Our minimum correlation algorithm outperforms the eigen-waveform solution and other non-cognitive waveform design approaches