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We present penalized weighted least-squares (PWLS) and penalized maximum-likelihood (PML) methods for reconstructing transmission images from positron emission tomography transmission data. First, we view the problem of minimizing the weighted least-squares (WLS) and maximum likelihood objective functions as a sequence of nonnegative least-squares minimization problems. This viewpoint follows from using certain quadratic functions as surrogate functions for the WLS and maximum likelihood objective functions. Second, we construct surrogate functions for a class of penalty functions that yield closed form expressions for the iterates of the PWLS and PML algorithms. Due to the slow convergence of the PWLS and PML algorithms, accelerated versions of them are developed that are theoretically guaranteed to monotonically decrease their respective objective functions. In experiments using real phantom data, the PML images produced the most accurate attenuation correction factors. On the other hand, the PWLS images produced images with the highest levels of contrast for low-count data.

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In this paper, we present new adaptive importance sampling techniques based on stochastic Newton recursions. Their applicability to the performance evaluation of communication systems is studied. Besides bit-error rate (BER) estimation, the techniques are used for system parameter optimization. Two system models that are analytically tractable are employed to demonstrate the validity of the techniques. As an application to situations that are analytically intractable and numerically intensive, the influence of crosstalk in a wavelength-division multiplexing (WDM) crossconnect is assessed. In order to consider a realistic system model, optimal setting of thresholds in the detector is carried out while estimating error rate performances. Resulting BER estimates indicate that the tolerable crosstalk levels are significantly higher than predicted in the literature. This finding has a strong impact on the design of WDM networks. Power penalties induced by the addition of channels can also be accurately predicted in short run-times.

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