We develop a sparse image reconstruction method for Poisson-distributed polychromatic X-ray computed tomography (CT) measurements under the blind scenario where the material of the inspected object and the incident energy spectrum are unknown. We employ our mass-attenuation spectrum parameterization of the noiseless measurements for single-material objects and express the mass-attenuation spectrum as a linear combination of B-spline basis functions of order one. A block coordinate-descent algorithm is developed for constrained minimization of a penalized Poisson negative log-likelihood (NLL) cost function, where constraints and penalty terms ensure nonnegativity of the spline coefficients and nonnegativity and sparsity of the density-map image; the image sparsity is imposed using a convex total-variation (TV) norm penalty term. This algorithm alternates between a Nesterov's proximal-gradient (NPG) step for estimating the density-map image and a limited-memory Broyden-Fletcher-Goldfarb-Shanno with box constraints (L-BFGS-B) step for estimating the incident-spectrum parameters. We establish conditions for biconvexity of the penalized NLL objective function, which, if satisfied, ensures monotonicity of the NPG-BFGS iteration. We also show that the penalized NLL objective satisfies the Kurdyka-Lojasiewicz property, which is important for establishing local convergence of block-coordinate descent schemes in biconvex optimization problems. Simulation examples demonstrate the performance of the proposed scheme.

We develop a beam-hardening correction method for polychromatic x-ray computed tomography (CT) reconstruction based on mass attenuation coefficient discretization. We assume that the inspected object consists of an unknown single material and that the incident x-ray spectrum is unknown. In this case, the standard photon-energy discretization of the Beer's law measurement equation leads to an excessive number of unknown parameters and scaling ambiguity. To obtain a parsimonious measurement model parametrization, we first rewrite the measurement equation in terms of integral expressions of the mass attenuation rather than photon energy. The resulting integrals can be discretized easily thanks to the fact that the range of mass attenuations is bounded and, in practice, fairly narrow. We then develop a constrained least-squares optimization approach for reconstructing the underlying object from log-scale measurements, where we impose the nonnegativity constraint to both the signal and the x-ray spectrum density estimates. We demonstrate the performance of the proposed method via a numerical example where we compare it with the standard filtered backprojection (FBP), which ignores the polychromatic nature of the measurements.

Abstract We present iterative channel estimation and decoding schemes for multi‐input multi‐output (MIMO) Rayleigh block fading channels in spatially correlated noise. An expectation‐maximization (EM) algorithm is utilized to find the maximum likelihood (ML) estimates of the channel and spatial noise covariance matrices, and to compute soft information of coded symbols which is sent to an error‐control decoder. The extrinsic information produced by the decoder is then used to refine channel estimation. Several iterations are performed between the above channel estimation and decoding steps. We derive modified Cramer–Rao Bound (MCRB) for the unknown channel and noise parameters, and show that the proposed EM‐based channel estimation scheme achieves the MCRB at medium and high SNRs. For a bit error rate of 10−6and long frame length, there is negligible performance difference between the proposed scheme and the ideal coherent detector that utilizes the true channel and noise covariance matrices. Copyright © 2006 John Wiley & Sons, Ltd.

We compute Crame/spl acute/r-Rao bounds (CRBs) for the target and compound-Gaussian clutter parameters using radar array measurements. In particular, we compute CRBs for (i) complex target amplitudes, (ii) the spatial covariance matrix of the speckle component, (iii) texture distribution parameters. We first derive general CRB expressions under an arbitrary texture model and simplify them for gamma and inverse gamma texture distributions. We use the generalized Gauss-Laguerre quadrature to compute the CRBs for gamma texture, whereas the CRBs for inverse-gamma texture do not require numerical integration. We use numerical simulations to validate our results.

We present methods for dynamic estimation and prediction of local mean (shadow) powers from instantaneous signal powers in composite fading-shadowing wireless communication scenarios. We adopt a Nakagami-m fading model for the instantaneous signal powers and a first-order autoregressive - AR(1) - model for the shadow process in decibels. Sequential Bayesian analysis is applied to estimate the shadow powers assuming that the Nakagami-m and AR(1) model parameters are known. We also develop a method for jointly estimating both the shadow powers and unknown model parameters. Numerical simulations demonstrate the performance of the proposed methods.

We propose maximum likelihood (ML) methods for estimating the parameters of composite gamma-lognormal fading channels. Newton-Raphson and expectation-maximization (EM) algorithms are developed to compute the ML estimates of the mean and variance of the shadowing component, and the Nakagami-m parameter of the fading component. We also derive Cramer-Rao bounds (CRBs) for the unknown parameters. Numerical simulations demonstrate the performance of the proposed method.

We derive Chernoff bounds on pairwise error probabilities of coherent and noncoherent space-time signaling schemes. First, general Chernoff bound expressions are derived for a correlated Ricean fading channel and correlated additive Gaussian noise. Then, we specialize the obtained results to the cases of space-time-separable noise, white noise, and uncorrelated fading. We derive approximate Chernoff bounds for high and low signal-to-noise ratios (SNRs) and propose optimal signaling schemes. We also compute the optimal number of transmitter antennas for noncoherent signaling with unitary mutually orthogonal space-time codes.

We propose finite-length multi-input multi-output adaptive equalization methods for "smart" antenna arrays using the statistical theory of canonical correlations. We show that the proposed methods are related to maximum likelihood reduced-rank channel and noise estimation algorithms in unknown spatially correlated noise, and to several recently proposed adaptive equalization schemes.

We present maximum likelihood (ML) methods for active estimation of range (time delay), velocity (Doppler shift), and direction of a point target with a radar array in spatially correlated noise with unknown covariance. We consider structured and unstructured array response models and compute the Cramer-Rao bound (CRB) for the time delay, Doppler shift, and direction of arrival. We derive ambiguity functions for the above models and discuss the relationship between identifiability, ambiguity, and the Fisher information matrix.