Aleksandar Dogandžić

AUTOMATIC HARD THRESHOLDING FOR SPARSE SIGNAL RECONSTRUCTION FROM NDE MEASUREMENTS

We propose an automatic hard thresholding (AHT) method for sparse‐signal reconstruction. The measurements follow an underdetermined linear model, where the regression‐coefficient vector is modeled as a superposition of an unknown deterministic sparse‐signal component and a zero‐mean white Gaussian component with unknown variance. Our method demands no prior knowledge about signal sparsity. Our AHT scheme approximately maximizes a generalized maximum likelihood (GML) criterion, providing an approximate GML estimate of the signal sparsity level and an empirical Bayesian estimate of the regression coefficients. We apply the proposed method to reconstruct images from sparse computerized tomography projections and compare it with existing approaches.

Defect Detection in Correlated Noise

We present methods for detecting NDE defect signals in correlated noise having unknown covariance. The proposed detectors are derived using the statistical theory of generalized likelihood ratio (GLR) tests and multivariate analysis of variance (MANOVA). We consider both real and complex data models. To allow accurate estimation of the noise covariance, we incorporate secondary data containing only noise into detector design. Probability distributions of the GLR test statistics are derived under the null hypothesis, i.e. assuming that the signal is absent, and used for detector design. We apply the proposed methods to simulated and experimental data and demonstrate their superior performance compared with the detectors that neglect noise correlation.

A Statistical Model for Eddy‐Current Signals from Steam Generator Tubes

We propose a model for characterizing amplitude and phase probability distributions of eddy‐current signals. The squared amplitudes and phases of the potential defect signals are modeled as independent, identically distributed (i.i.d.) random variables following gamma and von Mises distributions, respectively. We derive a maximum likelihood (ML) method for estimating the amplitude and phase distribution parameters from measurements corrupted by additive complex white Gaussian noise. Newton‐Raphson iteration is utilized to compute the ML estimates of the unknown parameters. The obtained estimates can be used for flaw detection as well as efficient feature extractors in a defect classification scheme. Finally, we apply the proposed method to analyze rotating‐probe eddy‐current data from tube inspection of a steam generator in a nuclear power plant.

Editorial: distributed signal processing techniques for wireless sensor networks

1Department of Electrical and Computer Engineering, Texas A&M University, College Station, TX 77843, USA 2Department of Electrical and Computer Engineering, Stevens Institute of Technology, Hoboken, NJ 07030, USA 3Department of Electrical and Computer Engineering, Iowa State University, Ames, IA 50011, USA 4Department of Electrical and Computer Engineering, North Carolina State University, Raleigh, NC 27695, USA 5Department of Electrical and Computer Engineering, University of Texas at San Antonio, San Antonio, TX 78249, USA

ECME Hard Thresholding Methods for Image Reconstruction from Compressive Samples

We propose two hard thresholding schemes for image reconstruction from compressive samples. The measurements follow an underdetermined linear model, where the regression-coefficient vector is a sum of an unknown deterministic sparse signal component and a zero-mean white Gaussian component with an unknown variance. We derived an expectation-conditional maximization either (ECME) iteration that converges to a local maximum of the likelihood function of the unknown parameters for a given image sparsity level. Here, we present and analyze a double overrelaxation (DORE) algorithm that applies two successive overrelaxation steps after one ECME iteration step, with the goal to accelerate the ECME iteration. To analyze the reconstruction accuracy, we introduce minimum sparse subspace quotient (minimum SSQ), a more flexible measure of the sampling operator than the well-established restricted isometry property (RIP). We prove that, if the minimum SSQ is sufficiently large, the DORE algorithm achieves perfect or near-optimal recovery of the true image, provided that its transform coefficients are sparse or nearly sparse, respectively. We then describe a multiple-initialization DORE algorithm (DOREMI) that can significantly improve DOREs reconstruction performance. We present numerical examples where we compare our methods with existing compressive sampling image reconstruction approaches.

Algorithms for sparse X-ray CT image reconstruction of objects with known contour

We develop algorithms for sparse X-ray computed tomography (CT) image reconstruction of objects with known contour, where the signal outside the contour is assumed to be zero. We first propose a constrained residual squared error minimization criterion that incorporates both the knowledge of the objects contour and signal sparsity in an appropriate transform domain. We then present convex relaxation and greedy approaches to approximately solving this minimization problem; our greedy mask iterative hard thresholding schemes guarantee monotonically non-increasing residual squared error. We also apply mask minimum norm (mask MN) and least squares (mask LS) methods that ignore signal sparsity and solve the residual squared error minimization problem that imposes only the object contour constraint. We compare the proposed schemes with existing large-scale sparse signal reconstruction methods via numerical simulations and demonstrate that, by exploiting both the object contour information in the underlying ima...

Image reconstruction from compressive samples via a max-product EM algorithm

We propose a Bayesian expectation-maximization (EM) algorithm for reconstructing structured approximately 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 hidden Markov tree (HMT). 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 employ a max-product algorithm to implement the maximization (M) step of our EM iteration. The noise variance is a regularization parameter that controls signal sparsity. 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. Our numerical examples show that the proposed algorithm achieves better reconstruction performance compared with the state-of-the-art methods.

SPARSE X‐RAY CT IMAGE RECONSTRUCTION USING ECME HARD THRESHOLDING METHODS

We apply expectation‐conditional maximization either (ECME) hard thresholding algorithms to X‐ray computed tomography (CT) reconstruction, where we implement the sampling operator using the nonuniform fast Fourier transform (NUFFT). The measurements follow an underdetermined linear model, where the regression‐coefficient vector is a sum of an unknown deterministic sparse signal component and a zero‐mean white Gaussian component with an unknown variance. Our ECME schemes aim at maximizing this model’s likelihood function with respect to the sparse signal and variance of the random signal component. These schemes exploit signal sparsity in the discrete wavelet transform (DWT) domain and yield better reconstructions than the traditional filtered backprojection (FBP) approach, which is demonstrated via numerical examples. In contrast with FBP, our methods achieve artifact‐free reconstructions in undersampled and limited‐angle projection examples. We also compare the ECME schemes with a state‐of‐the‐art convex...

Markov Chain Monte Carlo Defect Identification in NDE Images

We derive a hierarchical Bayesian method for identifying elliptically‐shaped regions with elevated signal levels in NDE images. We adopt a simple elliptical parametric model for the shape of the defect region and assume that the defect signals within this region are random following a truncated Gaussian distribution. Our truncated‐Gaussian model ensures that the signals within the defect region are higher than the baseline level corresponding to the noise‐only case. We derive a closed‐form expression for the kernel of the posterior probability distribution of the location, shape, and defect‐signal distribution parameters (model parameters). This result is then used to develop Markov chain Monte Carlo (MCMC) algorithms for simulating from the posterior distributions of the model parameters and defect signals. Our MCMC algorithms are applied sequentially to identify multiple potential defect regions. For each potential defect, we construct Bayesian confidence regions for the estimated parameters. Estimated ...

Bayesian Defect Signal Analysis

We develop a Bayesian framework for estimating defect signals from noisy measurements. We propose a parametric model for the shape of the defect region and assume that the defect signal within this region is random with unknown mean and variance. Markov chain Monte Carlo (MCMC) algorithms are derived for simulating from the posterior distributions of the model parameters and defect signals. These algorithms are utilized to identify potential defect regions and estimate their size and reflectivity. We specialize the proposed framework to elliptical defect shape and Gaussian signal and noise models and apply it to experimental ultrasonic C‐scan data from an inspection of a cylindrical titanium billet.