Multiple-input multiple-output forward-looking ground-penetrating radar (GPR) systems can be used to detect landmines. To enhance its performance, two data-dependent imaging algorithms, based on the sparse learning via iterative minimization (SLIM) and sparse covariance-based estimation (SPICE) techniques for high-resolution imaging, applied to the time-domain GPR data, were previously developed. Time-domain SLIM (TD-SLIM) and time-domain SPICE (TD-SPICE) yield higher resolution and lower sidelobe compared with data-independent approaches such as delay-and-sum and recursive sidelobe minimization. However, the two data-dependent imaging algorithms are computationally expensive. To provide both improved landmine detection performance and significantly reduced computational time compared with the TD-SLIM and TD-SPICE algorithms, we propose herein the frequency-domain SLIM algorithm.

Ground-penetrating radar (GPR) has been used in a number of applications including the detection of landmines and improvised explosive devices. Most existing algorithms for forward looking GPR image reconstruction require that a hyperparameter or regularization parameter be chosen by the user. Selecting these parameters in an optimal fashion is a challenging problem that, in theory, can be addressed using cross validation and the L-curve method. Unfortunately, these hyperparameter selection methods are time consuming and not well suited for real-time applications. In this paper, we propose a hyperparameter-free algorithm that follows from a maximum a posteriori (MAP) formulation where the prior probability density function is obtained by the so-called “integrate-out" approach. First, we model the reflection coefficients as statistically independent random variables that are identically distributed and Laplacian with parameter, λ. Then, we analytically integrate out the parameter, λ, and optimize the resulting MAP objective function using the majorize-minimize optimization technique and soft-thresholding operator. We tested the algorithm using synthetic and real experimental data, and compared the results subjectively and objectively with the results obtained from wellknown algorithms. Although the evaluation is not an exhaustive study, it demonstrates the feasibility of the proposed algorithm.

An estimation method known as least absolute shrinkage and selection operator (LASSO) or ℓ1-regularized LS estimation has been found to perform well in a number of applications. In this paper, we use the majorize-minimize method to develop an algorithm for minimizing the LASSO objective function, which is the sum of a linear LS objective function plus an ℓ1 penalty term. The proposed algorithm, which we call the LASSO estimation via majorization-minimization (LMM) algorithm, is straightforward to implement, parallelizable, and guaranteed to produce LASSO objective function values that monotonically decrease. In addition, we formulate an extension of the LMM algorithm for reconstructing ground penetrating radar (GPR) images, that is much faster than the standard LMM algorithm and utilizes significantly less memory. Thus, the GPR specific LMM (GPR-LMM) algorithm is able to accommodate the big data associated with GPR imaging. We compare our proposed algorithms to the state-of-the-art ℓ1-regularized LS algorithms using a time and space complexity analysis. The GPR-LMM greatly outperforms the competing algorithms in terms of the performance metrics we considered. In addition, the reconstruction results of the standard LMM and GPR-LMM algorithms are evaluated using both simulated and real GPR data.

In this letter, we address the problem of detecting anomalies in multispectral images that are due to the presence of land mines. The proposed detection scheme follows from a generalized likelihood ratio test (GLRT) involving a mixture of certain probability density functions. More specifically, the GLRT is based on the assumption that the pixel values of a subblock within a single spectral-plane image can be modeled as a mixture of two Gaussian density functions (model distribution of background pixels) and a uniform density function (model distribution of anomalous pixels when they are present). We extend the single spectral-plane GLRT to the multiple spectral-plane case where the subblocks are from multispectral images. To assess the proposed GLRT, which we call the Gaussian-uniform GLRT (GU-GLRT) algorithm, we applied the GU-GLRT and popular RX algorithms to images from a real multispectral image sequence and used receiver operating characteristic (ROC) curves as the figure of merit. In the experiments that we conducted, the GU-GLRT outperformed the RX algorithm in the sense that the area under the ROC curve was greatest for the GU-GLRT algorithm.

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.

Recently, Timmermann and Nowak developed algorithms for estimating the means of independent Poisson random variables. The algorithms are based on a multiscale model where certain random variables are assumed to obey a beta-mixture density function. Timmermann and Nowak simplify the density estimation problem by assuming the beta parameters are known and only one mixture parameter is unknown. They use the observed data and the method of moments to estimate the unknown mixture parameter. Taking a different approach, we generate training data from the observed data and compute maximum likelihood estimates of all of the beta-mixture parameters. To assess the improved performance obtained by the proposed modification, we consider a denoising application using Poisson data.

We develop algorithms for obtaining regularized estimates of emission means in positron emission tomography. The first algorithm iteratively minimizes a penalized maximum-likelihood (PML) objective function. It is based on standard de-coupled surrogate functions for the ML objective function and de-coupled surrogate functions for a certain class of penalty functions. As desired, the PML algorithm guarantees nonnegative estimates and monotonically decreases the PML objective function with increasing iterations. The second algorithm is based on an iteration dependent, de-coupled penalty function that introduces smoothing while preserving edges. For the purpose of making comparisons, the MLEM algorithm and a penalized weighted least-squares algorithm were implemented. In experiments using synthetic data and real phantom data, it was found that, for a fixed level of background noise, the contrast in the images produced by the proposed algorithms was the most accurate.

The authors present a method for determining the time-of-arrival (TOA) of the ground component of a laser altimetry return signal. The proposed method takes advantage of the fact that the ground component or ground return is approximately Gaussian shaped and occurs at the end of the return signal. In particular, the method exploits the well-known result that the TOA of a known signal in white Gaussian noise can be estimated using matched filtering. An important feature of the method is that it addresses the problem of overlap between ground and vegetation returns. Simulations using synthetic data indicate that the proposed method provides excellent estimates and greatly outperforms a conventional method. It is anticipated that the method will be applicable to laser altimetry applications where the ground return can be assumed to have an approximately known shape.

In this paper, two iterative methods for correcting attenuation errors in positron emission tomography (PET) are proposed. The first method is a maximum likelihood (ML) method that simultaneously estimates the emission intensity and attenuation density. The second one is a least squares (LS) reprojection method, where the survival probabilities are estimated by reprojecting a LS estimate of the attenuation density. Both methods are guaranteed to produce nonnegative estimates of the emission intensity and attenuation density, provided that the initial estimates are nonnegative. From simulation studies, it appears that the proposed methods have less noise and provide higher quality images, particularly for short transmission scans (less than 10 minutes), than the EMML algorithm with standard correction.

We present unpenalized and penalized weighted least-squares (WLS) reconstruction methods for positron emission tomography (PET), where the weights are based on the covariance of a model error and depend on the unknown parameters. The penalty function for the latter method is chosen so that certain a priori information is incorporated. The algorithms used to minimize the WLS objective functions guarantee nonnegative estimates and, experimentally, they converged faster than the maximum likelihood expectation-maximization (ML-EM) algorithm and produced images that had significantly better resolution and contrast. Although simulations suggest that the proposed algorithms are globally convergent, a proof of convergence has not yet been found. Nevertheless, we are able to show that the unpenalized method produces estimates that decrease the objective function monotonically with increasing iterations.

A class of algorithms is presented that estimates the displacement vector from two successive image frames consisting of signal plus noise. In the model, the signals are assumed to be either non-Gaussian or (quasistationary) deterministic; and, via a consistency result for cumulant estimators, the authors unify the stochastic and deterministic signal viewpoints. The noise sources are assumed to be Gaussian (perhaps spatially and temporally correlated) and of unknown covariance. Viewing image motion estimation as a 2D time delay estimation problem, the displacement vector of a moving object is estimated by solving linear equations involving third-order auto-cumulants and cross-cumulants. Additionally, a block-matching algorithm is developed that follows from a cumulant-error optimality criterion. Finally, the displacement vector for each pel is estimated using a recursive algorithm that minimizes a mean 2D fourth-order cumulant criterion. Simulation results are presented and discussed.

In this paper, we address the problem of estimating the parameters of a Hammerstein model. Hammerstein models, which consist of a nonlinear memoryless gain followed by a linear time-invariant system, have been used to identify nonlinear systems. We assume that the gain is in polynomial form, and that the system is an ARMA filter. The input and output are available, and the output is assumed to be corrupted by additive Gaussian noise of unknown covariance. Transforming the problem into the cumulant domain, we suppress the effect of the noise and estimate the model parameters using a linear, iterative method. Simulations are presented to illustrate the performance of the proposed method.>

A class of algorithms is presented that estimate the displacement vector from two successive image frames. The frames are assumed to be corrupted by Gaussian (perhaps correlated) noises of unknown covariance. Viewing image motion estimation as a 2-D time delay estimation problem, the displacement vector of a moving object is estimated by solving linear equations involving third-order auto-cumulants and cross-cumulants. Additionally, a block-matching type algorithm is developed which follows from a cumulant-error optimality criterion. Finally, using a recursive algorithm the displacement vector for each pel is estimated by minimizing a 2-D fourth-order cumulant criterion. Simulation results are presented and discussed.>