Estimation from PET data of transient changes in dopamine concentration induced by alcohol: support for a non-parametric signal estimation method.

We previously developed a model-independent technique (non-parametric ntPET) for extracting the transient changes in neurotransmitter concentration from paired (rest & activation) PET studies with a receptor ligand. To provide support for our method, we introduced three hypotheses of validation based on work by Endres and Carson (1998 J. Cereb. Blood Flow Metab. 18 1196-210) and Yoder et al (2004 J. Nucl. Med. 45 903-11), and tested them on experimental data. All three hypotheses describe relationships between the estimated free (synaptic) dopamine curves (FDA(t)) and the change in binding potential (DeltaBP). The veracity of the FDA(t) curves recovered by nonparametric ntPET is supported when the data adhere to the following hypothesized behaviors: (1) DeltaBP should decline with increasing DA peak time, (2) DeltaBP should increase as the strength of the temporal correlation between FDA(t) and the free raclopride (FRAC(t)) curve increases, (3) DeltaBP should decline linearly with the effective weighted availability of the receptor sites. We analyzed regional brain data from 8 healthy subjects who received two [11C]raclopride scans: one at rest, and one during which unanticipated IV alcohol was administered to stimulate dopamine release. For several striatal regions, nonparametric ntPET was applied to recover FDA(t), and binding potential values were determined. Kendall rank-correlation analysis confirmed that the FDA(t) data followed the expected trends for all three validation hypotheses. Our findings lend credence to our model-independent estimates of FDA(t). Application of nonparametric ntPET may yield important insights into how alterations in timing of dopaminergic neurotransmission are involved in the pathologies of addiction and other psychiatric disorders.

Spatial random tree grammars for modeling hierarchal structure in images with regions of arbitrary shape.

We present a novel probabilistic model for the hierarchal structure of an image and its regions. We call this model spatial random tree grammars (SRTGs). We develop algorithms for exact computation of likelihoods and MAP estimates and exact EM updates for model-parameter estimation. We collectively call these algorithms the center-surround algorithm. We use the center-surround algorithm to automatically estimate the ML parameters of SRTGs, classify images based on their likelihood and based on the MAP estimate of the associated hierarchal structure. We apply our method to the task of classifying natural images and demonstrate that the addition of hierarchal structure significantly improves upon the performance of a baseline model that lacks such structure.

A phantom-based forward projection approach in support of model-based iterative reconstructions for HAADF-STEM tomography.

We introduce a forward model for the computation of high angle annular dark field (HAADF) images of nano-crystalline spherical particles and apply it to image simulations for assemblies of nano-spheres of Al, Cu, and Au with a range of sizes, as well as an artificial bi-sphere, consisting of solid hemispheres of Al and Cu or Al and Au. Comparison of computed intensity profiles with experimental observations on Al spheres at different microscope accelerating voltages provides confidence in the forward model. Simulated tomographic tilt series for both HAADF and bright field (BF) images are then used to illustrate that the model-based iterative reconstruction (MBIR) approach is capable of reconstructing sphere configurations of mixed atomic number, with the correct relative reconstructed intensity ratio proportional to the square of the atomic number ratio.

Direct reconstruction of kinetic parameter images from dynamic PET data.

Our goal in this paper is the estimation of kinetic model parameters for each voxel corresponding to a dense three-dimensional (3-D) positron emission tomography (PET) image. Typically, the activity images are first reconstructed from PET sinogram frames at each measurement time, and then the kinetic parameters are estimated by fitting a model to the reconstructed time-activity response of each voxel. However, this "indirect" approach to kinetic parameter estimation tends to reduce signal-to-noise ratio (SNR) because of the requirement that the sinogram data be divided into individual time frames. In 1985, Carson and Lange proposed, but did not implement, a method based on the expectation-maximization (EM) algorithm for direct parametric reconstruction. The approach is "direct" because it estimates the optimal kinetic parameters directly from the sinogram data, without an intermediate reconstruction step. However, direct voxel-wise parametric reconstruction remained a challenge due to the unsolved complexities of inversion and spatial regularization. In this paper, we demonstrate and evaluate a new and efficient method for direct voxel-wise reconstruction of kinetic parameter images using all frames of the PET data. The direct parametric image reconstruction is formulated in a Bayesian framework, and uses the parametric iterative coordinate descent (PICD) algorithm to solve the resulting optimization problem. The PICD algorithm is computationally efficient and is implemented with spatial regularization in the domain of the physiologically relevant parameters. Our experimental simulations of a rat head imaged in a working small animal scanner indicate that direct parametric reconstruction can substantially reduce root-mean-squared error (RMSE) in the estimation of kinetic parameters, as compared to indirect methods, without appreciably increasing computation.

The Three-Dimensional Morphology of Growing Dendrites.

The processes controlling the morphology of dendrites have been of great interest to a wide range of communities, since they are examples of an out-of-equilibrium pattern forming system, there is a clear connection with battery failure processes, and their morphology sets the properties of many metallic alloys. We determine the three-dimensional morphology of free growing metallic dendrites using a novel X-ray tomographic technique that improves the temporal resolution by more than an order of magnitude compared to conventional techniques. These measurements show that the growth morphology of metallic dendrites is surprisingly different from that seen in model systems, the morphology is not self-similar with distance back from the tip, and that this morphology can have an unexpectedly strong influence on solute segregation in castings. These experiments also provide benchmark data that can be used to validate simulations of free dendritic growth.

A multiscale random field model for Bayesian image segmentation.

Many approaches to Bayesian image segmentation have used maximum a posteriori (MAP) estimation in conjunction with Markov random fields (MRF). Although this approach performs well, it has a number of disadvantages. In particular, exact MAP estimates cannot be computed, approximate MAP estimates are computationally expensive to compute, and unsupervised parameter estimation of the MRF is difficult. The authors propose a new approach to Bayesian image segmentation that directly addresses these problems. The new method replaces the MRF model with a novel multiscale random field (MSRF) and replaces the MAP estimator with a sequential MAP (SMAP) estimator derived from a novel estimation criteria. Together, the proposed estimator and model result in a segmentation algorithm that is not iterative and can be computed in time proportional to MN where M is the number of classes and N is the number of pixels. The also develop a computationally efficient method for unsupervised estimation of model parameters. Simulations on synthetic images indicate that the new algorithm performs better and requires much less computation than MAP estimation using simulated annealing. The algorithm is also found to improve classification accuracy when applied to the segmentation of multispectral remotely sensed images with ground truth data.

A unified approach to statistical tomography using coordinate descent optimization.

Over the past years there has been considerable interest in statistically optimal reconstruction of cross-sectional images from tomographic data. In particular, a variety of such algorithms have been proposed for maximum a posteriori (MAP) reconstruction from emission tomographic data. While MAP estimation requires the solution of an optimization problem, most existing reconstruction algorithms take an indirect approach based on the expectation maximization (EM) algorithm. We propose a new approach to statistically optimal image reconstruction based on direct optimization of the MAP criterion. The key to this direct optimization approach is greedy pixel-wise computations known as iterative coordinate decent (ICD). We propose a novel method for computing the ICD updates, which we call ICD/Newton-Raphson. We show that ICD/Newton-Raphson requires approximately the same amount of computation per iteration as EM-based approaches, but the new method converges much more rapidly (in our experiments, typically five to ten iterations). Other advantages of the ICD/Newton-Raphson method are that it is easily applied to MAP estimation of transmission tomograms, and typical convex constraints, such as positivity, are easily incorporated.

Optimal transforms for multispectral and multilayer image coding.

Multispectral images are composed of a series of images at differing optical wavelengths. Since these images can be quite large, they invite efficient source coding schemes for reducing storage and transmission requirements. Because multispectral images include a third (spectral) dimension with nonstationary behavior, these multilayer data sets require specialized coding techniques. The authors develop both a theory and specific methods for performing optimal transform coding of multispectral images. The theory is based on the assumption that a multispectral image may be modeled as a set of jointly stationary Gaussian random processes. Therefore, the methods may be applied to any multilayer data set which meets this assumption. Although the authors do not assume the autocorrelation has a separable form, they show that the optimal transform for coding has a partially separable structure. In particular, they prove that a coding scheme consisting of a frequency transform within each layer followed by a separate KL transform across the layers at each spatial frequency is asymptotically optimal as the block size becomes large. Two simplifications of this method are also shown to be asymptotically optimal if the data can be assumed to satisfy additional constraints. The proposed coding techniques are then implemented using subband filtering methods, and the various algorithms are tested on multispectral images to determine their relative performance characteristics.

Multiscale Bayesian segmentation using a trainable context model.

Multiscale Bayesian approaches have attracted increasing attention for use in image segmentation. Generally, these methods tend to offer improved segmentation accuracy with reduced computational burden. Existing Bayesian segmentation methods use simple models of context designed to encourage large uniformly classified regions. Consequently, these context models have a limited ability to capture the complex contextual dependencies that are important in applications such as document segmentation. We propose a multiscale Bayesian segmentation algorithm which can effectively model complex aspects of both local and global contextual behavior. The model uses a Markov chain in scale to model the class labels that form the segmentation, but augments this Markov chain structure by incorporating tree based classifiers to model the transition probabilities between adjacent scales. The tree based classifier models complex transition rules with only a moderate number of parameters. One advantage to our segmentation algorithm is that it can be trained for specific segmentation applications by simply providing examples of images with their corresponding accurate segmentations. This makes the method flexible by allowing both the context and the image models to be adapted without modification of the basic algorithm. We illustrate the value of our approach with examples from document segmentation in which test, picture and background classes must be separated.

Dual stack filters and the modified difference of estimates approach to edge detection.

The theory of optimal stack filtering has been used in the difference of estimates (DoE) approach to the detection of intensity edges in noisy images. The DoE approach is modified by imposing a symmetry condition on the data used to train the two stack filters. Under this condition, the stack filters obtained are duals of each other. Only one filter must therefore be trained; the other is simply its dual. This new technique is called the symmetric difference of estimates (SDoE) approach. The dual stack filters obtained under the SDoE approach are shown to be comparable. This allows the difference of these two filters to be represented by a single equivalent edge operator. This latter result suggests that an edge operator can be found by directly training a (possibly nonpositive) Boolean function to be used on each level of the threshold decomposition architecture. This approach, which is called the threshold Boolean filter (TBF) approach, requires less training time but produces operators that are less robust than those produced by the SDoE approach. This is demonstrated and interpreted via comparisons of results for natural images.

ML parameter estimation for Markov random fields with applications to Bayesian tomography.

Markov random fields (MRF's) have been widely used to model images in Bayesian frameworks for image reconstruction and restoration. Typically, these MRF models have parameters that allow the prior model to be adjusted for best performance. However, optimal estimation of these parameters(sometimes referred to as hyper parameters) is difficult in practice for two reasons: i) direct parameter estimation for MRF's is known to be mathematically and numerically challenging; ii)parameters can not be directly estimated because the true image cross section is unavailable.In this paper, we propose a computationally efficient scheme to address both these difficulties for a general class of MRF models,and we derive specific methods of parameter estimation for the MRF model known as generalized Gaussian MRF (GGMRF).The first section of the paper derives methods of direct estimation of scale and shape parameters for a general continuously valued MRF. For the GGMRF case, we show that the ML estimate of the scale parameter, sigma, has a simple closed-form solution, and we present an efficient scheme for computing the ML estimate of the shape parameter, p, by an off-line numerical computation of the dependence of the partition function on p.The second section of the paper presents a fast algorithm for computing ML parameter estimates when the true image is unavailable. To do this, we use the expectation maximization(EM) algorithm. We develop a fast simulation method to replace the E-step, and a method to improve parameter estimates when the simulations are terminated prior to convergence.Experimental results indicate that our fast algorithms substantially reduce computation and result in good scale estimates for real tomographic data sets.

Sequential scalar quantization of vectors: an analysis.

Proposes an efficient vector quantization (VQ) technique called sequential scalar quantization (SSQ). The scalar components of the vector are individually quantized in a sequence, with the quantization of each component utilizing conditional information from the quantization of previous components. Unlike conventional independent scalar quantization (ISQ), SSQ has the ability to exploit intercomponent correlation. At the same time, since quantization is performed on scalar rather than vector variables, SSQ offers a significant computational advantage over conventional VQ techniques and is easily amenable to a hardware implementation. In order to analyze the performance of SSQ, the authors appeal to asymptotic quantization theory, where the codebook size is assumed to be large. Closed-form expressions are derived for the quantizer mean squared error (MSE). These expressions are used to compare the asymptotic performance of SSQ with other VQ techniques. The authors also demonstrate the use of asymptotic theory in designing SSQ for a practical application (color image quantization), where the codebook size is typically small. Theoretical and experimental results show that SSQ far outperforms ISQ with respect to MSE while offering a considerable reduction in computation over conventional VQ at the expense of a moderate increase in MSE.

Hierarchical browsing and search of large image databases.

The advent of large image databases (>10000) has created a need for tools which can search and organize images automatically by their content. This paper focuses on the use of hierarchical tree-structures to both speed-up search-by-query and organize databases for effective browsing. The first part of this paper develops a fast search algorithm based on best-first branch and bound search. This algorithm is designed so that speed and accuracy may be continuously traded-off through the selection of a parameter lambda. We find that the algorithm is most effective when used to perform an approximate search, where it can typically reduce computation by a factor of 20-40 for accuracies ranging from 80% to 90%. We then present a method for designing a hierarchical browsing environment which we call a similarity pyramid. The similarity pyramid groups similar images together while allowing users to view the database at varying levels of resolution. We show that the similarity pyramid is best constructed using agglomerative (bottom up) clustering methods, and present a fast sparse clustering method which dramatically reduces both memory and computation over conventional methods.

Parallelizable Bayesian tomography algorithms with rapid, guaranteed convergence.

Bayesian tomographic reconstruction algorithms generally require the efficient optimization of a functional of many variables. In this setting, as well as in many other optimization tasks, functional substitution (FS) has been widely applied to simplify each step of the iterative process. The function to be minimized is replaced locally by an approximation having a more easily manipulated form, e.g., quadratic, but which maintains sufficient similarity to descend the true functional while computing only the substitute. We provide two new applications of FS methods in iterative coordinate descent for Bayesian tomography. The first is a modification of our coordinate descent algorithm with one-dimensional (1-D) Newton-Raphson approximations to an alternative quadratic which allows convergence to be proven easily. In simulations, we find essentially no difference in convergence speed between the two techniques. We also present a new algorithm which exploits the FS method to allow parallel updates of arbitrary sets of pixels using computations similar to iterative coordinate descent. The theoretical potential speed up of parallel implementations is nearly linear with the number of processors if communication costs are neglected.

Sequential linear interpolation of multidimensional functions.

We introduce a new approach that we call sequential linear interpolation (SLI) for approximating multidimensional nonlinear functions. The SLI is a partially separable grid structure that allows us to allocate more grid points to the regions where the function to be interpolated is more nonlinear. This approach reduces the mean squared error (MSE) between the original and approximated function while retaining much of the computational advantage of the conventional uniform grid interpolation. To obtain the optimal grid point placement for the SLI structure, we appeal to an asymptotic analysis similar to the asymptotic vector quantization (VQ) theory. In the asymptotic analysis, we assume that the number of interpolation grid points is large and the function to be interpolated is smooth. Closed form expressions for the MSE of the interpolation are obtained from the asymptotic analysis. These expressions are used to guide us in designing the optimal SLI structure. For cases where the assumptions underlying the asymptotic theory are not satisfied, we develop a postprocessing technique to improve the MSE performance of the SLI structure. The SLI technique is applied to the problem of color printer characterization where a highly nonlinear multidimensional function must be efficiently approximated. Our experimental results show that the appropriately designed SLI structure can greatly improve the MSE performance over the conventional uniform grid.

Optimization of sensor response functions for colorimetry of reflective and emissive objects.

This paper describes the design of color filters for a surface color measurement device. The function of the device is to return the XYZ tristimulus vector characterizing the color of the surface. The device is designed to measure emissive as well as reflective surfaces. It uses an internal set of LEDs to illuminate reflective surfaces while characterizing their color under assumed standard illuminants. In the design of the filters, we formulate a nonlinear optimization problem with the goal of minimizing error in the uniform color space CIE L*a*b*. Our optimization criteria employs a technique to retain a linear structure while approximating the true L*a*b* error. In addition, our solution is regularized to account for system noise, filter roughness, and filter implementation errors. Experimental results indicate average and worst-case device accuracy of 0.27 L*a*b* DeltaE units and 1.56 L*a*b* DeltaE units for a "system tolerance" of 0.0005.

A multiscale stochastic image model for automated inspection.

We develop a novel multiscale stochastic image model to describe the appearance of a complex three-dimensional object in a two-dimensional monochrome image. This formal image model is used in conjunction with Bayesian estimation techniques to perform automated inspection. The model is based on a stochastic tree structure in which each node is an important subassembly of the three-dimensional object. The data associated with each node or subassembly is modeled in a wavelet domain. We use a fast multiscale search technique to compute the sequential MAP (SMAP) estimate of the unknown position, scale factor, and 2-D rotation for each subassembly. The search is carried out in a manner similar to a sequential likelihood ratio test, where the process advances in scale rather than time. The results of this search determine whether or not the object passes inspection. A similar search is used in conjunction with the EM algorithm to estimate the model parameters for a given object from a set of training images. The performance of the algorithm is demonstrated on two different real assemblies.