Detection of multiple lesions in images is a medically important task and free-response receiver operating characteristic (FROC) analyses and its variants, such as alternative FROC (AFROC) analyses, are commonly used to quantify performance in such tasks. However, ideal observers that optimize FROC or AFROC performance metrics have not yet been formulated in the general case. If available, such ideal observers may turn out to be valuable for imaging system optimization and in the design of computer aided diagnosis techniques for lesion detection in medical images. In this paper, we derive ideal AFROC and FROC observers. They are ideal in that they maximize, amongst all decision strategies, the area, or any partial area, under the associated AFROC or FROC curve. Calculation of observer performance for these ideal observers is computationally quite complex. We can reduce this complexity by considering forms of these observers that use false positive reports derived from signal-absent images only. We also consider a Bayes risk analysis for the multiple-signal detection task with an appropriate definition of costs. A general decision strategy that minimizes Bayes risk is derived. With particular cost constraints, this general decision strategy reduces to the decision strategy associated with the ideal AFROC or FROC observer.

With increasing availability of multimodality imaging systems, high-resolution anatomical images can be used to guide the reconstruction of emission tomography studies. By measuring reader performance on a lesion detection task, this study investigates the improvement in image-quality due to use of prior anatomical knowledge, for example organ or lesion boundaries, during SPECT reconstruction. Simulated (67)Ga -citrate source and attenuation distributions were created from the mathematical cardiac-torso (MCAT) anthropomorphic digital phantom. The SIMIND Monte Carlo software was then used to generate SPECT projection data. The data were reconstructed using the De Pierro maximum a posteriori (MAP) algorithm and the rescaled-block-iterative (RBI) algorithm for comparison. We compared several degrees of prior knowledge about the anatomy: no knowledge about the anatomy; knowledge of organ boundaries; knowledge of organ and lesion boundaries; and knowledge of organ, lesion, and pseudo-lesion (non-emission uptake altering) boundaries. The MAP reconstructions used quadratic smoothing within anatomical regions, but not across any provided region boundaries. The reconstructed images were read by human observers searching for lesions in a localization receiver operating characteristic (LROC) study of the relative detection/localization accuracies of the reconstruction algorithms. Area under the LROC curve was computed for each algorithm as the comparison metric. We also had humans read images reconstructed using different prior strengths to determine the optimal trade-off between data consistency and the anatomical prior. Finally by mixing together images reconstructed with and without the prior, we tested to see if having an anatomical prior only some of the time changes the observer's detection/localization accuracy on lesions where no boundary prior is available. We found that anatomical priors including organ and lesion boundaries improve observer performance on the lesion detection/localization task. Use of just organ boundaries did not provide a statistically significant improvement in performance however. We also found that optimal prior strength depends on the level of anatomical knowledge, with a broad plateau in which observer performance is near optimal. We found no evidence that having anatomical priors use lesion boundaries only when available changes the observer's performance when they are not available. We conclude that use of anatomical priors with organ and lesion boundaries improves reader performance on a lesion-detection/localization task, and that pseudo-lesion boundaries do not hurt reader performance. However, we did not find evidence that a prior using only organ boundaries helps observer performance. Therefore we suggest prior strength should be tuned to the organ-only case, since a prior will likely not be available for all lesions.

For the 2-class detection problem (signal absent/present), the likelihood ratio is an ideal observer in that it minimizes Bayes risk for arbitrary costs and it maximizes the area under the receiver operating characteristic (ROC) curve [AUC]. The AUC-optimizing property makes it a valuable tool in imaging system optimization. If one considered a different task, namely, joint detection and localization of the signal, then it would be similarly valuable to have a decision strategy that optimized a relevant scalar figure of merit. We are interested in quantifying performance on decision tasks involving location uncertainty using the localization ROC (LROC) methodology. Therefore, we derive decision strategies that maximize the area under the LROC curve, A(LROC). We show that these decision strategies minimize Bayes risk under certain reasonable cost constraints. The detection-localization task is modeled as a decision problem in three increasingly realistic ways. In the first two models, we treat location as a discrete parameter having finitely many values resulting in an (L + 1) class classification problem. In our first simple model, we do not include search tolerance effects and in the second, more general, model, we do. In the third and most general model, we treat location as a continuous parameter and also include search tolerance effects. In all cases, the essential proof that the observer maximizes A(LROC) is obtained with a modified version of the Neyman-Pearson lemma. A separate form of proof is used to show that in all three cases, the decision strategy minimizes the Bayes risk under certain reasonable cost constraints.

In a Bayesian tomographic maximum a posteriori (MAP) reconstruction, an estimate of the object f is computed by iteratively minimizing an objective function that typically comprises the sum of a log-likelihood (data consistency) term and prior (or penalty) term. The prior can be used to stabilize the solution and to also impose spatial properties on the solution. One such property, preservation of edges and locally monotonic regions, is captured by the well-known median root prior (MRP), an empirical method that has been applied to emission and transmission tomography. We propose an entirely new class of convex priors that depends on f and also on m, an auxiliary field in register with f. We specialize this class to our median prior (MP). The approximate action of the median prior is to draw, at each iteration, an object voxel toward its own local median. This action is similar to that of MRP and results in solutions that impose the same sorts of object properties as does MRP. Our MAP method is not empirical, since the problem is stated completely as the minimization of a joint (on f and m) objective. We propose an alternating algorithm to compute the joint MAP solution and apply this to emission tomography, showing that the reconstructions are qualitatively similar to those obtained using MRP.

We address the problem of Bayesian image reconstruction with a prior that captures the notion of a clustered intensity histogram. The problem is formulated in the framework of a joint-MAP (maximum a posteriori) estimation with the prior PDF modeled as a mixture-of-gammas density. This prior PDF has appealing properties, including positivity enforcement. The joint MAP optimization is carried out as an iterative alternating descent wherein a regularized likelihood estimate is followed by a mixture decomposition of the histogram of the current tomographic image estimate. The mixture decomposition step estimates the hyperparameters of the prior PDF. The objective functions associated with the joint MAP estimation are complicated and difficult to optimize, but we show how they may be transformed to allow for much easier optimization while preserving the fixed point of the iterations. We demonstrate the method in the context of medical emission and transmission tomography.

A new technique for matching a 2-D or 3-D image to a translated, rotated, and uniformly scaled reference image is proposed. This method comprises three steps: (1) calculating the Radon transform of the reference image and the images to be matched, (2) calculating the Fourier invariant (FI) descriptor for each 1-D projection image, and (3) matching the FI descriptor in the projection space. The theory shows that information about translation, rotation and uniform scaling of a 2-D or 3-D image can be represented in its 1-D projections; thus a 2-D or 3-D matching can be accomplished as a set of 1-D operations. In particular, the presented technique provides a way to address the 3-D recognition problem when rigid motion is assumed.

While the ML-EM algorithm for reconstruction for emission tomography is unstable due to the ill-posed nature of the problem. Bayesian reconstruction methods overcome this instability by introducing prior information, often in the form of a spatial smoothness regularizer. More elaborate forms of smoothness constraints may be used to extend the role of the prior beyond that of a stabilizer in order to capture actual spatial information about the object. Previously proposed forms of such prior distributions were based on the assumption of a piecewise constant source distribution. Here, the authors propose an extension to a piecewise linear model-the weak plate-which is more expressive than the piecewise constant model. The weak plate prior not only preserves edges but also allows for piecewise ramplike regions in the reconstruction. Indeed, for the authors' application in SPECT, such ramplike regions are observed in ground-truth source distributions in the form of primate autoradiographs of rCBF radionuclides. To incorporate the weak plate prior in a MAP approach, the authors model the prior as a Gibbs distribution and use a GEM formulation for the optimization. They compare quantitative performance of the ML-EM algorithm, a GEM algorithm with a prior favoring piecewise constant regions, and a GEM algorithm with their weak plate prior. Pointwise and regional bias and variance of ensemble image reconstructions are used as indications of image quality. The authors' results show that the weak plate and membrane priors exhibit improved bias and variance relative to ML-EM techniques.

Proposes a Bayesian method whereby maximum a posteriori (MAP) estimates of functional (PET and SPECT) images may be reconstructed with the aid of prior information derived from registered anatomical MR images of the same slice. The prior information consists of significant anatomical boundaries that are likely to correspond to discontinuities in an otherwise spatially smooth radionuclide distribution. The authors' algorithm, like others proposed recently, seeks smooth solutions with occasional discontinuities; the contribution here is the inclusion of a coupling term that influences the creation of discontinuities in the vicinity of the significant anatomical boundaries. Simulations on anatomically derived mathematical phantoms are presented. Although computationally intense in its current implication, the reconstructions are improved (ROI-RMS error) relative to filtered backprojection and EM-ML reconstructions. The simulations show that the inclusion of position-dependent anatomical prior Information leads to further improvement relative to Bayesian reconstructions without the anatomical prior. The algorithm exhibits a certain degree of robustness with respect to errors in the location of anatomical boundaries.

A digital voxel phantom which closely resembles a typical male anatomy has been created. Organ outlines were manually drawn with 1-mm resolution in each of 78 transverses of the human torso. Such an anthropomorphic three-dimensional phantom has several interesting applications in the radiological sciences. Monte Carlo simulations can yield diagnostically realistic images of new investigational radiopharmaceuticals. Uptake characteristics approximated from small animal experiments can be used to test the imaging characteristics in human geometries. The resulting images can serve as ideal projection data of known source and attenuator distributions. This can lead to a better understanding of the image formation process for clinically realistic models, and can prove especially interesting in testing and improving tomographic reconstruction algorithms. Dose calculations for internal and external radiation sources using this phantom can give new insights in the field of health physics and therapy.>

We introduce an optimization approach for solving problems in computer vision that involve multiple levels of abstraction. Our objective functions include compositional and specialization hierarchies. We cast vision problems as inexact graph matching problems, formulate graph matching in terms of constrained optimization, and use analog neural networks to perform the optimization. The method is applicable to perceptual grouping and model matching. Preliminary experimental results are shown.

The minimum (symmetric) rank of a simple graph G over a field F is the smallest possible rank among all symmetric matrices over F whose ijth entry (for i≠j) is nonzero whenever {i,j} is an edge in G and is zero otherwise. The problem of determining minimum (symmetric) rank has been studied extensively. We define the minimum skew rank of a simple graph G to be the smallest possible rank among all skew-symmetric matrices over F whose ijth entry (for i≠j) is nonzero whenever {i,j} is an edge in G and is zero otherwise. We apply techniques from the minimum (symmetric) rank problem and from skew-symmetric matrices to obtain results about the minimum skew rank problem.