ADAPTIVE SMALL-ANIMAL SPECT/CT.

We are exploring the concept of adaptive multimodality imaging, a form of non-linear optimization where the imaging configuration is automatically adjusted in response to the object. Preliminary studies suggest that substantial improvement in objective, task-based measures of image quality can result. We describe here our work to add motorized adjustment capabilities and a matching CT to our existing FastSPECT II system to form an adaptive small-animal SPECT/CT.

Ideal-observer performance under signal and background uncertainty.

We use the performance of the Bayesian ideal observer as a figure of merit for hardware optimization because this observer makes optimal use of signal-detection information. Due to the high dimensionality of certain integrals that need to be evaluated, it is difficult to compute the ideal observer test statistic, the likelihood ratio, when background variability is taken into account. Methods have been developed in our laboratory for performing this computation for fixed signals in random backgrounds. In this work, we extend these computational methods to compute the likelihood ratio in the case where both the backgrounds and the signals are random with known statistical properties. We are able to write the likelihood ratio as an integral over possible backgrounds and signals, and we have developed Markov-chain Monte Carlo (MCMC) techniques to estimate these high-dimensional integrals. We can use these results to quantify the degradation of the ideal-observer performance when signal uncertainties are present in addition to the randomness of the backgrounds. For background uncertainty, we use lumpy backgrounds. We present the performance of the ideal observer under various signal-uncertainty paradigms with different parameters of simulated parallel-hole collimator imaging systems. We are interested in any change in the rankings between different imaging systems under signal and background uncertainty compared to the background-uncertainty case. We also compare psychophysical studies to the performance of the ideal observer.

Ideal observer approximation using Bayesian classification neural networks.

It is well understood that the optimal classification decision variable is the likelihood ratio or any monotonic transformation of the likelihood ratio. An automated classifier which maps from an input space to one of the likelihood ratio family of decision variables is an optimal classifier or "ideal observer." Artificial neural networks (ANNs) are frequently used as classifiers for many problems. In the limit of large training sample sizes, an ANN approximates a mapping function which is a monotonic transformation of the likelihood ratio, i.e., it estimates an ideal observer decision variable. A principal disadvantage of conventional ANNs is the potential over-parameterization of the mapping function which results in a poor approximation of an optimal mapping function for smaller training samples. Recently, Bayesian methods have been applied to ANNs in order to regularize training to improve the robustness of the classifier. The goal of training a Bayesian ANN with finite sample sizes is, as with unlimited data, to approximate the ideal observer. We have evaluated the accuracy of Bayesian ANN models of ideal observer decision variables as a function of the number of hidden units used, the signal-to-noise ratio of the data and the number of features or dimensionality of the data. We show that when enough training data are present, excess hidden units do not substantially degrade the accuracy of Bayesian ANNs. However, the minimum number of hidden units required to best model the optimal mapping function varies with the complexity of the data.

Feature selection with limited datasets.

Computer-aided diagnosis has the potential of increasing diagnostic accuracy by providing a second reading to radiologists. In many computerized schemes, numerous features can be extracted to describe suspect image regions. A subset of these features is then employed in a data classifier to determine whether the suspect region is abnormal or normal. Different subsets of features will, in general, result in different classification performances. A feature selection method is often used to determine an "optimal" subset of features to use with a particular classifier. A classifier performance measure (such as the area under the receiver operating characteristic curve) must be incorporated into this feature selection process. With limited datasets, however, there is a distribution in the classifier performance measure for a given classifier and subset of features. In this paper, we investigate the variation in the selected subset of "optimal" features as compared with the true optimal subset of features caused by this distribution of classifier performance. We consider examples in which the probability that the optimal subset of features is selected can be analytically computed. We show the dependence of this probability on the dataset sample size, the total number of features from which to select, the number of features selected, and the performance of the true optimal subset. Once a subset of features has been selected, the parameters of the data classifier must be determined. We show that, with limited datasets and/or a large number of features from which to choose, bias is introduced if the classifier parameters are determined using the same data that were employed to select the "optimal" subset of features.

Multiobjective genetic optimization of diagnostic classifiers with implications for generating receiver operating characteristic curves.

It is well understood that binary classifiers have two implicit objective functions (sensitivity and specificity) describing their performance. Traditional methods of classifier training attempt to combine these two objective functions (or two analogous class performance measures) into one so that conventional scalar optimization techniques can be utilized. This involves incorporating a priori information into the aggregation method so that the resulting performance of the classifier is satisfactory for the task at hand. We have investigated the use of a niched Pareto multiobjective genetic algorithm (GA) for classifier optimization. With niched Pareto GA's, an objective vector is optimized instead of a scalar function, eliminating the need to aggregate classification objective functions. The niched Pareto GA returns a set of optimal solutions that are equivalent in the absence of any information regarding the preferences of the objectives. The a priori knowledge that was used for aggregating the objective functions in conventional classifier training can instead be applied post-optimization to select from one of the series of solutions returned from the multiobjective genetic optimization. We have applied this technique to train a linear classifier and an artificial neural network (ANN), using simulated datasets. The performances of the solutions returned from the multiobjective genetic optimization represent a series of optimal (sensitivity, specificity) pairs, which can be thought of as operating points on a receiver operating characteristic (ROC) curve. All possible ROC curves for a given dataset and classifier are less than or equal to the ROC curve generated by the niched Pareto genetic optimization.

Automated seeded lesion segmentation on digital mammograms.

Segmenting lesions is a vital step in many computerized mass-detection schemes for digital (or digitized) mammograms. We have developed two novel lesion segmentation techniques-one based on a single feature called the radial gradient index (RGI) and one based on simple probabilistic models to segment mass lesions, or other similar nodular structures, from surrounding background. In both methods a series of image partitions is created using gray-level information as well as prior knowledge of the shape of typical mass lesions. With the former method the partition that maximizes the RGI is selected. In the latter method, probability distributions for gray-levels inside and outside the partitions are estimated, and subsequently used to determine the probability that the image occurred for each given partition. The partition that maximizes this probability is selected as the final lesion partition (contour). We tested these methods against a conventional region growing algorithm using a database of biopsy-proven, malignant lesions and found that the new lesion segmentation algorithms more closely match radiologists' outlines of these lesions. At an overlap threshold of 0.30, gray level region growing correctly delineates 62% of the lesions in our database while the RGI and probabilistic segmentation algorithms correctly segment 92% and 96% of the lesions, respectively.

Optimization and FROC analysis of rule-based detection schemes using a multiobjective approach.

Computerized detection schemes have the potential of increasing diagnostic accuracy in medical imaging by alerting radiologists to lesions that they initially overlooked. These schemes typically employ multiple parameters such as threshold values or filter weights to arrive at a detection decision. In order for the system to have high performance, the values of these parameters need to be set optimally. Conventional optimization techniques are designed to optimize a scalar objective function. The task of optimizing the performance of a computerized detection scheme, however, is clearly a multiobjective problem: we wish to simultaneously improve the sensitivity and false-positive rate of the system. In this work we investigate a multiobjective approach to optimizing computerized rule-based detection schemes. In a multiobjective optimization, multiple objectives are simultaneously optimized, with the objective now being a vector-valued function. The multiobjective optimization problem admits a set of solutions, known as the Pareto-optimal set, which are equivalent in the absence of any information regarding the preferences of the objectives. The performances of the Pareto-optimal solutions can be interpreted as operating points on an optimal free-response receiver operating characteristic (FROC) curve, greater than or equal to the points on any possible FROC curve for a given dataset and detection scheme. It is demonstrated that generating FROC curves in this manner eliminates several known problems with conventional FROC curve generation techniques for rule-based detection schemes. We employ the multiobjective approach to optimize a rule-based scheme for clustered microcalcification detection that has been developed in our laboratory.