Applying the J-optimal channelized quadratic observer to SPECT myocardial perfusion defect detection

Abstract

To evaluate performance on a perfusion defect detection task from 540 image pairs of myocardial perfusion SPECT image data we apply the J-optimal channelized quadratic observer (J-CQO). We compare AUC values of the linear Hotelling observer and J-CQO when the defect location is fixed and when it occurs in one of two locations. As expected, when the location is fixed a single channels maximizes AUC; location variability requires multiple channels to maximize the AUC. The AUC is estimated from both the projection data and reconstructed images. J-CQO is quadratic since it uses the first-and second-order statistics of the image data from both classes. The linear data reduction by the channels is described by an L × M channel matrix and in prior work we introduced an iterative gradient-based method for calculating the channel matrix. The dimensionality reduction from M measurements to L channels yields better estimates of these sample statistics from smaller sample sizes, and since the channelized covariance matrix is L × L instead of M × M , the matrix inverse is easier to compute. The novelty of our approach is the use of Jeffrey's divergence (J) as the figure of merit (FOM) for optimizing the channel matrix. We previously showed that the J-optimal channels are also the optimum channels for the AUC and the Bhattacharyya distance when the channel outputs are Gaussian distributed with equal means. This work evaluates the use of J as a surrogate FOM (SFOM) for AUC when these statistical conditions are not satisfied. MOTIVATIONOur work is motivated by the need to develop a detection methodology to sort image data between two classes of objects (e.g. defect present and defect absent). To introduce the detection method begin by considering the relationship between an image and an object as g = Hf + n. Here g is an M × 1 vector of measurements made by an imaging system that is represented as a continuous-to-discrete operator H. The measurements of the continuous object f are corrupted by measurement noise n. We will consider post-processing signal detection. That is to say the forward imaging model H is fixed and can even be unknown since only the statistics of the image data g will be used. We are interested in linear combinations of the image data of the form v = Tg where T is an L × M channel matrix and compression is achieved since L < M . Using terminology from the perception literature, each row of T is referred to as a channel and v is the channelized data. 1 Given a fixed set of L channels the optimal classifier will compute the channelized log-likelihoodand compare this decision variable λ to a threshold to sort the image data into one of two classes. For notational purposes the classes are denoted by i = 1, 2. In this work we assume the channelized likelihoods pr i (Tg) are Gaussian. Since the channelized data are weighted sums of the image data they may be at least approximately Gaussian distributed, as long as the image data are sufficiently independent, even if the original data are not. In this case we would ...