In SPECT/PET, the maximum-likelihood expectation-maximization (ML-EM) algorithm is getting more attention as the speed of computers increases. This is because it can incorporate various physical aspects into the reconstruction process leading to a more accurate reconstruction than other analytical methods such as filtered-backprojection algorithms. However, the convergence rate of the ML-EM alg...

Last week, we saw how we could represent clustering with a probabilistic model. In this model, called a Gaussian mixture model, we model each datapoint x i as originating from some cluster, with a corresponding cluster label y i distributed according to p(y), and the corresponding distribution for that cluster given by a multivariate Gaussian: p(x|y = k) =

Common-sense physical reasoning is an essential ingredient for any intelligent agent operating in the real-world. For example, it can be used to simulate the environment, or to infer the state of parts of the world that are currently unobserved. In order to match real-world conditions this causal knowledge must be learned without access to supervised data. To solve this problem, we present a no...

We introduce a novel framework for clustering that combines generalized EM with neural networks and can be implemented as an end-to-end differentiable recurrent neural network. It learns its statistical model directly from the data and can represent complex non-linear dependencies between inputs. We apply our framework to a perceptual grouping task and empirically verify that it yields the inte...

In this paper, we use a general mathematical and experimental methodology to analyze image deconvolution. The main procedure is to use an example image convolving it with a know Gaussian point spread function and then develop algorithms to recover the image. Observe the deconvolution process by adding Gaussian and Poisson noise at different signal to noise ratios. In addition, we will describe ...

We present Fitness Expectation Maximization (FEM), a novel method for performing ‘black box’ function optimization. FEM searches the fitness landscape of an objective function using an instantiation of the well-known Expectation Maximization algorithm, producing search points to match the sample distribution weighted according to higher expected fitness. FEM updates both candidate solution para...

So far, we discussed clustering algorithms that involve a hard assignment of each datapoint to a cluster, typically based on its proximity to other points in that cluster. However, simply assigning points to the nearest cluster is not always adequate to capture more complex structure. For example, the lecture slides show an example where one cluster is much larger and less dense than another. W...

In this article we consider a median variant of the learning vector quantization (LVQ) classifier for classification of dissimilarity data. However, beside the median aspect, we propose to optimize the receiver-operating characteristics (ROC) instead of the classification accuracy. In particular, we present a probabilistic LVQ model with an adaptation scheme based on a generalized ExpectationMa...

The purpose of this study was to investigate the influence of the Ordered Subsets Expectation Maximization (OSEM) reconstruction updates implemented in the 177Lu SPECT/CT imaging processing in molecular radiotherapy. A NEMA IEC Body PhantomTM was used to quantify activity in refillable spheres of five different sizes. Images were obtained with a hybrid dual-head SPECT-CT imaging system (Symbia ...