Exploring the similarity of medical imaging classification problems

Supervised learning is ubiquitous in medical image analysis. In this paper we consider the problem of meta-learning -- predicting which methods will perform well in an unseen classification problem, given previous experience with other classification problems. We investigate the first step of such an approach: how to quantify the similarity of different classification problems. We characterize datasets sampled from six classification problems by performance ranks of simple classifiers, and define the similarity by the inverse of Euclidean distance in this meta-feature space. We visualize the similarities in a 2D space, where meaningful clusters start to emerge, and show that the proposed representation can be used to classify datasets according to their origin with 89.3\% accuracy. These findings, together with the observations of recent trends in machine learning, suggest that meta-learning could be a valuable tool for the medical imaging community

Task adapted reconstruction for inverse problems

The paper considers the problem of performing a task defined on a model parameter that is only observed indirectly through noisy data in an ill-posed inverse problem. A key aspect is to formalize the steps of reconstruction and task as appropriate estimators (non-randomized decision rules) in statistical estimation problems. The implementation makes use of (deep) neural networks to provide a differentiable parametrization of the family of estimators for both steps. These networks are combined and jointly trained against suitable supervised training data in order to minimize a joint differentiable loss function, resulting in an end-to-end task adapted reconstruction method. The suggested framework is generic, yet adaptable, with a plug-and-play structure for adjusting both the inverse problem and the task at hand. More precisely, the data model (forward operator and statistical model of the noise) associated with the inverse problem is exchangeable, e.g., by using neural network architecture given by a learned iterative method. Furthermore, any task that is encodable as a trainable neural network can be used. The approach is demonstrated on joint tomographic image reconstruction, classification and joint tomographic image reconstruction segmentation

Shape reconstruction and classification using the response matrix

This dissertation presents a novel method for the inverse scattering problem for extended target. The acoustic or electromagnetic wave is scattered by the target and received by all the transducers around the target. The scattered field on all the transducers forms the response matrix which contains the information of the geometry of the target. The objective of the inverse scattering problem is to reconstruct the shape of the scatter using the Response Matrix. There are two types of numerical methods for solving the inverse problem: the direct imaging method and the iterative method. Two direct imaging methods, MUSIC method and Multi-tone method, are introduced in this dissertation. The direct imaging method generates the image, which contains the shape of the target, by defining the image function using the response matrix. Numerical examples show that the two direct imaging methods are efficient and robust, and the Multi-tone method can be used in synthetic aperture. The iterative method described in this dissertation achieves better accuracy than the direct imaging method. The result of the direct imaging method of the inverse problem is used as an initial estimation for this iterative method. One forward problem and one adjoint problem is solved in each iteration step. Numerical results show that the residual vanishes at a fixed wave number. The final result after iterations is more accurate than the result from the direct imaging method. This dissertation also introduces the application of the inverse problem: shape identification and classification. The response matrix used in shape classification can be generated by the forward solver or Born approximation. The distance function designed using a response matrix or its SVD information is effective and robust to noise. The classification method using the response matrix is tested on a large data set and compared with other classification algorithms on the retrieval accuracy