Learning the Sampling Pattern for MRI

The discovery of the theory of compressed sensing brought the realisation that many inverse problems can be solved even when measurements are "incomplete". This is particularly interesting in magnetic resonance imaging (MRI), where long acquisition times can limit its use. In this work, we consider the problem of learning a sparse sampling pattern that can be used to optimally balance acquisition time versus quality of the reconstructed image. We use a supervised learning approach, making the assumption that our training data is representative enough of new data acquisitions. We demonstrate that this is indeed the case, even if the training data consists of just 5 training pairs of measurements and ground-truth images; with a training set of brain images of size 192 by 192, for instance, one of the learned patterns samples only 32% of k-space, however results in reconstructions with mean SSIM 0.956 on a test set of similar images. The proposed framework is general enough to learn arbitrary sampling patterns, including common patterns such as Cartesian, spiral and radial sampling.

Mirror, Mirror, on the Wall, Who's Got the Clearest Image of Them All? - A Tailored Approach to Single Image Reflection Removal

Removing reflection artefacts from a single-image is a problem of both theoretical and practical interest. Removing these artefacts still presents challenges because of the massively ill-posed nature of reflection suppression. In this work, we propose a technique based on a novel optimisation problem. Firstly, we introduce an $H^2$ fidelity term, which preserves fine detail while enforcing global colour similarity. Secondly, we introduce a spatially dependent gradient sparsity prior, which allows user guidance to prevent information loss in reflection-free areas. We show that this combination allows us to mitigate some major drawbacks of the existing methods for reflection removal. We demonstrate, through numerical and visual experiments, that our method is able to outperform the state-of-the-art methods and compete against a recent deep learning approach.

Peekaboo - Where are the Objects? Structure Adjusting Superpixels

This paper addresses the search for a fast and meaningful image segmentation in the context of $k$-means clustering. The proposed method builds on a widely-used local version of Lloyd's algorithm, called Simple Linear Iterative Clustering (SLIC). We propose an algorithm which extends SLIC to dynamically adjust the local search, adopting superpixel resolution dynamically to structure existent in the image, and thus provides for more meaningful superpixels in the same linear runtime as standard SLIC. The proposed method is evaluated against state-of-the-art techniques and improved boundary adherence and undersegmentation error are observed, whilst still remaining among the fastest algorithms which are tested.