Abstract:
The behaviour of sparse regularization using the Lasso method is well understood when dealing with discretized linear models. However, the behaviour of Lasso is poor when dealing with models with very large parameter spaces and in recent years, there has been much interest in the use of "off-the-grid" approaches, using a continuous parameter space in conjunction with convex optimization problem over measures. In my talk, I will present some recent results which explain the behaviour of this method in arbitrary dimensions. Some highlights include the use of the Fisher metric to study the performance of Blasso over general domains and the application of this for quantitative MRI.