Convolutional Higher Order Matching Pursuit
Gergő Bohner, Gatsby Unit, University College London
Maneesh Sahani, Gatsby Unit, University College London

We introduce a greedy generalised convolutional algorithm to efficiently locate an unknown number of sources in a series of (possibly multidimensional) images, where each source contributes a localised and low-dimensional but otherwise variable signal to its immediate spatial neighbourhood. Our approach extends convolutional matching pursuit in two ways: first, it takes the signal generated by each source to be a variable linear combination of aligned dictionary elements; and second, it executes the pursuit in the domain of high-order multivariate cumulant statistics. The resulting algorithm adapts to varying signal and noise distributions to flexibly recover source signals in a variety of settings.