Heterogeneous multireference alignment: a single pass approach

Multireference alignment (MRA) is the problem of estimating a signal from many noisy and cyclically shifted copies of itself. In this paper, we consider an extension called heterogeneous MRA, where $K$ signals must be estimated, and each observation comes from one of those signals, unknown to us. This is a simplified model for the heterogeneity problem notably arising in cryo-electron microscopy. We propose an algorithm which estimates the $K$ signals without estimating either the shifts or the classes of the observations. It requires only one pass over the data and is based on low-order moments that are invariant under cyclic shifts. Given sufficiently many measurements, one can estimate these invariant features averaged over the $K$ signals. We then design a smooth, non-convex optimization problem to compute a set of signals which are consistent with the estimated averaged features. We find that, in many cases, the proposed approach estimates the set of signals accurately despite non-convexity, and conjecture the number of signals $K$ that can be resolved as a function of the signal length $L$ is on the order of $\sqrt{L}$.Comment: 6 pages, 3 figure

Color image segmentation using a self-initializing EM algorithm

This paper presents a new method based on the Expectation-Maximization (EM) algorithm that we apply for color image segmentation. Since this algorithm partitions the data based on an initial set of mixtures, the color segmentation provided by the EM algorithm is highly dependent on the starting condition (initialization stage). Usually the initialization procedure selects the color seeds randomly and often this procedure forces the EM algorithm to converge to numerous local minima and produce inappropriate results. In this paper we propose a simple and yet effective solution to initialize the EM algorithm with relevant color seeds. The resulting self initialised EM algorithm has been included in the development of an adaptive image segmentation scheme that has been applied to a large number of color images. The experimental data indicates that the refined initialization procedure leads to improved color segmentation