Spatial statistics, image analysis and percolation theory
This addresses image reconstruction challenges in fields like cryo-electron microscopy, though it appears incremental as it builds on existing percolation theory for a specific domain.
The paper tackles the problem of detecting multiple objects with unknown shapes and varying intensities in noisy images with nonparametric, heavy-tailed noise, using a novel method based on percolation theory, and proves consistency and algorithmic complexity results.
We develop a novel method for detection of signals and reconstruction of images in the presence of random noise. The method uses results from percolation theory. We specifically address the problem of detection of multiple objects of unknown shapes in the case of nonparametric noise. The noise density is unknown and can be heavy-tailed. The objects of interest have unknown varying intensities. No boundary shape constraints are imposed on the objects, only a set of weak bulk conditions is required. We view the object detection problem as a multiple hypothesis testing for discrete statistical inverse problems. We present an algorithm that allows to detect greyscale objects of various shapes in noisy images. We prove results on consistency and algorithmic complexity of our procedures. Applications to cryo-electron microscopy are presented.