# Simultaneous Video Stabilization and Moving Object Detection in
Turbulence

## Introduction

Turbulence mitigation refers to the stabilization of videos with
non-uniform deformations due to the influence of optical turbulence.
Typical approaches for turbulence mitigation follow averaging or
de-warping techniques. Although these methods can reduce the
turbulence, they distort the independently moving objects which can
often be of great interest. In this paper, we address the novel
problem of simultaneous turbulence mitigation and moving object
detection. We propose a novel threeterm low-rank matrix decomposition
approach in which we decompose the turbulence sequence into three
components: the background, the turbulence, and the object. We
simplify this extremely difficult problem into a minimization of
nuclear norm, Frobenius norm, and L1 norm. Our method is based on two
observations: First, the turbulence causes dense and Gaussian noise,
and therefore can be captured by Frobenius norm, while the moving
objects are sparse and thus can be captured by L1 norm. Second, since
the object’s motion is linear and intrinsically different than the
Gaussian-like turbulence, a Gaussian-based turbulence model can be
employed to enforce an additional constraint on the search space of
the minimization. We demonstrate the robustness of our approach on
challenging sequences which are significantly distorted with
atmospheric turbulence and include extremely tiny moving objects.

## Decomposition Examples