# A new approach for atmospheric turbulence removal using low-rank matrix factorization

## TL;DR

This paper introduces a new method using low-rank matrix factorization to remove atmospheric turbulence from images and restore high-quality visuals.

## Contribution

The novel approach combines geometric transformation and blur modeling via low-rank matrix factorization for turbulence removal.

## Key findings

- The method effectively reduces significant geometric distortions in turbulent images.
- It improves spatiotemporal varying blur and restores image details.
- Results are validated using both real and simulated datasets.

## Abstract

In this article, a novel method for removing atmospheric turbulence from a sequence of turbulent images and restoring a high-quality image is presented. Turbulence is modeled using two factors: the geometric transformation of pixel locations represents the distortion, and the varying pixel brightness represents spatiotemporal varying blur. The main framework of the proposed method involves the utilization of low-rank matrix factorization, which achieves the modeling of both the geometric transformation of pixels and the spatiotemporal varying blur through an iterative process. In the proposed method, the initial step involves the selection of a subset of images using the random sample consensus method. Subsequently, estimation of the mixture of Gaussian noise parameters takes place. Following this, a window is chosen around each pixel based on the entropy of the surrounding region. Within this window, the transformation matrix is locally estimated. Lastly, by considering both the noise and the estimated geometric transformations of the selected images, an estimation of a low-rank matrix is conducted. This estimation process leads to the production of a turbulence-free image. The experimental results were obtained from both real and simulated datasets. These results demonstrated the efficacy of the proposed method in mitigating substantial geometrical distortions. Furthermore, the method showcased the ability to improve spatiotemporal varying blur and effectively restore the details present in the original image.