Optimal and Efficient Streak Detection in Astronomical Images

TL;DR

This paper presents an efficient algorithm using the Radon transform for detecting linear streaks in astronomical images, enabling the identification of faint and short streaks with high accuracy.

Contribution

The authors develop a fast Radon transform-based method for optimal streak detection, extending it to efficiently identify arbitrarily short lines in astronomical images.

Findings

Successfully detects faint streaks in simulated and real images.

Recovers theoretical signal-to-noise ratios in streak detection.

Identifies low-Earth-orbit and GPS satellite streaks in diverse images.

Abstract

Identification of linear features (streaks) in astronomical images is important for several reasons, including: detecting fast-moving near-Earth asteroids; detecting or flagging faint satellites streaks; and flagging or removing diffraction spikes, pixel bleeding, line-like cosmic rays and bad-pixel features. Here we discuss an efficient and optimal algorithm for the detection of such streaks. The optimal method to detect streaks in astronomical images is by cross-correlating the image with a template of a line broadened by the point spread function of the system. To do so efficiently, the cross-correlation of the streak position and angle is performed using the Radon transform, which is the integral of pixel values along all possible lines through an image. A fast version of the Radon transform exists, which we here extend to efficiently detect arbitrarily short lines. While the brute force Radon transform requires an order of N^3 operations for an N by N image, the fast Radon transform has a complexity of the order of N^2 log(N). We apply this method to simulated images, recovering the theoretical signal-to-noise ratio, and to real images, finding long streaks of low-Earth-orbit satellites and shorter streaks of Global Positioning System satellites. We detect streaks that are barely visible to the eye, out of hundreds of images, without a-priori knowledge of the streaks' positions or angles. We provide implementation of this algorithm in Python and MATLAB.