Non-linear matched filtering for point source detection

Abstract

The task of object detection depends on the ability to suppress the noise present in images in order to increase the signal-to-noise ratio. The standard linear matched filter is the optimal filter on the assumption of the Gaussian distribution of the signal and the noise. However, as a rule the distribution of the signal in image processing is not Gaussian. The linear matched filter becomes sub-optimal. Any non-Gaussian distribution function can be closely approximated using the Gaussian Mixture Model (GMM). We use GMM to approximate the signal distribution function and derive the optimal filter by means of mean square error (MSE) minimization. The optimal non-linear filter is determined by the assumed signal distribution function. We use non-linear matched filtering for point source detection in astronomical images. We derive the GMM components by fitting the theoretical point source distribution function. The filtered images are subjected to image segmentation and subsequent point source detection. The non-linear matched filtering has been tested with simulated data and has been shown to significantly improve the quality of point source detection. Receiver operating characteristic technique has been used to evaluate performance of various Gaussian mixtures for point source detection. This algorithm is currently used for the Spitzer Spatial Telescope.