Non-linear fusion of images and the detection of point sources

This article considers the linear and quadratic fusion of a set of n-dimensional images. We aim to produce a single image that amplifies the signal and minimizes the noise. As a starting point, we consider wavelet subimages of a single image. We use three wavelets, the Mexican Hat Wavelet Family (MHWF) and the undecimated multiscale method to obtain 3N subimages. As an application we consider the detection of galaxies in Cosmic Microwave Background radiation maps. We use linear and quadratic fusion to produce a combined image for the detection. Moreover, we test these ideas for the simple case of point sources embedded in white noise and for the case of realistic simulations of microwave images for the 44 GHz channel of ESA's Planck satellite. Using quadratic fusion and allowing a 1% of false alarms we detect 25% more sources than using linear fusion. If we allow instead %5 false alarms, quadratic fusion yields 40% more sources than linear fusion.