Optimal Filters on the Sphere

We derive optimal filters on the sphere in the context of detecting compact objects embedded in a stochastic background process. The matched filter and the scale adaptive filter are derived on the sphere in the most general setting, allowing for directional template profiles and filters. The performance and relative merits of the two optimal filters are discussed. The application of optimal filter theory on the sphere to the detection of compact objects is demonstrated on simulated data. A naive detection strategy is adopted, with an initial aim of illustrating the application of the new filter theory derived on the sphere. Nevertheless, this simple object detection strategy is demonstrated to perform well, even at low signal-to-noise ratio.