Optimizing NILC Extractions of the Thermal Sunyaev-Zeldovich Effect with Deep Learning

All-sky maps of the thermal Sunyaev-Zel'dovich effect (SZ) tend to suffer from systematic features arising from the component separation techniques used to extract the signal. In this work, we investigate one of these methods known as needlet internal linear combination (NILC) and test its performance on simulated data. We show that NILC estimates are strongly affected by the choice of the spatial localization parameter ($\Gamma$), which controls a bias-variance trade-off. Typically, NILC extractions assume a fixed value of $\Gamma$ over the entire sky, but we show there exists an optimal $\Gamma$ that depends on the SZ signal strength and local contamination properties. Then we calculate the NILC solutions for multiple values of $\Gamma$ and feed the results into a neural network to predict the SZ signal. This extraction method, which we call Deep-NILC, is tested against a set of validation data, including recovered radial profiles of resolved systems. Our main result is that Deep-NILC offers significant improvements over choosing fixed values of $\Gamma$.