We consider the convolution model: $Y = X + \varepsilon$, where $ X $ and $ \varepsilon$ are independent. We aim to estimate $ \int_\mathbb{R} f^2(x)dx$, where $ f$ is the unknown density of the signal $X$ from $n$ observations of $Y$. We introduce a novel projection estimator based on expanding $f$ in the Hermite basis. Convergence rates for $f$ within the Sobolev-Hermite ball are provided for various error types. We also present a novel adaptive procedure inspired by Goldenshluger and Lepski (2011) to select the appropriate space, and we demonstrate an oracle inequality for the adaptive estimator. Numerical experiments are conducted to illustrate the effectiveness of our methodology.