The projection of sample measurements onto a reconstruction space represented by a basis on a regular grid is a powerful and simple approach to estimate a probability density function. In this paper, we focus on Riesz bases and propose a projection operator that, in contrast to previous works, guarantees the bona fide properties for the estimate, namely, non-negativity and total probability mass $1$. Our bona fide projection is defined as a convex problem. We propose solution techniques and evaluate them. Results suggest an improved performance, specifically in circumstances prone to rippling effects.