Paper detail

Recovery of singularities for the weighted cone transform appearing in the Compton camera imaging

We study the weighted cone transform $I_κ$ of distributions with compact support in a domain $M $ of $\mathbb{R}^3$, over cone surfaces whose vertexes are located on a smooth surface away from $M$ and opening angles are limited to an open interval of $(0,π/2)$. We show that when the weight function has compact support and satisfies certain nonvanishing assumptions, the normal operator $I^*_κI_κ$ is an elliptic $Ψ$DO at the accessible singularities. Then the accessible singularities are stably recoverable from local data. We prove a microlocal stability estimate for $I_κ$. Moreover, we show the same analysis can be applied to the restricted cone transform.