Compton camera imaging of gamma rays relies on the inversion of a Radon transform on conical surfaces. Algebraic reconstruction methods have been proposed since the invention of the camera in late 1970s. More recently, iterative algorithms based on statistical modeling of the acquisition have been established as a reference. Although versatile and well adapted to best account for acquisition geometry and for the statistical model of the data, these algorithms require relatively heavy computing resources and implementation on specific hardware to avoid prohibitive computing delays. On the opposite, analytic methods have limited capability to account for model alterations, for low statistics and for noise in the data, but they can provide reliable results in few seconds with standard computing resources. In this work we focus on numerical aspects of the analytic inversion of a conical Radon transform. We discuss some ways to improve the quality of images and we show that a semi-iterative TV-regularized approach allows strong improvement of results with negligible additional computation costs. The proposed method will be illustrated on Monte-Carlo data simulating a low-dose SPECT acquisition.