Abstract : This work deals with Dynamic Positron Emission Tomography (PET) data reconstruction, considering time as an additional variable (space+time). A convex optimization approach closely related to a Bayesian framework is adopted. The objective function to be minimized is expressed in the wavelet-frame domain and is non-necessarily differentiable in order to promote sparsity. We propose an adapted version of Forward-Backward- Douglas-Rachford (FBDR) algorithm to solve the resulting min- imization problem. The effectiveness of this approach is shown with simulated dynamic PET data. Comparative results are also provided.