Recent imaging methods based on ultrafast sequences associated with adaptive spatiotemporal SVD clutter filtering have improved blood flow detection. In this context, we proposed in [Shen, IUS 2019] a new approach (referred as DRPCA hereafter) that enabled higher resolution flow estimation, by solving a dedicated inverse problem. The main originality of DRPCA was to embed a deconvolution step into the robust principal component analysis (RPCA). However, DRPCA suffers from an important drawback: an experimental measurement of the system point spread function (PSF) is required, hence difficult in clinical applications. In this work, we investigate the joint estimation of both the blood flow and the PSF from IQ Doppler data.