Classical full waveform inversion (FWI) is an unconstrained data fitting/parameter estimation problem where the exact solution of the wave equation is enforced in the objective function, leading to highly non-linear problem prone to cycle skipping. To extend the linear regime of FWI, the wavefield reconstruction inversion (WRI) computes wavefields with wave equation relaxation to foster data fidelity before estimating parameters by minimizing the source residuals the relaxation generated. This wave equation relaxation was first implemented with a penalty method, which requires a dynamic control of the penalty parameter. To overcome this issue, iteratively refined (IR)-WRI replaces the penalty method by the alternating direction method of multipliers (ADMM) in which the Lagrange multipliers provide additional leverages to control the solution accuracy. Furthermore, ADMM provides a suitable framework to equip IR-WRI with bound constraint and hybrid Tikhonov+total variation regularization (BTT). Here, we assess the robustness of BTT-regularized IRWRI against sparse long-offset stationary-recording acquisitions. We show how the blockiness and sparsity-promoting properties of the BTT regularization narrow the null space of the FWI resulting from incomplete illumination and mitigate aliasing artifacts when a few sources and receivers are deployed on regular or random grids.