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Large polyatomic molecules typically exhibit low ionization potentials, Ip, leading to over-the-barrier ionization (OBI) already at relatively low intensities (~1013 W/cm2). We revisit laser-induced electron diffraction (LIED) in the over-the-barrier ionization (OBI) regime and answer the question of whether imaging of molecular structure is still possible with LIED. We employ a hydrogen-like model system mimicking a molecule with low Ip using a classical trajectory-based model (CT) that incorporates the Coulomb potential; we also use the numerical solution to the time-dependent Schrodinger equation (TDSE). Specifically, we adopt the Fourier transform variant of LIED (FT-LIED) to show that even a significant contribution of short trajectories in the OBI regime does not preclude structure retrieval from strong-field diffractive patterns. This theoretical investigation shows that LIED can be well described by the classical recollision model even when ionization occurs within the OBI regime. This study paves the way towards strong-field imaging of chemical transformations of large polyatomic molecules in real-time based on strong-field electron recollision.