Numerical stabilization techniques are frequently employed to mitigate the arising of spurious oscillations, a common occurrence in simulations of convection dominated flows modeled by the incompressible Navier-Stokes equations, particularly when utilizing full order models (FOMs) in under-resolved or marginally-resolved scenarios. However, the precise role of numerical stabilization in the context of reduced order models (ROMs) for simulating convection-dominated, under- or marginally-resolved flows remains not well understood. This talk aims to present and analyze a novel regularized reduced order model (Reg- ROM) based on approximate deconvolution [1], ADL-ROM. In the first part of this talk, we introduce a well-known Reg-ROM for the incompressible Navier-Stokes equations, i.e., L-ROM, and our new one, i.e., ADL-ROM. In L-ROM, a differential filter is used to smooth the numerical oscillations that arise in the Galerkin ROM (G-ROM) for large Reynolds numbers in the under-resolved regime. In ADL-ROM, the aim is to deconvolve the filtered variable in L-ROM to increase its accuracy without compromising its stability. In the second part of the talk, we comment on and compare these Reg-ROMs with each other and with G-ROM by showing: ADL-ROM numerical results, the comparison between the different ROMs and the analysis of the errors, alongside their implementation in RBniCSx. In the end, we think that this type of regularization can bring great benefits in different practical applications, especially in cardiovascular models.