•Has proven applicability in recovering the flow profile in intra-cranial aneurysms.•Results in lower error metrics compared to the state-of-the-art denoising methods.•Enables more accurate computation of flow derived patho-physiological parameters. 4D-Flow MRI has emerged as a powerful tool to non-invasively image blood velocity profiles in the human cardio-vascular system. However, it is plagued by issues such as velocity aliasing, phase offsets, acquisition noise, and low spatial and temporal resolution. In imaging small blood vessel malformations such as intra-cranial aneurysms, the spatial resolution of 4D-Flow is often inadequate to resolve fine flow features. In this paper, we address the problem of low spatial resolution and noise by combining 4D-Flow MRI and patient specific computational fluid dynamics using Least Absolute Shrinkage and Selection Operator. Extensive experiments using numerical phantoms of two actual intra-cranial aneurysms geometries show the applicability of the proposed method in recovering the flow profile. Comparisons with the state-of-the-art denoising methods for 4D-Flow show lower error metrics. This method can enable more accurate computation of flow derived patho-physiological parameters such as wall shear stresses, pressure gradients, and viscous dissipation.