This paper addresses the problem of super-resolution (SR) for medical ultrasound (US) images. Contrary to device-based approaches, we investigate a post-processing method to invert the direct linear model of US image formation. Given the ill-posedness of single image SR, we proposed an ℓp-norm (1 ≤ p ≤ 2) regularizer for the US tissue reflectivity function/image to be estimated. To solve the associated optimization problem, we propose a novel way to explore the decimation and blurring operators simultaneously. As a consequence, we are able to compute the analytical solution for the ℓ2-norm regularized SR problem and to embed the analytical solution to an alternating direction method of multipliers for the ℓp-norm regularized SR problem. The behavior of the proposed algorithm is illustrated using synthetic, simulated and in vivo US data.