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Ultrasound image resolution enhancement is an ongoing challenge to date. Though many works have been performed using device-based approach, there exists few works dealing with post-processing methods. This paper investigates a technique based on the Alternating Direction Method of Multipliers for the resolution enhancement in ultrasound imaging, which includes the deblurring and denoising tasks. We here point out the characteristics of the proposed technique and thereby underline the features that must be dealt with for successful ultrasound image restoration. Synthetic and in vivo ultrasound images are processed in order to asses its performances.