MR data are acquired in the frequency domain, known as k-space. Acquiring high-quality and high-resolution MR images can be time-consuming, posing a significant challenge when multiple sequences providing complementary contrast information are needed or when the patient is unable to remain in the scanner for an extended period of time. Reducing k-space measurements is a strategy to speed up acquisition, but often leads to reduced quality in reconstructed images. Additionally, in real-world MRI, both under-sampled and full-sampled images are prone to artefacts, and correcting these artefacts is crucial for maintaining diagnostic accuracy. Deep learning methods have been proposed to restore image quality from under-sampled data, while others focused on the correction of artefacts that result from the noise or motion. No approach has however been proposed so far that addresses both acceleration and artefacts correction, limiting the performance of these models when these degradation factors occur simultaneously. To address this gap, we present a method for recovering high-quality images from under-sampled data with simultaneously correction for noise and motion artefact called USArt (Under-Sampling and Artifact correction model). Customized for 2D brain anatomical images acquired with Cartesian sampling, USArt employs a dual sub-model approach. The results demonstrate remarkable increase of signal-to-noise ratio (SNR) and contrast in the images restored. Various under-sampling strategies and degradation levels were explored, with the gradient under-sampling strategy yielding the best outcomes. We achieved up to 5x acceleration and simultaneously artefacts correction without significant degradation, showcasing the model's robustness in real-world settings.