Ultrasound imaging (US) is susceptible to several types of artifacts. Most artifacts appear because of transducer limitations and simplified assumptions on the wave propagation. The artifacts are sometimes used as a component that contains tissue information; however, they often lead to a misinterpretation in the clinical diagnosis. Therefore, to improve the clinical utility of ultrasound in difficult-to-image patients and settings, a number of artifact removal methods have been proposed that aim at boosting image quality. Classical optimization-based methods have severe limitations due to their limited performance and high computation requirements. Furthermore, it is difficult to obtain parameters for producing high-quality output. A quick remedy for the aforementioned issues is the deep learning approach, which offers high performance compared with the traditional methods despite the significantly reduced runtime complexity. Another big advantage is that the same parameters as those learned during the training phase can be used to process different input images. This has motivated the scientific community to design deep-neural-network-based approaches for US artifact removal tasks.

The objective of this chapter is to discuss a very important issue of the effect of finite sampling with respect to either the finite length of the record or the finite sampling intervals. A few sampling theorems are discussed.