Guest Editorial Special Issue on Sparsity Driven Methods in Medical Ultrasound

The fundamentals of ultrasound signal and image processing relied for a long time on the hypothesis of Gaussianity, justified by the central limit theorem and the point-scattering model widely accepted in ultrasound imaging. Assuming a large number of scatterers per resolution cell, the probability distribution function of the backscattered radio frequency (RF) signals converges indeed to a Gaussian law, leading to Rayleigh-distributed envelope images. Over the last three decades, several studies questioned this paradigm, based on observations proving that in several clinical applications, the Gaussian distribution did not fit the data well. Consequently, a wide range of non-Gaussian laws were used to model the backscattered signals in a number of ultrasound imaging applications such as tissue characterization and image segmentation. In the early 2000s, heavy-tailed statistical models were shown to be well adapted to ultrasound images, paving the way to new prospects in ultrasound signal processing and ultimately leading to growing interest in the concept of sparsity for ultrasound imaging. Sparse signals are a special class of signals with a particular structure, i.e., they contain many coefficients equal to or close to zero either in the time domain or when represented in an appropriate basis or dictionary.