## 1 Introduction  
In the last years, lung ultrasonography has gained ever-growing clinical interest and curiosity because of its peculiar ability to acquire clinical information at bedside, its non-invasiveness and low cost. In particular settings (emergency medicine, intensive care unit) its utility has been well demonstrated [1; 2; 3]. More recently, pulmonologists and pediatrics started to use chest ultrasound for detecting pleural diseases, consolidations, bronchiolitis, interstitial lung pathology and critical pulmonary conditions of the newborn [4; 5]. However, the development of lung ultrasonography for exploring non-consolidated organs, has been disordered and not supported by a strong knowledge of the physical mechanisms that underlie pulmonary artifacts. Lung ultrasonography is comparable to a standard morphological sonography only when assessing a pulmonary consolidation, a tissue without air, which is in direct contact with the visceral pleural. In this case, the clinicians evaluate anatomic images, representing the real structure of the diseased organ. Normally, chest X ray is the first diagnostic tool for pneumonia, pulmonary contusions, lung cancer, and pulmonary infarction. The possibility to assess lung consolidations in several conditions by using ultrasound has a wide clinical impact, limiting, optimizing and justifying ionizing radiations [6; 7; 8; 9]. On one hand, however, chest X ray has the advantage to show a panoramic view, while lung consolidations not reaching the visceral pleura can be completely missed by ultrasound [10]. On the other hand, chest ultrasonography is able to provide more information about the characteristics of consolidations reaching the visceral pleura [11; 12] such as: air dynamic or static bronchogram [13], fluid bronchogram [11], parenchymal abscesses, necrotic areas, vascularization and sonographic contrast-enhancement information [14]. Pleural diseases are the other relevant target for clinical ultrasound. For pleural effusions ultrasound can be considered the main diagnostic tool, giving us the possibility to evaluate the sonographic appearance, extension, mechanical effects on work of breathing, and interventional guidance [15; 16; 17]. Neither chest X-ray nor Chest CT scan is able to provide such relevant details to clinicians. Differently, when the lung surface is denser but not yet consolidated, the large acoustic impedance gradient between the chest wall and the pulmonary tissue containing air prevents every anatomic representation, and the scan results in the visualization of many kind of vertical artifacts generally known as B-Lines [18; 19]. Little is known about the best method for evaluating vertical lung artifacts because they look different at different depths, depend on the machine/probe and on the frequency employed. Probably, many \"cosmetic\" regulations of modern machines influence the visualization of the artifacts. Tissue Harmonic Imaging, compound imaging, pre- and post-processing techniques and filters can modify the appearance of the artifacts [19]. When imaging the pathologic yet not fully consolidated lung surface, the basic assumptions behind standard ultrasound imaging are severely unmet. Firstly, the presence of air in the volume of interest results in strong heterogeneities in speed of sound. Consequently, performing the typical time-to-space conversion based on an average speed of sound value, as normally implemented in commercial scanners, is not appropriate in this case. Secondly, the high reflection coefficient experienced by ultrasound waves at multiple and distributed air-tissue interfaces produces a highly scattering environment, where multiple scattering phenomena are strong, and it is therefore not possible to model the echo-signals received by the probe by simply assuming a first-order scattering medium. In this context, it is impossible to link the time of arrival of the echo signals to the spatial location of the corresponding scatterers.