Applied Sciences  
Special Issue on Computational Ultrasound Imaging and Applications  
[PERSON] 12,1*(r), [PERSON] 2*(r) and [PERSON] 2,3,*(r)  
Scientific and technical progress is driven particularly by the ability to \"look\" into new areas. Imaging technologies such as optical and electron microscopy, X-ray, positron emission tomography, magnetic resonance imaging, and most recently gravitational wave astronomy have each provided humanity with a window into a new world. Ultrasound (US) imaging, which emerged in the last century, has enabled us to probe otherwise opaque media in a non-invasive, safe, and cost-efficient manner. This has led to a multitude of new applications, particularly in the fields of medical diagnostics and non-destructive testing. However, some practical limitations of ultrasound imaging have held some very desirable applications just out of reach:  
1. **Susceptibility to aberrations**: The quality of a US image degrades if there are deviations from the assumed speed of sound or reflections that are not accounted for during beamforming. In the context of process metrology, for instance, having a multi-mode wave guide in the acoustical path to shield the transducer array from hot melts prevents in situ flow imaging [1]. In medical context, the strong aberrations induced by the skull bone hinder transcranial US imaging and therapy [2]. This limitation impedes non-invasive, pre-hospital or bed-side diagnostics and continuous monitoring of the brain. 2. **Limited processing bandwidth**: The bandwidth of capturing and processing the information conveyed in the sound field is often limited by the ultrasound device. This makes it very hard to simultaneously achieve real-time 3D imaging with high spatial and temporal resolution over a large field of view. As a result, it is still challenging to comprehensively capture fast-moving volumetric objects with complex structures, such as the beating heart [3]. 3. **Diffraction limit**: The diffraction of sound waves limits the resolution of classical US imaging and hinders the ability to visualize sub-wavelength objects or structures. By overcoming this limitation, anatomical and functional imaging of microvasculature in vivo [4] or high-resolution flow mapping in technical processes [5] becomes feasible. In the future, this may even enable imaging and tracking of medical microrobots, which is essential for their application in vivo [6]. 4. **Manual decision-making process**: Deriving diagnostic decisions from ultrasound images is a complex and to date mostly manual process. Augmenting or automating parts of the decision-making process through advanced statistical or machine learning methods could potentially lead to faster and more objective diagnostic results [7]. 5. **Limited modalities:** Restriction to the classical modalities of US imaging, such as brightness mode (B-mode) and Doppler, reduces its diagnostic value. Acquiring additional modalities through computational or physical methods can provide more information. For example, shear wave elastography can infer the mechanical stiffness of tissues and materials [8], and photoacoustic imaging can reveal their optical properties [9]. In recent decades, enormous computational resources have become available and cost efficient. This allows addressing the aforementioned challenges with a combination of novel methods; for example, computational, software-defined ultrasound imaging allows for the use of more complex signal processing algorithms. Such methods enable super-resolution imaging, correction of strong aberrations, and reconstruction of the shear wave speed of the insonified medium. Further down the signal processing pipeline, machine learning methods can assist in interpreting the acquired data. This Special Issue comprises a total of nine papers that address the aforementioned challenges. 1. [PERSON] et al. show that geometry-based phase aberration correction enhances the contrast and resolution of transcranial images [10]. [PERSON] et al.