# A High-Efficiency Super-Resolution Reconstruction Method for Ultrasound Microvascular Imaging
## 1 Introduction  
Ultrasound has become a commonly used method of medical examination because of its fast, non-destructive and inexpensive characteristics. However, the main problem of ultrasound imaging lies in its low image quality. Compared to other modalities, such as the computed tomography (CT) and the magnetic resonance imaging (MRI), ultrasound imaging has a lower resolution. The reason is that the resolution of ultrasound imaging is limited by the emission wavelength [1]. Usually, the center frequency of the ultrasound is at the megahertz order, resulting in the wavelengths at the order of a hundred microns. With a resolution of this magnitude, it is not possible to observe the microvessels in microns, which are of great importance in the early diagnosis of cancer [2]. In 2016, [PERSON] et al. [3] proposed the epoch-making ultrasound imaging method called super-resolution ultrasound imaging. This method uses microbubbles as the resolution units andbreaks through the resolution limitations of traditional ultrasound imaging. Through continuous plane wave transmissions, the complete trajectory of microbubbles can be recorded. After trajectory tracking, tiny blood vessels can be observed. This technique was tested on rat cerebral vascular and has been proved to be effective [3]. The concept of ultrasound super-resolution imaging originates from optical imaging [4; 5; 6], and both processes are very similar [7; 8; 9]. In ultrasound super-resolution imaging, the beamformed images corresponding to the plane wave transmissions are preprocessed firstly by the wall filter [10; 11]. Then following are the two most important steps of the reconstruction, the microbubble localization and the trajectory tracking [7]. The sub-pixel localization of a single microbubble with an accuracy below the diffraction limit is the basis of super-resolution reconstruction methods [12]. Because a single microbubble can be treated as an incoherent point source in the beamformed image sequence, the result of fitting a point-spread-function (PSF) model to an image of a point-like emitter is an estimate of the microbubble position, its imaged size and intensity. It has been shown that the Gaussian function provides a very good approximation of the real PSF of an ultrasound scanner [13]. The advantages of Gaussian PSF models are their simplicity, robustness, and computational efficiency. However, due to the lack of adaptability, the original Gaussian PSF has a limited accuracy for positioning. As for the trajectory tracking, the scatter plot is the simplest and most common visualization method [14], and does not always provide high-quality results. A simple binary image is created with the pixel intensity value set to one at locations corresponding to microbubble positions. All other pixel intensity values are set to zero. This method is fast but does not reflect the density of microbubbles. Due to the above problems, the existing reconstruction methods can only get good super-resolution results when the collected signals are long enough (usually up to 10,000 frames) [15]. In this paper, we propose a novel super-resolution reconstruction method, in which brand-new microbubble localization and trajectory tracking techniques were presented for better reconstruction results with fewer sampling frames. Taking the characteristics of ultrasound images and the microbubble density into consideration, we innovatively adopted the integrated form of the 2D Gaussian function [16] and the averaged shifted histograms (ASH) [17] for the two steps respectively. The introduction of the methods helps enhance the quality of the reconstructed images significantly, and in turn improves the imaging time resolution. In order to prove the validity of the proposed method, we conducted in vivo experiments on the kidney of a rabbit. The structure of the paper is arranged as follows: Materials and Methods section introduces the mathematical background of our proposed method. The setup of in vivo experiments is also given in this section.