# The Feasibility of Shadowed Image Restoration Using the Synthetic Aperture Focusing Technique
## 1 Introduction  
The advantageous properties of ultrasound scanning (US), such as non-invasiveness and non-radiation, are widely used in medical diagnosis [1; 2; 3]. US uses the interaction of high-frequency acoustic energy in a specimen to produce an original image that reveals tissues inside the human body. High-frequency (1 to 20 MHz) sound energy is transmitted into a specimen by an ultrasound machine in the form of multiple pulses, and the echoes are relayed on a monitor and form a two-dimensional image. However, the US still suffers from limitations in resolution, contrast, and signal-to-noise ratio (SNR), and is not free from artefacts [4]. Acoustic shadowing, a feature of ultrasound images, is one of the artefacts inherent in US imaging.  
Acoustic shadowing is detected as an ultrasonic manifestation. Occurrences of anechoic zones caused by acoustic shadowing are devoid of echo and fail to render reliable images in US [3; 5]. In response to acoustic shadowing, the anechoic zone displays as a dark area, e.g., due to the echogenic appearance of tissue posterior to kidney stones, gallstones, benign or malignant tumors, foreign bodies, complex sclerosing lesions, postoperative scars, fibrous or dense breast tissue, etc. [6; 7; 8; 9]. Hence, in a traditional sonographic examination, acoustic shadowing is often used to explore possible relevant differential diagnoses rather than the further use of ultrasound to diagnose the shadowed lesions [10].  
In medical sonography, a shadowed tissue induced by acoustic shadowing cannot be revealed by increasing the power or gain of the ultrasound machine. However, due to the directionality of acoustic shadowing and the acoustic radiation (beam) pattern, a shadowed target that is echo-free at a specific scan position can be echoed in other scan positions in a multi-channel scan [11; 12]. Hence, it is critical and worthwhile for us to overcome the artefacts resulting from acoustic shadowing that degrade the attainable ultrasonic image. Typically, a posterior restoration process is employed to reconstruct the original image from observations.  
Nowadays, restoration techniques are significantly advanced, owing to the development of digital processes [13; 14]. With the heuristic principle of signal superposition via constructive interference, the synthetic aperture focusing technique (SAFT) algorithm allows each point within the target to be focused upon by mathematically simulating the action of a lens specifically formed for imaging the target inside the structure. The efficiencies and easy manipulation make SAFT one of the most popular processing technologies used to improve image quality and maximize the resolution from acquired echo signals. SAFT is proposed to facilitate the original image restoration by trying to \"undo\" the effects of acoustic shadowing on an ultrasonic image [15; 16].  
The acoustic shadowing encountered in the sonographic examination is often used to explore possible relevant differential diagnoses, rather than to reveal the shadowed lesions [7; 17]. In this study, a forward model study is carried out to demonstrate the phenomenon of acoustic shadowing in US and to perform data acquisition. In the posterior stage of image restoration, the acquired data are then processed by SAFT. It is hoped that a potential target hidden under acoustic shadowing can be revealed from restored images. The remainder of this article is therefore organized as follows. First, the laboratory manipulation designed to facilitate the acoustic shadowing experiment is introduced. Subsequently, the theoretical background of SAFT, which is used to perform shadowed image restoration, is briefly described, and the results of laboratory work are presented. Finally, the applications and limitations of the restoration algorithm are addressed in the discussions and conclusions.