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Top1. Introduction
Medical imaging is the method of creating images of human or animal parts to collect data concerning the structure or properties of tissue, bone, or even physiological characteristics by injecting particular substances into the body (National Research Council, 2006). For the past years, medical imaging has been rapidly changing clinical diagnosis. With the advancement of media and information technology, numerous intelligent and sophisticated diagnosis and treatment methods have been presented (Feng, 2019). In 1885, Wilhelm Roentgen discovered X-ray; hence, medical imaging was born. In the past century, a significant change has been originated from X-ray to MRI, CT, PET, SPECT, ultrasound, etc. The efficiency of non-intrusive imaging systems has made a considerable step along with computer science.
Nowadays, there are a vast number of biological imaging methods, as mentioned above. However, in our study, we only focus on ultrasound because it is one of the most popular and often considered a golden standard in essential diagnoses such as obstetric or cardiac issues.
The use of sonar in 1910 led to the popularity of imaging techniques using sound waves later. One of the most popular sonar-based imaging methods is B-mode (Schueler et al., 1984), which is used for non-intrusive diagnosis and medical imaging. It qualitatively presents the change of sound resistance, which then allows us to distinguish different environments. The image's spatial resolution can be received by an array transducer (Macovski, 1979) and highly-converged, single-element transducers (Kino, 1987). Even though the quality can be worsened by uncertainties in amplitude and phase (Zhu & Steinberg, 1993), B-mode is overall considered uncomplicated and reliable. However, due to its qualitative nature, medical diagnosis using these images is subjective and heavily based on the doctor's expertise.
A qualitative ultrasound technique (also known as tomographic ultrasound) is considered superior to B-mode in offering more valuable information (Jonathan & Oelze, 2013). However, this method still downsides, including its limitation to only weak scattering media, high computation complexity, and commercial equipment capabilities. The application of this method is limited, mostly used with breast cancer.
Tomographic ultrasound is a technique based on inverse scattering theory. The Distorted-Born iterative method (DBIM) is often used to solve the inverse problem. In this method, Green's function is repeated each iteration, causing DBIM to converge quickly (Montero & Janniel, 2009). A significant disadvantage of this approach is its divergence in strong scattering media. In reality, Born approximations hypothesize that the scattering pressure is so small that it can be neglected. It is only correct in weak scattering media. In stronger scattering media, Born approximation is not accurate anymore (Slaney et al., 1984). This problem can be solved by using multiple frequencies for reconstruction based on sound contrast (Haddadin & Ebbini, 1997), (Haddadin & Ebbini, 1998). In these studies, frequencies f1 and f2 are utilized to reconstruct the subject in Nf1 and Nf2 iterations. The low-frequency f1 ensures the convergence of the algorithm to a contrast level near the true level at the cost of low spatial resolution. After that, the high-frequency f2 can improve spatial resolution as maintaining the convergence. The reason behind this is the relatively small difference between the true contrast and initial contrast (Born approximation satisfied). In (Jonathan & Oelze, 2013), (Tijhuis et al., 2001), (Lavarello & Oelze, 2010), (Tran et al., 2016), the authors suggested using more than two frequencies to get the resolution of a tomographic ultrasound image closer to the level of tissue image reconstruction. Not only for ultrasound tomography, the multiple - frequency technique is also applied for ultrasound images in (Ma et al., 2015; Sayed, 2018; Varray et al., 2012; Yoshizumi et al., 2009). However, the use of different frequencies in different iterations is still inconsistent. Frequency hop is usually chosen based on the scenarios being simulated or tested, in fact. Using a multi-frequency approach, we proposed an effective method to increase tomographic ultrasound imaging quality with a fundamental tone and overtones (FTaOT). The fundamental tone is used in the first DBIM iteration, then its overtones for the next iterations. Numerous scenarios have been tested to prove the feasibility of our proposed method.