Investigations of echo signal models for medical ultrasound imaging systems.
Date of Issue2012
School of Electrical and Electronic Engineering
Medical ultrasound images are degraded representations of the true acoustical reflectors in the imaged anatomical tissue. In theory, the qualities of medical ultrasound images rely mainly on the collected ultrasound echo signals. If ultrasound echo signals were accurate representations of biological tissues, the resolution of medical ultrasound images would be improved correspondingly. However, ultrasound echo signals do not provide a direct description of biological tissues usually because they are regarded as the reflected echoes arising from the interactions between ultrasound system and biological tissues. In order to retrieve the true properties of tissues of interest, we need to resort to accurate models of ultrasound echo signals. A reasonable and accurate model is very instructive in understanding the essential characteristics of ultrasound imaging systems. This thesis focuses on the investigations of current models and development of novel models for ultrasound imaging systems. A theoretical model based on classical ultrasound acoustics was developed in 1970s. This model with integration format has been verified and cited for decades. However, from both the signal and system point of view, it purely concerns ultrasound physics and is difficult to be applied in engineering field. Since 1990s, a conventional convolution model was fully derived based on the theoretical model and presented an appealing format for engineers. In this convolution model, ultrasound echo signals are modeled mathematically as a spatio-temporal convolution between the spacevariant ultrasonic system impulse response or point-spread function (PSF) and the biological tissues, with the addition of observation noise introduced in the image formation process. Furthermore, a simple discrete convolution model directly arising from continuous conventional model was proposed and widely applied in ultrasound deconvolution filtering techniques. The first contribution of our work is the development of a new convolution model with reasonable and feasible conditions. After careful studies, we find there is a flawed approximation in the conventional convolution model which plays the key role in the original derivations such that the original convolution model is not fully theoretically sound and valid. Consequently, the deconvolution-related techniques for processing ultrasound echo signals no longer have theoretical foundation. In this thesis, a new convolution model of medical ultrasound echo process is proposed and its derivation and formulation are provided. Based on the investigations of classical acoustical equations, the new convolution model presents dominant terms under common practically feasible conditions of medical ultrasound. It provides a new theoretical foundation for the prevailing deconvolution techniques in ultrasound signal processing and new insight in exploring interactions between ultrasound pulses and body tissues in ultrasound scanning and imaging. The second contribution of our work is the proposal of two new discrete models of ultrasound echo signals. The conventional discrete model does not provide a convincing discretization from conventional continuous convolution model. The reason behind is that time dimension is ignored deliberately during the discretization without strict proof. Meanwhile, tissue information is only conceptual 2-D sequences of signals without specific indications on how to connect the so-called tissue signals with real soft tissues' anatomy. Meanwhile, the simple discrete model is quite general and symbolic such that it is not mathematically straightforward and accurate enough. Besides, we have pointed out the problematic approximation in the derivation of conventional convolution model and proposed new convolution model with reasonable conditions. Hence, starting from the original theoretical model and new convolution model proposed in Chapter 3, two new discrete models and their careful derivations are presented, respectively. In comparison with the conventional discrete model, they are of familiar format of standard discrete systems. Also, inside the models, there are clear indications on how the tissue property parameters interact with the input impulse signals exactly. Hence, provided the proposed discrete models, the tissue property parameters can be separated with ease from the echo signals, which are exactly what are of ultrasound imaging interest. In summary, this thesis is a contribution to the development of novel ultrasound echo models for medical ultrasound imaging systems. Several new models and their extensive studies for medical ultrasound imaging are provided. Our work establishes a new foundation for ultrasound deconvolution techniques in modern signal processing.
DRNTU::Engineering::Electrical and electronic engineering