Sinusoidal Frequency Estimation with Applications to Ultrasound

Section 1.2. Thesis Outline and Contributions 5RF signal onto the space orthogonal to the clutter subspace, as depicted in Figure 1.1, wherethe clutter subspace is spanned by basis vectors u 1 and u 2 . However, the computational costof evaluating the required SVD, or alternatively the estimation of the correlation matrix ofthe examined RF signal and the computation of its EVD is often prohibitive, limiting thepractical applicability of the eigenfilter in CFI. Therefore, there is a real need for the computationallyefficient implementation of this approach. In this thesis, we exploit the factthat the clutter signal has a slowly time-varying nature both in the temporal and spatialdirection, enabling an efficient evaluation of the consecutive SVDs using a subspace trackingtechnique refining the sliding window adaptive SVD (SWASVD) algorithm proposed byBadeau et al. [BRD04].1.2 Thesis Outline and ContributionsThis thesis consists of two parts, estimation using a single carrier or multiple carriers anda focus application: ultrasound. This section presents the outline and contributions of thisthesis.1.2.1 Estimation Using a Single Carrier Or Multiple CarriersThis part of the thesis includes Chapter 2 and Chapter 3 which deal with general singletone estimation as well as multiple-carrier based velocity estimation. As some of this part ofthe thesis is associated with Part II, which mainly concerns with the application of medicalultrasound, readers can also refer to Chapter 4 in Part II to obtain some fundamentals ofultrasound.