Multiple-Frequency Formulation of DBIM-TwIST Algorithm Sample Clauses

Multiple-Frequency Formulation of DBIM-TwIST Algorithm. ‌ The DBIM is an iterative inverse scattering algorithm which is commonly used to estimate the spatial distribution of dielectric properties within a region V [134]. Under the Born approximation, a linear integral equation at each iteration can be discretized for all Tx-Rx pairs, leading to a linear system that can be solved by various methods including the TwIST method, as presented in the previous chapter [132]. The chapter presented a methodology to increase the robustness of the DBIM–TwIST algorithm, as well as ways to optimise its parameters for a particular application such as microwave breast imaging. This robustness is an important advantage of the TwIST method relative to other iterative solvers such as CGLS and LSQR, as suggested by the comparison results in Section 4.5.3.      ℜ{A(ω1)} ℜ{A(ω1)}+ω1 τℑ2 {A(ω1)} 1+(ω τ)1 1+(ω τ)1 ℑ{A(ω1)} ℑ{A(ω1)}−ω1 τℜ2 {A(ω1)} 1+(ω τ)2 ℜ{A(ω2)} ℜ{A(ω2)}+ω2 τℑ2 {A(ω2)} ω∗ω−1 1ℑ{A(ω1)} −ω∗ω−1 1ℜ{A(ω1)} ω∗ω−2 1ℑ{A(ω2)}       o∞        ℜ{A(ω1)}   ℑ{A(ω1)}  ℜ{A(ω2)} .    ℑ{A(ω2)} ℑ{A(ω2)}−ω2 τℜ2 {A(ω2)} −ω∗ω−2 1ℜ{A(ω2)}   o∆  =  ℑ{A(ω2)}  1+(ω2τ)        . . .    oσ ϵ 0ω∗  ℜ{A(ω f )} ℜ{A(ω f )}+ω f τℑ{A(ω f )} ω∗ω−1ℑ{A(ω f )}   ℜ{A(ω f )}  )}  ℑ{A(ω f ℑ{A(ω f )}−ω f τℜ{A(ω f )} 1+(ω f τ)2 −ω∗ω−f 1ℜ{A(ω f )}   ℑ{A(ω f )} 