3. Phantom specification

For the evaluation of low-contrast resolution, a contrast-detail (CD) phantom was used with epoxy slabs. The CD phantoms of different diameters (signal region, CaCO3) and thicknesses were arranged within the epoxy slabs. For X-ray imaging, we placed polymethyl methacrylate (PMMA) slabs (200 � 200 mm) with 50 mm thickness on the top of the CD phantom (Figure 1).

Figure 1. Illustration of the CD phantom used in this study.

shown to be very relevant to image quality [21, 24]. In our study, we minimized the image

β ¼ 1:0; np; 100 q; 50

x !¼ <sup>0</sup>

x0 !¼<sup>x</sup> !

! <sup>þ</sup><sup>β</sup> <sup>1</sup> P i∈ Ω<sup>t</sup> Aij X i ∈ Ω<sup>t</sup> Aij

for i ¼ 1 : Ni, if xi < 0 then xi ¼ 0

xres ! <sup>¼</sup> <sup>x</sup> !

Δx ¼ x

^dx <sup>¼</sup> <sup>d</sup> ! x . d ! x � � � � � �

d ! x ¼ ∇ x ! x ! � � � � � � TV

x ! <sup>¼</sup> <sup>x</sup> � � �

! � <sup>x</sup> ! 0

! � <sup>q</sup><sup>∗</sup>Δx<sup>∗</sup>^dx

return x ! res

For the evaluation of low-contrast resolution, a contrast-detail (CD) phantom was used with epoxy slabs. The CD phantoms of different diameters (signal region, CaCO3) and thicknesses were arranged within the epoxy slabs. For X-ray imaging, we placed polymethyl methacrylate (PMMA) slabs (200 � 200 mm) with 50 mm thickness on the top of the CD phantom (Figure 1).

� � � bi � A ! <sup>i</sup> � x !

P<sup>n</sup> <sup>j</sup>¼<sup>1</sup> Aij

quality by using these optimal parameters for the SART-TV algorithms.

for <sup>i</sup> <sup>¼</sup> <sup>1</sup> : Nd, x!¼<sup>x</sup>

repeat main loop

(enforce positivity)

for i = 1:np do TV-minimization loop

72 Medical Imaging and Image-Guided Interventions

3. Phantom specification

(SART)

end

The SART-TV algorithm is expressed in the form of a pseudo code as follows:
