Scatter estimation

As described in the previous section, SPSFs were calculated using a geometry with and without uniform phantoms, corresponding to SPSF (which includes a phantom of particular thickness and glandularity) and SPSFsys respectively. Therefore, a set

of scatter kernels based on SPSF was used within the breast phantom region and a different set (based on SPSFsys) outside during the convolution process. A binary

146 Chapter 6. Convolution-based scatter prediction for DBT

Figure 6.21: SPSF contribution for each of the layers included in the system using a 4cm thick breast phantom of glandularity 0% and AG = 0mm. When the scattered radiation recorded within the detector comes from more than one layer, this has been labeled as ’multiple’.

template was used to calculate all the pixels inside and outside the breast phantom projection.

The total scatter image ST ,φ(x, y) for a projection angle φ was estimated as a combi-

nation of the scatter image within the breast area Sbre,φ(x, y) and the scatter outside

the breast region Ssys,φ(x, y):

ST ,φ(x, y) = Sbre,φ(x, y) + Ssys,φ(x, y) [eV ]. (6.9)

Sbre(x, y) was estimated as previously illustrated in Equation 6.5, where Kφ,t,G,AG was

calculated using the SPSF for the realistic geometry. Note that SPSFs calculated for a single projection (at either 0, 7.5 or 25o) was used across the entire breast phantom area. Therefore, it was assumed parallel X-ray beam within the breast phantom region. The scatter contribution from the system Ssys,φ(x, y) was estimated after convolving

the primary image at the image receptor P (x, y) with a scatter kernel Ksys,φ,T in the

region outside the phantom.

Ssys,φ(x, y) = a X k1=−a b X k2=−b P (k1, k2)Ksys,φ,T(x − k1, y − k2) [eV ]. (6.10)

Ksys,φ,T depends only on the distance from the compression paddle to the breast sup-

port, i.e. breast thickness T , as the air gap distance between the breast support and image receptor is constant.

As previously described, Ksys,φ,T was calculated in the absence of any scattering mate-

6.2. Realistic DBT geometry 147

by the breast tissue in the region near the breast phantom edge. Therefore, the calcu- lated SPSFsys needs to be attenuated by the corresponding breast tissue thickness.

Figure 6.22 represents a diagram to understand this process, where two cases of scat- tered X-ray photons within the compression paddle are shown. In the case O-B, an X-ray photon is recorded within the image receptor at point (x1’,y1’) after a scattering

interaction within the paddle (corresponding to point (x,y) at the receptor) without being attenuated by any other tissue. Thus, the results agree with the previously cal- culated SPSFsys. In contrast, the scattered photon O-A is attenuated along the path

that the X-ray photon traverses until it reaches the image receptor at (x2’,y2’).

Figure 6.22: Systematic diagram showing two cases of scattered photons from the compression paddle. The ray O-B shows an unattenuated X-ray photon which reach the image receptor at (x1’,y1’). The X-ray photon

scattered from the paddle following O-A path, recorded at (x2’,y2’), should

be attenuated due to the path traversed within the breast phantom.

Previously when the methodology for the idealised DBT geometry was described, it was introduced the idea of a distance-to-the-edge of the breast phantom correction factor. This option was explored here to account for the attenuation of the X-ray photons as they traverse through the breast phantom. In order to avoid using the breast phantom to calculate the correction factor, a series of D-shape phantoms were used. However, it was found that due to the non-symmetry curvature of the breast phantom models, this methodology did not show good performance and was discarded, motivating the exploration of an alternative method.

In this alternative method, Ksys,φ,T was weighted accordingly to account for the path

traversed by the X-ray photons from the compression paddle to the image receptor. This weight map α(x, y, x0, y0) compensates for the lack of scattering material outside the breast phantom (α = 1) and for the attenuation due to the breast tissue (α < 1) and was calculated as the ratio of the energy deposited within the image receptor with and without the breast phantom as follows:

α(x, y, x0, y0) =

PEmax

E=Emin(E) · w(E) · E · e

P

i−µi(E)·ti(x,y,x0,y0)_dE

PEmax

E=Emin(E) · w(E) · E · e

P

148 Chapter 6. Convolution-based scatter prediction for DBT

where (E) and w(E) correspond to the energy efficiency of the detector and the energy spectrum (normalised to an area of 1) observed after the compression paddle respec- tively. The linear attenuation coefficients µ(E) and distances from the compression paddle to the image receptor t(x, y, x0, y0) along the X-ray photon beam were also in- cluded. The subscripts i and j correspond to the number of tissues found along the X-ray beam in the presence and absence of the breast phantom respectively. When breast tissue was found, the µ(E) was set to the average glandularity of the breast phantom G (see Table 6.3). The distances t(x, y, x0, y0) were calculated using the Sid- don X-ray tracing methodology [194].

The task of calculating the distances from every point in the compression paddle to each pixel in the detector was very time consuming. Thus, in order to reduce the computation time, the evaluated points in the compression paddle were separated by 3mm. Furthermore, only the pixels within the projected breast phantom shadow were evaluated.

Once α(x, y, x0, y0) was calculated for each point within the compression paddle, Ssys

was estimated as follows

Ssys(x, y) = a X k1=−a b X k2=−b P (k1, k2)Ksys,φ,T(x−k1, y −k2)α(x, y, x0, y0) [eV ]. (6.12)

In order to account for the X-ray incident angle at each evaluated point in the compres- sion paddle, the X-ray incident angle and the direction of the primary X-ray photons were taken into account. For a given point in the compression paddle (outside the breast phantom area), the closest simulated incident angle (previously calculated from 0 to 35o in steps of 5o) was used.

An example of these incident (white circular lines) and direction angles (yellow lines) are shown in Figure 6.23 for a projection angle of 0o and a 5cm thick breast phantom (red contour).