Proposing Rapid Source Pulsing for Improved Super-Resolution in Digital Breast Tomosynthesis

Abstract

Our previous work showed that digital breast tomosynthesis (DBT) systems are capable of super-resolution, or subpixel resolution relative to the detector. Using a bar pattern phantom, it is possible to demonstrate that there are anisotropies in super-resolution throughout the reconstruction. These anisotropies are lessened in acquisition geometries with narrow spacing between source positions. This paper demonstrates that by re-arranging the source positions in the scan, the anisotropies can be minimized even further. To this end, a theoretical model of the reconstruction of a high-frequency sinusoidal test object was developed from first principles. We modeled the effect of clustering additional source positions around each conventional source position in fine increments (submillimeter). This design can be implemented by rapidly pulsing the source during a continuous sweep of the x-ray tube. It is shown that it is not possible to eliminate the anisotropies in a conventional DBT system with uniformly-spaced source positions, even if the increments of spacing are narrower than those used clinically. However, super-resolution can be achieved everywhere if the source positions are re-arranged in clusters with submillimeter spacing. Our previous work investigated a different approach for optimizing super-resolution through the use of detector motion perpendicular to the breast support. The advantage of introducing rapid source pulsing is that detector motion is no longer required; this mitigates the need for a thick detector housing, which may be cumbersome for patient positioning.

Keywords: Aliasing; Digital Breast Tomosynthesis; Digital Imaging; Fourier Transform; Image Quality; Image Reconstruction; Mammography; Super-Resolution.

Figure 1.

Shown are two different subsets of seven projections (dark grey), varying in terms of spacing between source positions.

Figure 2.

There are fewer aliasing artifacts (denoted by the arrows) in the scan with narrowly-spaced source positions.

Figure 3.

A DBT system design with clustered source positions is modeled. The parameter N₁ controls the number of clusters, while the parameter N₂ controls the number of source positions per cluster. In this example, N₁ = 7 and N₂ = 5.

Figure 4.

In the conventional acquisition geometry (Θ = 20°, N_t = 15), the ability to achieve super-resolution is dependent on the z₀-coordinate of the object. Two z₀-coordinates are shown here as examples. In order for super-resolution to be achieved with high quality, the ratio of amplitudes A₁ to A₂ (r-factor) in Fourier space should be as small as possible.

Figure 5.

(a) In the conventional acquisition geometry (Θ = 20°, N_t = 15), the r-factor varies between 0.067 and 1.92 in the histogram of 1,000 randomly-sampled points in the VOI. (b) The proportion of points in the VOI with high-quality super-resolution is calculated by introducing a threshold (r-factor < 1/3). Based on 200 bootstrapped re-samplings of this proportion, the 95% confidence interval varies between 0.607 and 0.665.

Figure 6.

As N₂ increases, the maximum amplitude of the r-factor decreases. Therefore, in order for super-resolution to be achieved uniformly throughout the image with high quality, the source positions should be clustered together as much as possible (in this example, with 0.05° spacing).

Figure 7.

As N₂ increases, there are more points in the VOI at which super-resolution is achieved with high quality (r-factor < 1/3). The error bars denote 95% confidence intervals for the proportion.