Achieving Isotropic Super-Resolution with a Non-Isocentric Acquisition Geometry in a Next-Generation Tomosynthesis System

Abstract

We have constructed a prototype next-generation tomosynthesis (NGT) system that supports a non-isocentric acquisition geometry for digital breast tomosynthesis (DBT). In this geometry, the detector gradually descends in the superior-to-inferior direction. The aim of this work is to demonstrate that this geometry offers isotropic super-resolution (SR), unlike clinical DBT systems which are characterized by anisotropies in SR. To this end, a theoretical model of a sinusoidal test object was developed with frequency exceeding the alias frequency of the detector. We simulated two geometries: (1) a conventional geometry with a stationary detector, and (2) a non-isocentric geometry. The input frequency was varied over the full 360° range of angles in the plane of the object. To investigate whether SR was achieved, we calculated the Fourier transform of the reconstruction. The amplitude of the tallest peak below the alias frequency was measured relative to the peak at the input frequency. This ratio (termed the r-factor) should approach zero to achieve high-quality SR. In the conventional geometry, the r-factor was minimized (approaching zero) if the orientation of the frequency was parallel with the source motion, yet exceeded unity (prohibiting SR) in the orientation perpendicular to the source motion. However, in the non-isocentric geometry, the r-factor was minimized (approaching zero) for all orientations of the frequency, meaning SR was achieved isotropically. In summary, isotropic SR in DBT can be achieved using the non-isocentric acquisition geometry supported by the NGT system.

Keywords: Digital breast tomosynthesis; Fourier transform; aliasing; digital imaging; image quality; image reconstruction; super-resolution.

Figure 1.

(a) Projection images of a point-like object are illustrated in a DBT system with lateral source motion. (b) In a conventional geometry, SR is achieved in the x direction due to shifts in this direction; shifts are minimal in the PA direction. (c) In a non-isocentric geometry, the detector descends in the –z direction during the scan, resulting in more pronounced shifts in the PA direction and thus SR in the PA direction.

Figure 2.

X-ray source motion follows a circular arc in the chest-wall plane with angular range Θ. The COR at the origin (point O) is taken to be the midpoint of the breast support in this plane. The sinusoidal test object (thickness ε) is simulated in both conventional and non-isocentric geometries.

Figure 3.

The frequency angle (α) is varied from 0° to 360° to investigate the orientation dependency of SR. The Fourier transform of the reconstruction is calculated along the x′ direction between endpoints x′₁ and x′₂.

Figure 4.

(a) With frequency oriented along a 30° angle, the peaks and troughs of the reconstruction match the sinusoidal test object with frequency 9.5 mm⁻¹. (b) In this orientation, the major peak in Fourier space matches the input frequency, 9.5 mm⁻¹, and thus the object is resolved. (c) By contrast, with frequency oriented along an 80° angle, each peak and trough are not resolved properly. (d) In this orientation, the major peak (amplitude A₁) is at the frequency 3.1 mm⁻¹ and thus the input waveform is aliased.

Figure 5.

In the conventional geometry, the r-factor is calculated at 1,000 randomly-sampled points in a VOI, using a 30° frequency angle as an example. (a) This histogram illustrates the anisotropy of image quality. (b) This cumulative histogram shows the proportion of points at which r-factor meets a given threshold. (c) With 200 bootstrapped resamplings of the proportion of points for which r-factor ≤ 1.0, it is possible to generate a 95% confidence interval from the middle 95% of this histogram.

Figure 6.

(a) In the conventional geometry, the r-factor varies broadly over the 360° range of frequency angles. (b) By contrast, in the non-isocentric geometry, the r-factor is minimized (approaching zero) at all angles, yielding isotropic SR.

Figure 7.

The anisotropy of the r-factor throughout the VOI is analyzed with cumulative histograms. Shaded areas denote 95% confidence intervals. To ensure isotropic SR, the r-factor should be below 1.0 for all frequency angles; this can be achieved by increasing the detector motion range.

Figure 8.

(a) In the reconstruction of a 360°-star pattern in the conventional geometry, there are anisotropies in the PA direction, as evidenced by Moiré artifacts. (b) The FSD metric was calculated in a 30° sector of the phantom to quantify aliasing in the PA direction. (c) Unlike the MTF which does not capture aliasing artifacts, the CTF captures these artifacts at frequencies exceeding the detector alias frequency (5.9 mm⁻¹).

Figure 9.

(a) With the use of a non-isocentric geometry, there are no longer Moiré artifacts in the PA direction in the 360°-star pattern. (b) Spectral leakage in the FSD metric is minimized relative to the conventional geometry in Figure 8. (c) The CTF illustrates how aliasing artifacts at frequencies exceeding the detector alias frequency (5.9 mm⁻¹) are suppressed relative to Figure 8.