In digital tomosynthesis, one of the limitations is the presence of out-of-plane blur due to the limited angle acquisition. The point spread function (PSF) characterizes blur in the imaging volume, and is shift-variant in tomosynthesis. The purpose of this research is to classify the tomosynthesis imaging volume into four different categories based on PSF-driven focus criteria. We considered linear tomosynthesis geometry and simple back projection algorithm for reconstruction. The three-dimensional PSF at every pixel in the imaging volume was determined. Intensity profiles were computed for every pixel by integrating the PSF-weighted intensities contained within the line segment defined by the PSF, at each slice. Classification rules based on these intensity profiles were used to categorize image regions. At background and low-frequency pixels, the derived intensity profiles were flat curves with relatively low and high maximum intensities respectively. At in-focus pixels, the maximum intensity of the profiles coincided with the PSF-weighted intensity of the pixel. At out-of-focus pixels, the PSF-weighted intensity of the pixel was always less than the maximum intensity of the profile. We validated our method using human observer classified regions as gold standard. Based on the computed and manual classifications, the mean sensitivity and specificity of the algorithm were 77+/-8.44% and 91+/-4.13% respectively <i>(t=-0.64, p=0.56, DF=4)</i>. Such a classification algorithm may assist in mitigating out-of-focus blur from tomosynthesis image slices.
Tomosynthesis is widely used for three-dimensional reconstruction of objects acquired from limited angle X-ray projection imaging with stationary digital detector. Traditionally, the point-spread function (PSF) in digital tomosynthesis is assumed to be symmetrical with respect to the central axis and shift invariant. The purpose of this research is to characterize the true nature of the PSF by intensity and shape considerations. We assumed that tomosynthesis PSF depended on the imaging geometry and the reconstruction algorithms. In this paper, we describe PSF characterization with respect to the linear geometry and back projection reconstruction. We considered the following parameters: source to image distance (SID) (mm), total number of slices reconstructed after reconstruction, distance (in z-direction) from the first and the last slice to the detector (mm), resolution in X, Y & Z (pix/mm), and total number of projections. Using these parameters, we determined the PSF at every location of the reconstructed volume. The PSF was contained in the plane formed by the linear source trajectory and the point under consideration that extended through all the slices. The results show that the PSF is shift variant and unique at every location and gradually changing over the entire reconstructed volume. The shift from the central axis and central reconstructed slice caused the PSF to exhibit shear corresponding to the X-shift, tilt with the Y-shift and asymmetry with the Z-shift. In summary, we have characterized tomosynthesis PSF to be globally shift variant exhibiting shear, tilt and asymmetry.