Stochastic noise characteristics in matrix inversion tomosynthesis (MITS)

Matrix inversion tomosynthesis (MITS) uses known imaging geometry and linear systems theory to deterministically separate in-plane detail from residual tomographic blur in a set of conventional tomosynthesis ("shift-and-add") planes. A previous investigation explored the effect of scan angle (ANG), number of projections (N), and number of reconstructed planes (NP) on the MITS impulse response and modulation transfer function characteristics, and concluded that ANG = 20 degrees, N = 71, and NP = 69 is the optimal MITS imaging technique for chest imaging on our prototype tomosynthesis system. This article examines the effect of ANG, N, and NP on the MITS exposure-normalized noise power spectra (ENNPS) and seeks to confirm that the imaging parameters selected previously by an analysis of the MITS impulse response also yield reasonable stochastic properties in MITS reconstructed planes. ENNPS curves were generated for experimentally acquired mean-subtracted projection images, conventional tomosynthesis planes, and MITS planes with varying combinations of the parameters ANG, N, and NP. Image data were collected using a prototype tomosynthesis system, with 11.4 cm acrylic placed near the image receptor to produce lung-equivalent beam hardening and scattered radiation. Ten identically acquired tomosynthesis data sets (realizations) were collected for each selected technique and used to generate ensemble mean images that were subtracted from individual image realizations prior to noise power spectra (NPS) estimation. NPS curves were normalized to account for differences in entrance exposure (as measured with an ion chamber), yielding estimates of the ENNPS for each technique. Results suggest that mid- and high-frequency noise in MITS planes is fairly equivalent in magnitude to noise in conventional tomosynthesis planes, but low-frequency noise is amplified in the most anterior and posterior reconstruction planes. Selecting the largest available number of projections (N = 71) does not incur any appreciable additive electronic noise penalty compared to using fewer projections for roughly equivalent cumulative exposure. Stochastic noise is minimized by maximizing N and NP but increases with increasing ANG. The noise trend results for NP and ANG are contrary to what would be predicted by simply considering the MITS matrix conditioning and likely result from the interplay between noise correlation and the polarity of the MITS filters. From this study, the authors conclude that the previously determined optimal MITS imaging strategy based on impulse response considerations produces somewhat suboptimal stochastic noise characteristics, but is probably still the best technique for MITS imaging of the chest.