Resolution and noise performance of sparse view X-ray CT reconstruction via Lp-norm regularization

Adaptive steepest descent projection onto convex sets (ASD-POCS) algorithms with Lp-norm (0 < p ≤ 1) regularization have shown great promise in sparse-view X-ray CT reconstruction. However, the difference in p value selection can lead to varying algorithm performance of noise and resolution. Therefore, it is imperative to develop a reliable method to evaluate the resolution and noise properties of the ASD-POCS algorithms under different Lp-norm priors.

A comparative performance evaluation of ASD-POCS algorithms under different Lp-norm (0 < p ≤ 2) priors were performed in terms of modulation transfer function (MTF), noise power spectrum (NPS) and noise equivalent quanta (NEQ). Simulation data sets from the EGSnrc/BEAMnrc Monte Carlo system and an actual mouse data set were used for algorithms comparison.

A considerable MTF improvement can be achieved with the decrement of p. L1 regularization based algorithm obtains the best noise performance, and shows superiority in NEQ evaluation. The advantage of L1-norm prior is also confirmed by the reconstructions from the actual mouse data set through contrast to noise ratio (CNR) comparison.

Although the ASD-POCS algorithms using small Lp-norm (p ≤ 0.5) priors yield a higher MTF than do the high Lp-norms, the best noise-resolution performance is achieved when p is between 0.8 and 1. The results are expected to be a reference to the choice of p in Lp-norm (0 < p ≤ 2) regularization.