X-ray computed tomography (CT) is used regularly at synchrotrons to study the internal morphology of materials at high resolution. However, experimental constraints, such as radiation sensitivity, can result in noisy or undersampled measurements. Further, depending on the resolution, sample size and data acquisition rates, the resulting noisy dataset can be terabyte-scale. Advanced iterative reconstruction techniques can produce high-quality images from noisy measurements, but their computational requirements have made their use exception rather than the rule. We propose here a novel memory-centric approach that avoids redundant computations at the expense of additional memory complexity. We develop a system, MemXCT, that uses an optimized SpMV implementation with multi-stage buffering and two-level pseudo-Hilbert ordering. We evaluate MemXCT on both KNL and GPUs architectures. MemXCT can reconstruct a large (11Kx11K) mouse brain tomogram in ~10 seconds using 4,096 KNL nodes (256K cores), the largest iterative reconstruction achieved in near-real time.t