MLEM Reconstruction With Fractional-Order Multi-Notch Spectral Regularization

  Maximum-likelihood expectation-maximization (MLEM) is a widely used statistical reconstruction method in computed tomography (CT), but under ill-posed acquisition it progressively amplifies high-frequency noise and structured artifacts. This letter introduces a fractional-order multi-notch filter (FONF)-regularized MLEM framework with twofold novelty: (i) fractional-order spectral shaping embedded as a training-free, geometry-agnostic prior directly inside the MLEM iteration rather than as post-processing; and (ii) a data-driven rule that activates targeted Gaussian notches only when narrowband artifacts are detected, so one framework covers broadband noise and periodic artifacts (proof of mechanism on a synthetic stripe). The scheme is a plug-and-play (PnP)-inspired fixed-point method: the spectral step is averaged and non-expansive; convergence of the complete iteration is supported empirically. The regularization suppresses broadband noise while preserving weak anatomical structures and retains the statistical consistency and non-negativity of classical MLEM. Across four datasets (ten noise realizations), MLEM+FONF attains the best PSNR, SNR, and RMSE among six training-free methods (e.g., thorax PSNR 31.08 dB versus 26.91 dB for PnP-ADMM(TV) and 17.54 dB for MLEM, with PSNR/SNR gains significant at $p< 0.001$) at roughly half the runtime of PnP-ADMM(TV).