Traditional computed tomography (CT) reconstruction methods, such as Filtered Backprojection Techniques (FBPT), haveM long been valued for their speed. However, advancements in modern imaging present new challenges: achieving high-quality reconstructions with limited data, managing noise, and enhancing computational efficiency. For full projection sets, challenges include addressing projection data inconsistencies like noise. In sparse data scenarios, challenges shift to managing unobservable object patterns and mitigating the evolving estimation errors caused by uncontrolled prediction inaccuracies. We present a novel MENT-based reconstruction approach that delivers exceptional speed and accuracy, addressing image quality, noise resilience, and sparse data processing challenges. Our method, the Extended High Efficiency Computed Tomography (eHECTOR), incorporates MENT within an Extended Kalman Filter-Type (eKFT) feedback loop, resolving lack of observability and effectively managing data inconsistencies. This approach enables faster, more precise reconstructions under sparse and noisy data conditions, marking a significant advancement over traditional methods and paving the way for next-generation diagnostic imaging.