Optical coherence tomography (OCT) is a widely used imaging technique in biomedical research and non-destructive testing. It provides high spatial resolution, but for some applications, such as non-destructive testing, a further improvement in resolution is required. The paper presents an approach to processing OCT signals that can significantly improve the longitudinal spatial resolution. This approach is based on the root-MUSIC spectral estimation algorithm, which parameters, ensuring the accurate determination of reflector coordinates within the sample were found. Experimental verification of the method was conducted by measuring the geometric parameters of multimode and single-mode optical fibers, demonstrating the effectiveness of the approach.