This work focuses on enhancing the quality of A-and B-scans of a novel linear optical coherence tomography system (LOCT), addressing the image degradation caused by noise and the blurring characteristics of the system's three-dimensional point spread function. The enhancement procedure includes an initial spatial and frequencybased pre-filtering that is applied to the measured interference pattern. Subsequently, a more robust envelope detection technique based on the Hilbert transform is employed. Lastly, image structures are reconstructed using a deconvolution algorithm based on maximum likelihood estimation, tailored to meet our unique requirements by adapting it to Rician distributed intensity values and employing a sparseness regularization term. For the deconvolution, both the lateral and axial blur of the system are considered. Emphasis is placed on the optimization of signal detection in high-noise regions, while simultaneously preventing image boundary artifacts. The efficacy of this approach is demonstrated across multiple types of measurement objects, including both artificial and biological samples. All results show a significant reduction in noise as well as enhanced resolution. Structure distinguishability is also increased, which plays a crucial role in tomography applications. In summary, the proposed enhancement method substantially improves image quality. This is achieved by still using the same initial measurement data, but incorporating prior knowledge and maximizing the amount of extracted information. Although initially designed for LOCT systems, the processing steps have potential for broader application in other types of optical coherence tomography and imaging systems.