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Optical coherence tomography (OCT) allows for non-invasive 3D visualization of biological tissue at cellular level resolution. Often hindered by speckle noise, the visualization of important biological tissue details in OCT that can aid disease diagnosis can be improved by speckle noise compensation. A challenge with handling speckle noise is its inherent non-stationary nature, where the underlying noise characteristics vary with the spatial location. In this study, an innovative speckle noise compensation method is presented for handling the non-stationary traits of speckle noise in OCT imagery. The proposed approach centers on a non-stationary spline-based speckle noise modeling strategy to characterize the speckle noise. The novel method was applied to ultra high-resolution OCT (UHROCT) images of the human retina and corneo-scleral limbus acquired in-vivo that vary in tissue structure and optical properties. Test results showed improved performance of the proposed novel algorithm compared to a number of previously published speckle noise compensation approaches in terms of higher signal-to-noise ratio (SNR), contrast-to-noise ratio (CNR) and better overall visual assessment.