Endoscopic optical coherence tomography (OCT) is an emerging method for noninvasive microscopic probing in biomedicine. In this paper, the feasibility of alleviating the pixelated structural artifacts created by a fiber bundle-based OCT imaging method is investigated using a novel statistical analysis. We demonstrate an efficient nonparametric iterative compressive sensing (CS) technique that is efficient in reconstructing the original pattern shape from a pixelated image of a reference US Air Force resolution chart. An efficient implementation scheme for the shape recovery is presented along with the results of experiments that demonstrate a peak signal-to-noise ratio of 18 dB and a noise variation of less than 0.3 dB with no honeycomb effect in the image is obtained after 40 iterations which is significantly efficient than the previous iterative method of learning image priors. (C) 2015 Elsevier GmbH. All rights reserved.