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We show the feasibility and the potential of a new signal processing algorithm for the high-resolution deconvolution of OCT signals. Our technique relies on the description of the measures in a parametric form, each set of four parameters describing the optical characteristics of a physical interface (e.g., complex refractive index, depth). Under the hypothesis of a Gaussian source light, we show that it is possible to recover the 4K parameters corresponding to K interfaces using as few as 4K uniform samples of the OCT signal. With noisy data, we can expect the robustness of our method to increase with the oversampling rate - or with the redundancy of the measures. The validation results show that the quality of the estimation of the parameters (in particular the depth of the interfaces) is narrowly linked to the noise level of the OCT measures - and not to the coherence length of the source light - and to their degree of redundancy.