Successive Noise Cancelation Method of the Time Domain Layer Peeling Algorithm

Abstract

Layer peeling algorithm (LPA) can be applied to solve the optical problems governed by the inverse scattering theory [1, 2]. The reconstruction depth of a LPA is limited by error accumulation due to noise as the LPA evolves into a deeperlayer, and regularization approaches improve this error accumulation at the expense of accuracy [3, 4]. In this paper, we propose a successive noise cancelation (SNC) method to improve both the reconstruction accuracy and reconstruction depth of the time domain LPA (TDLPA). Assuming additive white gaussian noise, we prove the layer-by-layer independency (LLI) of the reconstruction error of the TDLPA. With the aid of this LLI property, noise is estimated and removed in a sequential manner. As far as we know, the proposed SNC-TDLPA is the first scheme that can suppress the reconstruction error due to noise. Note that the reconstruction error due to noise is different with the discretization error in [5].We propose a successive noise cancelation (SNC) method of the time domain layer peeling algorithm (TDLPA) assuming AWGN. The proposed SNC-TDLPA can improve both the reconstruction accuracy and reconstruction depth of the TDLPA.