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The signal-to-noise ratio and bandwidth of photonic time-stretch (PTS) systems have previously been limited due to the nonlinear distortion caused by modulator response and dispersive propagation. In this paper, we present a novel method for the reconstruction of the input signal from two phase-diverse intensity measurements. The method consists of optical phase retrieval at the measurement point followed by simulated optical backpropagation to the modulation point. By numerical simulation of a PTS system with realistic parameters, we analyze the proposed method and compare it with the previously suggested maximum ratio combining (MRC) method. We show that the proposed optical backpropagation method, unlike the MRC method that treats the system as being linear from electrical input to output, can reconstruct the signal even at a large modulation depth and that the method is insensitive to biasing error or drift and not overly sensitive to misestimation of system parameters. Furthermore, to reduce the computational effort associated with the simulation of PTS systems, we present a numerical propagation method whereby the required number of sampling points is reduced by several orders of magnitude.