Recovery of optical phases using direct intensity detection methods is an ill-posed problem and some prior information is required to regularize it. In the case of multi-mode fibers, the known structure of eigenmodes is used to recover optical field and find mode decomposition by measuring intensity distribution. Here we demonstrate numerically and experimentally a mode decomposition technique that outperforms the fastest previously published method in terms of the number of modes while showing the same decomposition speed. This technique improves signal-to-noise ratio by 10 dB for a 3-mode fiber and by 7.5 dB for a 5-mode fiber.