An approximate Bayesian formulation for deep image reconstruction in the presence of signal-dependent noise
Résumé
Recently, a variety of unrolled networks have been proposed for image reconstruction. These can be interpreted as parameter-optimized algorithms that incorporate steps that are traditionally encountered during the optimization of a hand-crafted objective or in the Bayesian formulation. Here, we address the problem of training such networks in the presence of signal-dependent noise, which is more realistic that the common additive Gaussian noise; however, it is also much more computationally demanding, when possible. In particular, we focus on the deep expectation-maximization network and describe how to approximate the Bayesian denoised completion step to reduce the computational cost and memory requirements while limiting the reconstruction error. We present reconstruction results from simulated data at different noise levels. Our network yields higher reconstruction peak signal-to-noise ratios than other similar approaches. In particular, our network shows greater robustness in the practical case where the noise level is unknown or is badly estimated.
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