We propose an hyper-parameter inference method in the manner of Bayesian inference for image reconstruction from Radon transformed observation which often appears in the computed tomography. Hyper-parameters are often introduced in Bayesian inference to control the strength ratio between prior information and the fidelity to the observation. Since the quality of the reconstructed image is influenced by the estimation accuracy of these hyper-parameters, we apply Bayesian inference into the filtered back projection (FBP) reconstruction method with hyper-parameters inference, and demonstrate that estimated hyper-parameters can adapt to the noise level in the observation automatically.
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