Beyond MSE: Rician Likelihood Denoising for Self-Supervised Cardiac T2 and T1ρ MRI

Magnetic resonance imaging involves an inherent trade-off among spatial resolution, acquisition time, and noise. This trade-off contributes to long scan times and high cost. Deep learning has improved image denoising, but cardiac MRI remains difficult because high-resolution, rapid acquisitions generally lack corresponding low-noise ground truth. Self-supervised denoising offers a potential solution by learning from noisy image pairs or even single noisy acquisitions. However, we show that Noise2Void-style blind-spot denoising, which uses a mean squared error (MSE) loss and assumes zero-mean, independent and identically distributed (i.i.d.) noise, is poorly suited to MR magnitude images. When applied to short-axis T2-weighted and T1ρ-weighted cardiac MRI with synthetic Rician noise, it produces biased denoised images and biased parametric maps of T2 and T1ρ. To address this limitation, we formulate self-supervised denoising as maximum likelihood estimation under a known Rician noise model. This yields unbiased denoisers that are competitive with supervised baselines.