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Beyond MSE: Rician Likelihood Denoising for Self-Supervised Cardiac $T2$ and $T1\rho$ MRI

Nicholas A. Jacobs, Jason Mendes, Ravi Ranjan, Edward DiBella, Shireen Elhabian

arXiv:2609.31777v2eess.IVcs.CV

TL;DR

High-resolution, low-noise cardiac MRI data can be impractical to acquire, limiting paired-target denoising. This paper uses an analytic Rician likelihood in a self-supervised blind-spot image denoiser. On synthetic Rician cardiac MRI, it reports reduced map bias and performance matching supervised baselines on T1ρ bias.

  • Problem

    High-resolution, low-noise cardiac images needed for paired supervised denoising can be rare and impractical to acquire.

    Source: §1 · p. 2

  • Method

    The method trains a spatial blind-spot image denoiser with an analytic Rician negative log-likelihood and a known scalar noise level, without paired calibration data.

    Source: §1 · p. 2, §3 · p. 4

  • Results

    T1ρ parameter-map bias falls from nearly 13 ms to under 1.2 ms, matching fully supervised baselines while using only noisy images and a scalar noise level.

    Source: §5 · pp. 7–8

  • Takeaways & Limitations

    The method yields unbiased weighted-image denoising competitive with supervised baselines and carries bias reduction through to T2 and T1ρ maps without paired data.

    Source: §1 · p. 3

    Experiments use synthetic Rician noise, whereas raw scanner reconstructions can have spatially correlated noise; sensitivity to noise-level mismatch is uncharacterized.

    Source: §5 · p. 8

Abstract

from arXiv · show

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 $T1\rho$-weighted cardiac MRI with synthetic Rician noise, it produces biased denoised images and biased parametric maps of $T2$ and $T1\rho$. 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.

1 Introduction

Cardiac MRI faces a resolution, scan-time, and SNR trade-off, while paired clean data for supervised denoising can be scarce. The paper argues that standard self-supervised regression is biased for Rician magnitude data and proposes a Rician-likelihood blind-spot method.

1 Introduction

  • Parametric mapping fits multiple contrast-weighted images to estimate tissue-specific magnetization decay or growth constants, including T1ρ for myocardial characterization.The introduction notes that these maps are also limited by noise.Source: §1 · p. 1
  • Cardiac imaging forces a choice between resolution and SNR because acquisition time is constrained by the cardiac cycle.The broader MRI trade-off is among spatial resolution, acquisition time, and SNR.Source: §1 · p. 2
  • Rician noise makes standard self-supervised regression biased on magnitude MRI, while high-resolution, low-noise cardiac images needed for supervised training can be impractical to acquire.The paper notes that Gaussian approximations fail at low SNR and that regression estimates a noisy-signal summary rather than the clean image.Source: §1 · p. 2
  • The paper combines an analytic Rician likelihood with spatial blind-spot denoising, using a known scalar noise level without paired calibration data.It distinguishes this image-space approach from PN2V's empirical calibration histogram and Parker et al.'s voxel-wise parameter prediction.Source: §1 · p. 2
  • Self-supervised Rician Likelihood Denoising yields unbiased weighted-image denoising competitive with supervised baselines, with bias reduction carrying through to T2 and T1ρ maps without paired data.The paper also reports that Noise2Void-style regression produces biased denoised images and significantly biased parametric maps on Rician-corrupted cardiac MRI.Source: §1 · pp. 2–3

2 Related Work

Prior denoising approaches differ in their data requirements and noise assumptions: paired-target methods need aligned acquisitions, while single-image blind-spot methods can be biased on Rician magnitude data. The paper positions its method against these limitations and related MRI approaches.

2 Related Work

  • Noise2Noise removes the need for clean targets but still requires two aligned noisy acquisitions.Conventional supervised methods such as DnCNN require paired clean and noisy images.Source: §2 · p. 3
  • Noise2Void trains from a single noisy image using masked context, but its implicit zero-mean noise assumption biases estimates on Rician magnitude data.Probabilistic Noise2Void supports arbitrary noise models but requires calibration data.Source: §2 · p. 3
  • Noise2Contrast uses registered paired contrasts and MSE, while Parker et al. apply an NLR loss to voxel-wise diffusion parameters without a spatial prior.The paper notes that Noise2Contrast's requirements are difficult under cardiac motion and that its MSE objective inherits Rician bias.Source: §2 · p. 3

3 Methods

The method analyzes the conditional-mean behavior of blind-spot regression under different noise assumptions, then applies a Rician negative log-likelihood to image-space blind-spot denoising. Its experiments specify synthetic-noise training, model and masking choices, and ROI-based error metrics.

3 Methods

  • With zero-mean independent noise, blind-spot MSE learns the conditional expectation of the noisy target given masked context, which reduces to the clean-signal conditional expectation.The decomposition relies on the center pixel being excluded and on the noise term having conditional expectation zero.Source: §3 · pp. 3–4
  • Under magnitude-domain Rician noise, the noisy-pixel conditional expectation is not the clean signal, motivating maximum-likelihood denoising with an NLR loss in image space.The paper distinguishes its spatial image denoiser from Parker et al.'s voxel-wise diffusion-parameter prediction without a spatial prior.Source: §3 · p. 4
  • The pixel-averaged NLR loss uses an exponentially scaled modified Bessel function; its stable log form is log(Ie0(z))+z.The paper notes that its first log term differs from the expression printed in, which has an extra factor of two in the denominator.Source: §3 · p. 4
  • Synthetic Rician noise is added for quantitative evaluation, with one realization per split for self-supervised models and fresh realizations each epoch for supervised training.Clean references are retained to compute quantitative metrics despite training without labels.Source: §3 · pp. 4–5
  • The study trains supervised, Noise2Void-style, and Rician-likelihood models, including a shared T2/T1ρ network and UNet and dense vision-transformer architectures.Regression models use L1 loss, likelihood models require strictly positive outputs, and the ViTs use pixel-wise attention with learned or rotary position embeddings.Source: §3 · p. 5
  • Training masks 16 pixels per patch by replacing each with a uniformly sampled neighbor value; inference uses overlapping patches and Gaussian-weighted averaging.Loss is computed only at selected training indices; evaluation perturbs no pixels and uses 25% patch overlap.Source: §3 · p. 5
  • Metrics are computed over the manually segmented LV ROI, separating mean absolute per-image bias from dataset-mean variance and RMSE.Biases are averaged in absolute value so opposite signs do not cancel; variance is the population variance of per-pixel differences from ground truth.Source: §3 · p. 5
  • Table 1 reports dataset composition by split, giving series counts and weighted-image counts in parentheses.Source: Table 1 · p. 6

4 Experiments

The experiments evaluate denoising on a subject-disjoint canine cardiac MRI dataset. Rician likelihood denoising reduces bias in weighted images and parameter maps, while T1ρ map evaluation has specific limitations.

Dataset

  • The in-house dataset contains short-axis 2D canine cardiac MRI from nine subjects, totaling 302 series and 1,271 weighted images, split into disjoint training, validation, and test sets by subject.Low-quality series were manually removed from validation and test; test T2 series contain three images and T1ρ series four.Source: §4 · p. 6

Experimental setup

  • Models were trained for 200 epochs; patch-based models used 1,024 patches per batch and 96 random 32 × 32 crops per image each epoch.Images were normalized per series by the 99th percentile, and smaller acquisitions were bilinearly upsampled before evaluation against the resulting ground truth.Source: §4 · p. 6

Results

  • Rician likelihood reduces Noise2Void’s bias by up to 8.4-fold in weighted images, recovering supervised-level performance on the test set.The excess RMSE of Noise2Void relative to supervised models is higher for both T2 and T1ρ and is almost entirely bias.Source: §4 · p. 7, Table 2 · p. 7
  • On T1ρ maps, Rician likelihood reduces Noise2Void’s average bias from almost 13 ms to 1.15 ms while also lowering variance.The parameter-map bias and variance arise as the spatially varying weighted-image bias propagates through nonlinear fitting.Source: §4 · p. 7
  • T1ρ map performance is worse than T2, likely reflecting noisier ground truth and less-uniform preparation times, though its test series contain more images per map.Four weighted images per T1ρ map versus three for T2 better constrain the nonlinear fit at each pixel.Source: §4 · p. 7

5 Conclusion

The conclusion reports that Rician likelihood denoising removes systematic bias from Noise2Void-style blind-spot denoising on Rician magnitude MRI. It reduces T1ρ map bias while matching fully supervised baselines, but depends on assumptions that limit its current scope.

Conclusion

  • Rician likelihood denoising reduces T1ρ parameter-map bias from nearly 13 ms to under 1.2 ms, matching fully supervised baselines using only noisy images and a scalar noise level.Figure 1 shows representative T2 and T1ρ maps where Rician likelihood recovers reference values, unlike Noise2Void’s retained bias.Source: §5 · pp. 7–8, Figure 1 · p. 9

Limitations

  • The method assumes synthetic Rician noise with pixel-wise independence and a known noise level; sensitivity to noise-level mismatch is uncharacterized.Raw scanner reconstructions such as GRAPPA and compressed sensing can produce spatially correlated noise that violates the independence assumption.Source: §5 · p. 8

Future work

  • Future work could generalize the noise model to spatially varying noise or non-central chi noise and relax locality and patching assumptions.The image-level model had higher SSIM but worse LV accuracy than patch-based models, a global-versus-local trade-off proposed for further exploration.Source: §5 · p. 8

Results

  • Table 3 reports bias, variance, and RMSE in milliseconds for parameter maps on the LV ROI.Source: Table 3 · p. 8

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