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Geometry-Aware Diffusion Approximate Posterior Sampling for Sparse-View and Limited-Angle CT

Honglei Brinkmann, Carola-Bibiane Schönlieb, Ander Biguri

arXiv:2610.08866v1eess.IVcs.LG

TL;DR

Incomplete CT measurements can leave images ambiguous because they do not uniquely and stably determine all image directions. The paper uses a noise-weighted pullback metric to adapt reconstruction updates and stochastic exploration to measurement sensitivity. It reports improved reconstruction quality across tested settings and spatially resolved uncertainty estimates that indicate less reliably determined structures.

  • Problem

    Sparse-view and limited-angle measurements can leave image directions weakly constrained or unobservable, so the measured sinogram may not determine the image uniquely and stably.

    Source: §1 · p. 1

  • Method

    A regularized noise-weighted pullback metric derived from the CT operator and noise covariance adapts measurement-aware updates and stochastic exploration to directional sensitivity.

    Source: §1 · p. 3, §5 · p. 34

  • Results

    The geometry-aware design improves reconstruction quality across sparse-view, noisy, and limited-angle CT settings and provides posterior uncertainty estimates.

    Source: §1 · p. 3, §5 · p. 34

  • Takeaways & Limitations

    Empirical sample standard-deviation maps indicate where reconstructions are less reliably determined, including structures weakly constrained by missing angular coverage.

    Source: §5 · p. 34

    The current posterior uses a Gaussian approximation to CT noise, which may become inaccurate in very low-dose CT.

    Source: §5 · p. 34

Abstract

from arXiv · show

Sparse-view computed tomography (CT) reduces radiation dose and acquisition time and may mitigate motion artifacts. However, angular undersampling provides insufficient information to determine the image uniquely and stably. Limited-angle CT, arising from restricted angular coverage, produces strongly directional information loss associated with the missing angular range. In both settings, image directions may be strongly observed, weakly constrained, or unobservable, leading to severe ill-posedness and reconstruction ambiguity. Existing diffusion-based approaches incorporate measurement information through likelihood guidance, data-consistency operations, or range-null-space corrections. However, they do not generally use the continuously varying measurement sensitivity of the acquisition to jointly shape both reconstruction updates and stochastic exploration. We propose a geometry-aware diffusion-guided stochastic reconstruction framework for sparse-view and limited-angle CT. Its central component is a regularized noise-weighted pullback metric constructed from the CT forward operator and measurement-noise covariance. This metric continuously adapts both the measurement-aware update and stochastic exploration according to directional measurement sensitivity, suppressing changes along strongly constrained directions while permitting greater exploration along weakly constrained and unobservable directions. We complement this geometry-aware update with a regularized data-consistency correction and approximately null-space-restricted stochastic perturbations, implemented matrix-free using forward and backprojection operations together with conjugate-gradient solves. Experiments on sparse-view, noisy, and limited-angle CT demonstrate competitive reconstruction quality, strong measurement consistency, and spatially resolved empirical uncertainty estimates.

1 Introduction

Sparse-view and limited-angle CT leave image directions weakly constrained or unobservable, making reconstruction ambiguous. The paper proposes a diffusion-guided framework that adapts updates and stochastic exploration to measurement sensitivity, alongside data-consistency correction and approximate null-space exploration.

1 Introduction

  • Sparse-view and limited-angle acquisition lose information differently, yet both can leave image directions weakly constrained or unobservable.The resulting forward operator may be rank deficient or severely ill-conditioned, and the measurements may not determine the image uniquely or stably.Source: §1 · p. 1
  • Classical regularized methods depend on the selected regularizer, which may remove fine anatomy, and commonly return one reconstruction without quantifying uncertainty in weakly constrained components.Learning-based methods can also return a single reconstruction without directly characterizing ambiguity from missing or noisy measurements.Source: §1 · p. 2
  • Diffusion methods incorporate measurement information through conditional transitions, likelihood guidance, or data-consistency operations, while range–null-space methods treat visible and invisible components separately.Examples include DDRM, DPS, DDS, ReSample, DDNM, RN-SDE, RNSD+, and CSN.Source: §1 · pp. 2–3
  • The regularized noise-weighted pullback metric adapts diffusion-guided updates and stochastic exploration to directional measurement sensitivity in sparse-view and limited-angle CT.Strongly measurement-sensitive directions receive smaller updates and less stochastic variation, while weakly constrained directions receive relatively greater exploration.Source: §1 · p. 3
  • The framework complements its whole-space metric update with approximate null-space exploration and regularized data-consistency correction, using matrix-free forward and backprojections with conjugate-gradient solves.It does not explicitly form a Moore–Penrose pseudoinverse.Source: §1 · p. 3
  • The framework is reported to achieve competitive reconstruction quality, strong agreement with measured data, and spatially resolved empirical uncertainty estimates across sparse-view, noisy, and limited-angle CT.These are the reported outcomes; no specific benchmark values are provided in the cited passage.Source: §1 · p. 3

2 Related Work

Prior work incorporates diffusion priors into inverse-problem sampling and incomplete-view CT through several forms of measurement conditioning and correction. This work instead uses acquisition-derived geometry for the main update and stochastic exploration, with range–null-space operations in supporting roles.

Diffusion priors for inverse problems

  • Diffusion inverse-problem methods incorporate measurements through operator-conditioned transitions, likelihood-gradient guidance, refined conditional-score guidance, or optimization and consistency operations.Examples include DDRM, DPS, MCG, ΠGDM, DDS, ReSample, PSLD, and DMPlug.Source: §2 · p. 4

Riemannian MCMC methods

  • Riemannian Langevin methods use a metric to shape both deterministic movement and random perturbations; this framework instead derives its geometry from the CT operator and measurement-noise covariance.The resulting geometry represents directional sensitivity of the particular acquisition.Source: §2 · p. 4

Diffusion models for incomplete-view CT

  • Incomplete-view CT diffusion methods encode acquisition geometry through learned degradation, restoration, or conditioning, whereas this framework incorporates the forward operator and noise model directly into reconstruction dynamics.Its pullback geometry adapts both the measurement-aware update and stochastic exploration to directional sensitivity.Source: §2 · p. 4

Data consistency and range–null-space methods

  • Data-consistency and range–null-space methods correct measurement-visible content while retaining or estimating invisible content, but the proposed primary update does not rely on that binary decomposition.Instead, it uses a whole-image-space pullback-metric update and reserves regularized data consistency and approximately null-space-restricted perturbations for complementary operations.Source: §2 · pp. 4–5

3 Method

This section presents a diffusion-guided CT reconstruction method that distinguishes exact observability from noise-weighted measurement sensitivity and combines geometry-aware updates, regularized data consistency, and stochastic exploration of weakly constrained directions.

3 Method

  • The framework combines pullback-metric-preconditioned diffusion updates, regularized data consistency, and approximately null-space-restricted stochastic perturbations to support spatial uncertainty estimation.The method is implemented using forward and backprojection operations and conjugate-gradient solves.Source: §3 · p. 5

3.1 Problem Formulation and Posterior Geometry

  • The posterior combines noise-weighted measurement information with a learned image prior, distinguishing exact null-space directions from weakly observable effective null-space directions.Posterior uncertainty reflects both sources of information, since the prior may constrain directions invisible to the forward operator.Source: §3.1 · p. 7

3.2 Geometry-Aware Diffusion Sampling via a Pullback Metric

  • The regularized pullback metric shapes both drift and stochastic updates, suppressing changes in strongly observed directions while allowing greater exploration along weakly constrained and unobservable directions.The ideal continuous dynamics retain the posterior as an invariant density; the practical method uses a pretrained DDPM to estimate the prior score.Source: §3.2 · pp. 9–11

3.3 Orthogonal Direct Sum Decomposition

  • The orthogonal direct-sum decomposition separates image directions that affect measurements from directions invisible to the forward operator, linking the subspaces to components of the sampling process.The paper identifies these components with the data-consistency correction and stochastic perturbations introduced in Sections 3.4 and 3.5.Source: §3.3 · p. 12
  • The direct-sum decomposition identifies range-space components as measurement-determined under exact feasible consistency, while null-space components remain unidentifiable from measurements alone.With noisy likelihoods, sensitivity is not binary: exact null directions receive no likelihood information, while small noise-weighted singular-value directions may be weakly informed; the pullback metric captures this variation.Source: §3.3 · p. 12

3.4 Data Consistency via Riemannian Gradient Projection

  • The regularized correction reduces measurement mismatch along measurement-sensitive directions while leaving the exact null-space component unchanged.It remains well-defined regardless of rank or exact-constraint feasibility; under noisy measurements, exact consistency may be infeasible or fit noise, and the correction does not generally enforce exact equality.Source: §3.4 · pp. 13–14

3.5 Approximately Null-Space-Restricted Stochastic Sampling

  • Approximately null-space-restricted perturbations retain more stochastic variation along weakly constrained and unobservable directions while suppressing measurement-sensitive components.For finite γnull the perturbation is not generally exactly null-space; conjugate-gradient solves using forward and backprojection operations avoid forming a pseudoinverse or dense matrix.Source: §3.5 · pp. 14–15

3.6 Overall Algorithm

  • The iterative algorithm combines DDPM score and data-fidelity guidance, a pullback-metric-preconditioned update, optional stochastic perturbations, and scheduled regularized data-consistency corrections.It is a practical geometry-aware reconstruction procedure, not an exact discretization of ideal posterior dynamics, because it uses approximate guidance, finite steps and CG solves, approximate null-space perturbations, and scheduled corrections.Source: §3.6 · pp. 16–17

4 Experiments

The experiments assess reconstruction quality and empirical posterior variability across sparse-view, noisy, and limited-angle CT, including how acquisition geometry shapes reconstructions and uncertainty. They examine pullback preconditioning, signal-dependent precision under Poisson noise, and variability in approximately measurement-invisible directions.

4.1.1 Quantitative Benchmark Comparison

  • In benchmark Configs i and v, the method achieves the best performance among compared methods: 34.04 dB/0.89 and 33.82 dB/0.88, respectively.In Config i it exceeds INR by 0.83 dB, SwinIR by 1.59 dB, and ReSample by 2.01 dB; in Config v it exceeds INR by 2.81 dB and 0.07 SSIM.Source: Table 2 · p. 19, §4.1.1 · p. 20
  • In noisy sparse-view Config ii, the method achieves 28.98 dB/0.81 SSIM and outperforms DPS, DDS, PGDM, and ReSample; in Config iii, MCG has higher PSNR, 28.90 versus 28.83 dB, but lower SSIM, 0.71 versus 0.80.With ring artifacts in Config iv, it obtains 29.42 dB/0.81; ReSample is slightly higher in PSNR, while the method has higher SSIM. The passage notes that projection consistency may retain ring artifacts.Source: Table 2 · p. 19, §4.1.1 · pp. 20–21

4.1.2 Qualitative Comparison across Acquisition Degradations

  • In controlled comparisons, the method achieves the best PSNR and SSIM in settings i–iv, while setting v favors DPS in PSNR and the proposed method in posterior-method SSIM.The method reports 33.32 dB/0.897, 29.84 dB/0.846, 33.19 dB/0.893, and 29.17 dB/0.843 in settings i–iv; in setting v, DPS reaches 27.42 dB versus 27.26 dB, while the proposed method reaches 0.786 SSIM. Figure 1 shows the visual comparisons across the five settings.Source: §4.1.2 · p. 22, Figure 1 · p. 22

4.2 Empirical Sample-Variability Analysis

  • Sample variability is low and concentrated near boundaries in noise-free sparse-view and milder limited-angle settings, but spreads with Poisson noise and becomes structured along missing-angle directions as coverage narrows.With 10 noisy projections, variability is high around the body boundary, lung region, and internal interfaces; the standard-deviation and error maps are shown in Figure 2.Source: §4.2 · p. 23, Figure 2 · p. 24
  • Mean pixel-wise sample standard deviation is 0.0079 in Config i, 0.0081 in Config iii, 0.0082 in Config iv, 0.0260 in Config ii, and 0.0205 in Config v.The method generally has lower variability than DDS, DPS, and PGDM; ReSample is lower in Config ii (0.0182 versus 0.0260) but higher in Configs i, iii, iv, and v. These are empirical diagnostics, not calibrated posterior-uncertainty estimates.Source: §4.2 · pp. 23–24, Table 3 · p. 24

4.3 Geometry-aware analysis

  • The geometry-aware analysis examines range–null components, stochastic variability in approximately measurement-invisible directions, pullback-metric updates versus Euclidean drift, and signal-dependent precision weighting under CT noise.These analyses are framed as tests of whether variability follows acquisition geometry and whether preconditioning favors weakly constrained directions while maintaining measurement consistency.Source: §4.3 · p. 25

4.3.1 Regularized Range–Null Component Analysis

  • The regularized range–null diagnostic uses the unweighted acquisition operator to separate geometry from reconstruction noise weighting; its finite-regularization components are approximate, not exact orthogonal projections.The complementary null-like component emphasizes weakly constrained or unobservable directions, and its measurement response is used to assess how nearly invisible it is.Source: §4.3.1 · pp. 25–26
  • For posterior means, the range component accounts for 99.631% and 99.729% of squared reconstruction norm, while ρnull stays below 2 × 10−4 in both noise-free and Poisson cases.The null-like component is interpreted as approximately measurement-invisible; these component ratios describe posterior means, not posterior uncertainty.Source: Figure 3 · p. 26, §4.3.1 · p. 27

4.3.2 Geometry-Aware Posterior Variability Analysis

  • Relative sinogram variability is 0.0399 (40-view noise-free), 0.2737 (40-view Poisson), and 0.3043 (20-view Poisson), indicating less suppression with noisier, sparser data.In the 40-view noise-free setting, r̄null = 1.046 versus r̄range = 0.184; under Poisson noise r̄null remains larger at 0.618 versus r̄range = 0.422, and reaches 0.697 for 20-view Poisson data.Source: Table 5 · p. 28, §4.3.2 · pp. 28–29

4.3.3 Effect of Pullback-Metric Preconditioning

  • Pullback preconditioning raises PSNR/SSIM from 31.98 dB/0.8339 to 33.17 dB/0.8852 (full-angle) and 31.63 dB/0.8359 to 33.04 dB/0.8816 (limited-angle).The comparison disables Langevin noise and the additional null-space perturbation; all four relative data errors remain below 2.3 × 10−4.Source: §4.3.3 · pp. 29–30, Figure 4 · p. 30, Table 6 · p. 31
  • Pullback preconditioning reduces update response by factors of approximately 263 (full-angle) and 381 (limited-angle), while the null-like-to-range ratio rises well above one over most of the trajectory.These diagnostics indicate that the deterministic displacement suppresses changes strongly affecting the measured sinogram while retaining relatively more movement along weakly constrained or unobservable directions.Source: §4.3.3 · pp. 30–32, Figure 5 · p. 31

4.3.4 Effect of Signal-Dependent Precision Weighting

  • Under Poisson noise, signal-dependent weighting reaches 29.84 dB/0.846, beating unit precision (28.23 dB/0.691) and DPS (28.62 dB/0.800).The variants are identical without noise (33.32 dB/0.897) and under Gaussian noise (31.62 dB/0.867); weighting down-weights less reliable, low-photon-count measurements.Source: §4.3.4 · pp. 32–33, Figure 6 · p. 33

5 Conclusion and Future Work

The conclusion reports improved reconstruction quality across acquisition settings and uncertainty maps that highlight ambiguous structures. The appendix details the measurement-noise approximations underlying the method and identifies low-count and computational limits.

5 Conclusion and Future Work

  • The pullback metric reduces the deterministic update’s measurement response and redirects it toward approximately measurement-invisible directions.It reduces updates that would strongly change the measured sinogram while allowing the prior to act in weakly constrained directions.Source: §5 · p. 34
  • The geometry-aware design improves reconstruction across sparse-view, noisy, and limited-angle CT, while reducing streaks and noise amplification and preserving anatomical boundaries more clearly than the considered posterior-sampling baselines.The pullback update also improves PSNR and SSIM over the Euclidean update while keeping measurement residuals very small.Source: §5 · p. 34
  • Empirical sample standard-deviation maps show greatest uncertainty near boundaries, fine structures, noise-sensitive regions, and structures weakly constrained by missing angular coverage.These areas often coincide with larger reconstruction errors, and the maps indicate which structures are less reliably determined by the measured data.Source: §5 · p. 34
  • The current method requires iterative linear solves to apply the inverse pullback metric, making it more expensive than a Euclidean update; faster matrix-free solvers are proposed for scaling to larger images and 3D CT.Suggested directions include preconditioned conjugate gradients, warm-starting, adaptive stopping, multigrid, low-rank approximations, and learned inverse-metric approximations.Source: §5 · p. 34

A.1 Gaussian Approximation of CT Measurements

  • The appendix motivates its approximate linear–Gaussian model from an idealized Poisson photon-counting model and describes a diagonal, signal-dependent post-log covariance with fixed plug-in precision.The idealization omits possible electronic noise, scatter, beam hardening, detector correlations, and calibration or preprocessing effects.Source: §A.1 · pp. 38–39, §A.1.1 · p. 39

A.1.1 Poisson photon-counting model

  • Under the monoenergetic Beer–Lambert model, expected transmitted counts depend on the image’s ray line integrals, and raw-count variance depends on the expected count.The appendix models the image as linear-attenuation coefficients and identifies the ray line integral as (AΩx)i.Source: §A.1.1 · p. 39

A.1.2 Gaussian approximation of Poisson counts

  • A Poisson count is approximated by a Gaussian with the same mean and variance when transmitted counts are sufficiently large; highly attenuated rays can remain in the low-count regime despite a relatively large incident count.The approximation’s validity depends on transmitted count λ, not only incident count I0.Source: §A.1.2 · pp. 39–40

A.1.3 Propagation through the logarithmic transform

The appendix propagates Poisson count noise through the logarithmic transform to motivate a weighted post-log likelihood. Its approximations omit a low-count bias and assume conditionally independent detector-bin errors.

A.1.3 Propagation through the logarithmic transform

  • The leading post-log error is approximately Gaussian with zero mean and variance λ^-1 after the first-order approximation.The derivation temporarily neglects count clipping and assumes positive counts.Source: §A.1.3 · p. 40
  • The zero-mean Gaussian model neglects the leading logarithmic bias 1/(2λi) and is most accurate when transmitted counts are sufficiently large.Retaining the quadratic term in the logarithmic expansion exposes the bias.Source: §A.1.3 · p. 40

A.1.4 Post-log covariance and likelihood

  • The post-log covariance construction assumes conditionally independent detector-bin errors and applies the Gaussian model after the logarithmic transformation.Source: §A.1.4 · p. 41
  • Highly attenuated rays receive lower precision, motivating a post-log weighted least-squares data-fidelity functional.Source: §A.1.4 · p. 41

A.1.5 Fixed effective precision

The method uses a stabilized, measurement-dependent precision proxy because ideal post-log precision depends on unknown transmitted counts. The proxy is fixed during reconstruction and is not an unbiased estimate of ideal Poisson precision.

A.1.5 Fixed effective precision

  • Ideal post-log precision depends on unknown transmitted counts, so the implementation uses a stabilized, normalized, scaled, and clipped measurement-dependent precision proxy.Zero detected counts are replaced by one before applying the logarithm; ε, δ, s, wmin, and wmax stabilize and bound the weights.Source: §A.1.5 · p. 41
  • The effective precision and covariance are computed from the measured sinogram and held fixed throughout reconstruction.Source: §A.1.5 · p. 41
  • The weights are a stabilized measurement-dependent precision approximation, not an unbiased estimate of ideal Poisson precision.Source: §A.1.5 · p. 41
  • The Gaussian approximation deteriorates at low counts, where logarithmic bias and zero-count handling matter; a pre-log Poisson or hybrid model can be preferable.Source: §A.1.5 · p. 41
  • A metric based directly on ideal raw-count Fisher information would depend on the image position and generally require additional drift terms in a Riemannian Langevin construction.Those terms vanish for the fixed metric used here.Source: §A.1.5 · p. 42

A.2 Orthogonal Decomposition of the Image Space

The appendix establishes the orthogonal decomposition of image space used in Section 3.3, separating measurement-sensitive and null-space components.

A.2 Orthogonal Decomposition of the Image Space

  • The appendix proves the orthogonal decomposition stated in Section 3.3.Source: §A.2 · p. 42
  • The decomposition represents a measurement-sensitive component as r = AΩ^T z and places v in N(AΩ).Source: §A.2 · p. 42
  • The two orthogonal subspaces span Rn.Source: §A.2 · p. 42

A.3 Posterior Geometry Under Incomplete-View CT

The appendix characterizes how incomplete-view measurements and prior curvature shape posterior geometry, then develops exact and regularized range/null-space operators with matrix-free conjugate-gradient computation.

A.3 Posterior Geometry Under Incomplete-View CT

  • Likelihood curvature vanishes along exact null-space directions but is positive along nonzero measured-range directions, though it can be very small in weakly constrained directions.Posterior covariance also depends on prior curvature and cross-directional couplings, so null-space directions do not necessarily all have greater variance than range-space directions.Source: §A.3 · p. 43

A.4 Projection Operators and Conjugate Gradient Computation

  • The exact operators PR and PN are Euclidean orthogonal projectors onto the measured range and its complementary null space.The stated identities hold without requiring AΩ to have full row rank.Source: §A.3 · p. 43, §A.4 · p. 44

A.4.1 Matrix-free computation via conjugate gradient

  • For finite γ⋆, the symmetric regularized filters are not exact projectors, and their nontrivial eigenvalues lie strictly between zero and one.The linear systems are symmetric positive definite and can be solved by conjugate gradient without forming dense matrices; each image-space iteration uses one forward projection, one precision application, and one backprojection.Source: §A.4 · p. 44, §A.4.1 · pp. 44–45

A.5 Pullback Metric and Preconditioned Langevin Dynamics

The fixed pullback metric defines preconditioned Langevin dynamics, and covariance matching makes the target density invariant under the stated regularity conditions.

A.5 Pullback Metric and Preconditioned Langevin Dynamics

  • The ideal continuous-time process uses a fixed metric, so position-dependent metric-derivative terms vanish.The treatment concerns an exact, time-independent target score, not the complete finite-step practical algorithm.Source: §A.5 · pp. 45–46

A.5.1 Fokker–Planck equation and invariance

  • For the constant-covariance Langevin family, the target density is invariant for every smooth target if and only if the diffusion covariance D equals 2M.The equation uses continuous Langevin time s, distinct from a DDPM timestep.Source: §A.5.1 · p. 46, §A.5 · p. 46
  • Under smoothness, nonexplosion, and boundary assumptions, the target density is reversible and invariant for the ideal process.The stationary probability current vanishes under these stated conditions.Source: §A.5.1 · p. 46

A.5.2 Discrete-time approximation and matrix-free noise

The discrete-time discussion gives an ideal Euler–Maruyama approximation and a matrix-free noise sampler, while clarifying that the practical algorithm is not thereby proven to sample the exact posterior.

A.5.2 Discrete-time approximation and matrix-free noise

  • The matrix-free noise sampler constructs the perturbation without forming a matrix square root.It uses independent standard Gaussian vectors in measurement and image spaces.Source: §A.5.2 · p. 47
  • The covariance-matching result justifies the ideal continuous model, but does not establish exact posterior invariance for the finite-step practical algorithm.The practical method uses an approximate time-dependent DDPM score, finite CG solves, scheduled data-consistency corrections, and optional additional perturbations.Source: §A.5.2 · p. 47
  • Euler–Maruyama has weak order one over a fixed finite interval under standard smoothness and moment assumptions, but this alone gives no invariant-distribution bias bound.Such stationary-bias or nonasymptotic sampling bounds require additional assumptions, such as smoothness and strong log-concavity.Source: §A.5.2 · p. 47

B.1 Single-Image Quantitative Comparison

The single-image comparison shows configuration-dependent PSNR and SSIM rankings across the five benchmark settings, and is presented as illustrative rather than dataset-level evidence.

B.1 Single-Image Quantitative Comparison

  • 33.33 dB/0.90 versus ReSample’s 32.37 dB/0.88 is the Config i comparison, but the one-image results are intended to illustrate behavior rather than establish dataset-level performance.The observations are broadly consistent with the full 526-image evaluation, although individual-method rankings may vary between configurations.Source: §B.1 · p. 47
  • 28.47 dB PSNR is highest in Config ii, exceeding ReSample by 0.08 dB, while the proposed method ties DPS for highest SSIM at 0.78.In Config iii, the proposed method obtains 29.24 dB/0.81, narrowly exceeding ReSample in PSNR (29.21 dB) and achieving higher SSIM than DPS, PGDM, and ReSample (0.80).Source: §B.1 · p. 47
  • 29.55 dB is ReSample’s highest PSNR in Config iv, while the proposed method has the second-highest PSNR (29.40 dB) and highest SSIM (0.83).The differing rankings show a trade-off between reference-based pixel error and structural similarity on this image, but do not establish the underlying mechanism.Source: §B.1 · p. 48
  • 33.18 dB/0.90 is the proposed method’s Config v result, exceeding DDS by 1.84 dB PSNR and 0.02 SSIM, and ReSample by 4.29 dB and 0.08, respectively.The passage cautions that causal interpretation of this single-image result should rely on geometry ablation and full-dataset evaluation.Source: §B.1 · p. 48

B.2 Sample-Variability Maps for Baseline Methods

Figure 7 compares spatial sample variability across four samplers and five acquisition settings. The proposed method has lower mean variability than DDS, DPS, and PGDM, but the maps do not establish calibrated uncertainty.

B.2 Sample-Variability Maps for Baseline Methods

  • The proposed maps show comparatively concentrated variability in settings i, iii, and iv, with increases under noisy or more severely undersampled settings ii and v.Baseline maps commonly show increased variability around anatomical boundaries and undersampling-related streaks.Source: §B.2 · p. 48
  • Sample variability is only a diagnostic: high values may reflect ambiguity or sampling instability, while low values may reflect concentration or insufficient sampler exploration.Interpret the maps jointly with reconstruction quality, measurement residuals, and the posterior-mean and error maps in Figure 2.Source: §B.2 · pp. 48, 50, Figure 7 · p. 49
  • DDS, DPS, and PGDM have higher mean sample variability than the proposed method in all five settings; ReSample is lower only in setting ii.In setting ii, ReSample's value is 0.0182 versus 0.0260 for the proposed method.Source: §B.2 · p. 48, Figure 7 · p. 49
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