You Cannot Recover What Was Never Measured: Quantifying the Information Ceiling of Ultra-Low-Field MRI Super-Resolution

Prathamesh Pradeep Khole; Shreya Handa; Utkarsh Gupta; Razvan Marinescu

cs.CVSep 29, 2026

You Cannot Recover What Was Never Measured: Quantifying the Information Ceiling of Ultra-Low-Field MRI Super-Resolution

Authors: Prathamesh Pradeep Khole, Shreya Handa, Utkarsh Gupta, Razvan Marinescu

Organizations: University of California, Santa Cruz · Johns Hopkins University

Abstract

Generative super-resolution models can turn portable 64 mT MRI into images that look like 3T scans, and the field evaluates them with PSNR, SSIM, and pixelwise uncertainty, most often on pairs built by synthetically degrading high-field images. Prior work acknowledges that these models hallucinate and that the problem is ill posed, but to our knowledge no study measures how much information about the individual subject the real low-field scan actually contains. We measure it. Using paired 64 mT and 3T scans of the same subjects from three public datasets, and a measurement protocol validated on tests whose correct answer is known in advance, we find that, judged over the whole brain, real 64 mT scans carry structure specific to the individual only down to approximately 3 to 4 mm half-pitch in plane, and coarser still through plane. Standard synthetic degradations preserve subject information roughly 1 mm beyond this ceiling, so models trained and benchmarked on synthetic pairs are evaluated on information that real scanners never record. We then test trained diffusion models and a publicly released external model on real paired acquisitions; 24 trained runs of five architectures (GAN, diffusion, and transformer families) give the coverage of the audit. On every subject where faithfulness can be measured, fine output detail is no more correlated with the subject's own 3T scan than with a stranger's, while sample-variance uncertainty does not distinguish fabricated structure from reconstruction difficulty. Because PSNR and SSIM score resemblance to a reference rather than whether detail belongs to the subject, a benchmark scored by them cannot tell recovery from fabrication. Code for the measurement protocol will be released so that recoverability claims can be tested for newer models.

Figures & tables

Quantity	Role	Dataset	$n$	mm [HP]	mm [FP]	CI [HP]
Ceiling, cross-FSC half-bit	measurement	Zenodo T1w	8	3.157	6.313	2.46–3.61
Ceiling, cross-FSC half-bit	measurement	OpenNeuro T1w	11	4.814	9.628	3.91–9.38
Ceiling, cross-FSC half-bit	measurement	Zenodo T2w	10	3.187	6.373	1.90–3.67
Anisotropy, in / through plane	measurement	Zenodo T1w	8	–	6.13 / 11.07	–
Gap vs S-KSP+N (primary)	measurement	Zenodo T1w	8	1.162	2.324	–
Gap vs S-BIC+N / S-GAU+N	measurement	Zenodo T1w	8	0.921 / 0.937	1.842 / 1.873	–

Table 1: Headline measurements (full table with controls: Table 8 ). [HP] is

1/(2k_{c})

, [FP] is

1/k_{c}

; a dash means the row is tabulated in one convention only.

Figure 1: Left: Recoverability ceiling. Cross-FSC half-bit crossing between the real 64 mT and 3T scans of the same subject (median over subjects, 95% CI), mm [HP]: Zenodo T1w 3.16 (2.46–3.61,

n=8

), Zenodo T2w 3.19 (1.90–3.67,

n=10

), OpenNeuro T1w 4.81 (3.91–9.38,

n=11

). Dashed: end of the directly validated range, 7 mm [FP] (3.5 mm [HP]); values above it are coarser than the range the estimator was validated on. Right: Gap between real and synthetic degradation. Per-subject half-bit crossings [HP] for the real 64 mT scan and the three noise-matched synthetics (one line per subject). Zenodo T1w gap to S-KSP+N (difference of median crossings) 1.16 mm [HP], above the 0.24 mm [HP] registration bound. Two OpenNeuro subjects sit at the grid cap (0.58 mm [HP]) and are shown as capped values.

Subject	Dataset	G-M2	G-M3	Anchor	Raw-input	Oracle	Diffusion	SynthSR
sub-0048	Zenodo	pass	pass	6.9	5.0	–	16.0	12.0
sub-0064	Zenodo	fail	marginal	14.04	12.0	–	24.0	24.0
sub-HYPE21	OpenNeuro	pass	pass	10.9	6.0	2.5	6.0 (5.0)	6.0
sub-HYPE22	OpenNeuro	fail	pass	21.6	16.0	2.5	12.0	10.0

Table 2: Control ladder for the direct measurement, all mm [FP]. Anchor: whole-brain cross-FSC of the subject’s input. Raw-input benchmark: the registered 64 mT input through the identical band readout (a correlation benchmark, not an information bound). Oracle: S-KSP+N of the subject’s own 3T (“–”: no merge within the grid). Diffusion: z-score arm, 50 samples (posterior mean in parentheses where it differs). SynthSR: deterministic. G-M2, G-M3: audit status of the input (Section 3 , Appendix B ); a subject passing both is certified. †

Figure 2: Fabrication against the raw-input benchmark. REC (output vs own 3T), SWAP (output vs stranger 3T) and CON (between samples) by band feature size [FP] for the four held-out subjects (z-score arm, 50 samples); grey dashed: raw-input benchmark; dotted: whole-brain FSC anchor. Merges in Table 2 .

Appendix figures & tables11 assets

Supplementary material from the paper’s appendix.

Appendix

Gate	Test	Pre-specified criterion	Outcome
A1	recovery of an imposed cutoff (3, 4, 5, 6, 8 mm [FP])	within 10%	FSC: 2.5–7.5% error at 3–6 mm (pass over the operative range); 9–11% at 8 mm (fails the strict
			criterion; brain field of view); decorrelation fails (0 of 15) and is kept qualitative
A2	3T self-split (binomial 1FRC) vs native 2.0 mm	within 25%	2.44–2.77 mm (22–38%): fails; used only as a fine upper bound, far finer than the 6.31 mm [FP] crossing
A3	grid invariance (1.0 vs 1.25 mm grid)	within 10%	within 3%: pass
A4	registration robustness (0 to 2 mm injected shift)	bound below every gap	crossings move 0.02–0.57 mm [FP]; a 1 mm shift moves the crossing 0.47 mm [FP], below the 2.32 mm [FP] gap
A5	response to added blur (FWHM 2–6 mm)	strictly monotone	FSC strictly monotone: pass; decorrelation fails

Appendix

Table 3: Known-answer gates run on Zenodo before any reported value (3 subjects). Pass criteria are pre-specified; decision D1 is reported in Section 3 .

Subject	G-M1	Anchor (ladder / gate)	G-M2	Anchor $\leq$ 7	G-M3 required	G-M3 (ladder / gate)	Certified
sub-0048	2.53	6.90 / 6.41	pass	yes	$\geq$ 8	17.6 / 36.4 pass	yes
sub-0064	2.42	14.04 / 14.60	fail	no	$\geq$ 16	16.01 / 10.97 marginal	no
sub-HYPE21	1.16	10.90 / 11.52	pass	no	$\geq$ 12	absent / 69.3 pass	yes
sub-HYPE22	1.16	21.60 / 22.72	fail	no	$\geq$ 24	47.8 / 45.0 pass	no

Appendix

Table 4: Audit checks on the direct-arm inputs, all mm [FP]. G-M1: 3T self-split fine bound (1FRC on Zenodo, checkerboard split on OpenNeuro). G-M2: anchor inside the dataset CI (Zenodo T1w 4.91–7.22, OpenNeuro T1w 7.82–18.77, both on the E1 frame). G-M3: input cross-FSC against the frozen stranger’s 3T, required at least one band coarser than the own anchor or absent, under the ladder and the gate anchor recipes. G-M4: deterministic rerun. Certified: G-M2 and G-M3 both pass.

Frames (CI / anchors)	Dataset ceiling and CI	sub-HYPE21 anchor	sub-HYPE22 anchor	Outcome
E1 / v3 (paper)	9.628 (7.82–18.77)	10.90	21.60	pass / fail
E1 / E1	9.628 (7.82–18.77)	51.4 (no crossing, gate recipe)	55.8 / 101.3	fail / fail
v3 / v3	158 (22–512)	10.90	21.60	fail / pass

Appendix

Table 5: OpenNeuro T1w gate G-M2 under each frame pairing, mm [FP]. The paper’s evaluation mixes frames (CI on E1, anchors on the validated v3 frame). Like against like on E1 the held-out inputs do not register; like against like on v3 the dataset ceiling is degenerate (12 subjects, foreground mask). No pairing passes both subjects.

Subject	$c=16$	$c=12$	$c=8$	$c=6$	$c=4$	$B$ alone	$A$ alone
sub-0048	16 (0)	12 (0)	8 (0)	6 (0)	4 (0)	24	none
sub-0064	12 (1)	10 (1)	6 (1)	5 (1)	3 (2)	24	none
sub-HYPE21	12 (1)	10 (1)	6 (1)	5 (1)	3 (2)	24	none
sub-HYPE22	16 (0)	12 (0)	8 (0)	6 (0)	4 (0)	24	none

Appendix

Table 6: Known-answer test of the merge readout, recovered merge in mm [FP] (error in grid steps). End cases:

B

alone merges at 24 mm, the coarsest reportable band;

A

alone never merges.

band centre mm [FP] or group	RHO_own	partial RHO	RHO_stranger	AUROC
8.0	0.171	0.123	0.115	0.566
6.0	0.270	0.189	0.219	0.659
5.0	0.342	0.239	0.280	0.725
4.0	0.388	0.269	0.315	0.758
3.5	0.395	0.271	0.318	0.763
3.0	0.392	0.265	0.313	0.766

Appendix

Table 7: Uncertainty controls per band (band centres in mm [FP]) and grouped into bands of 4 mm [FP] and coarser versus finer than 4 mm [FP] (the split point used by the analysis; the whole-brain ceiling is 6.31 mm [FP]). Computed on the original registration frame; the validated-frame recompute is reported in Section 5.3 . RHO: Spearman correlation between sample variance and band error against the own 3T (own), after partialling out band energy (partial), and against a stranger (stranger); AUROC: variance flagging top-decile band error.

Figure 3: Faithful information stops at the measured ceiling (display only). One representative run per family on its own held-out subject, matched on the anterior lateral-ventricle margin: GAN on Zenodo T2w, ViT on NIST b0, diffusion on Zenodo T1w (posterior mean). Row 1: 64 mT input, true 3T, zoom ladder; row 2: model output at identical coordinates; last column: band-pass finer than the input ceiling (NIST, which has no cross-field ceiling: finer than the 64 mT self-resolution, 5.06 mm [FP]). Finer than the ceiling the input carries little subject information while every output renders fine detail; faithfulness is computed only for the diffusion row (Table 9 ), and the GAN and ViT rows are not computable (NC-ANCHOR, NC-EPI).

Figure 4: Synthetic degradations keep a band the real acquisition lacks (display only). Zenodo T1w sub-0048: true 3T, real 64 mT, and noiseless S-KSP, S-GAU, S-BIC, with zooms and a 4.0–6.3 mm [FP] band-pass between the synthetic and real crossings. Annotations are the noise-matched crossings: real 6.31 [FP], S-KSP+N 3.99, S-GAU+N 4.44, S-BIC+N 4.47.

Figure 5: Cross-FSC curves. Median over subjects of FSC against the 3T for the real 64 mT scan and the noise-matched synthetics (noiseless S-KSP dashed; it shares the 3T noise, so its curve is inflated), with the half-bit threshold, the empirical null band, and the 3T self-split scalar (2.47 mm [FP]).

Figure 6: Left: Uncertainty controls on the original registration frame, bands of 4 mm [FP] and coarser vs finer than 4 mm [FP]. Fine bands: AUROC 0.77, RHO_own 0.39 vs RHO_stranger 0.31; coarse bands: AUROC 0.68 (Table 7 ). The validated-frame recompute is reported in Section 5.3 . Right: Apparent sharpness vs input ceiling , 24 reference runs (marker = family) and SynthSR (star), by dataset column; horizontal lines mark each column’s input ceiling (OpenNeuro T2w: registration-limited, qualitative, shading indicative only; NIST: no cross-field ceiling). Every trained run renders detail finer than its ceiling; SynthSR (5.2–6.1 mm [FP]) sits at it.

Figure 7: Fabrication in image space (display only). Zenodo T1w held-out subjects sub-0048 and sub-0064: 64 mT input, two posterior samples, posterior mean, own 3T and stranger 3T, with zooms and a high-pass strip finer than the ceiling. Quantities for these subjects are in Table 2 and Figure 2 .

Figure 8: Confident detail across audit arms (display only). Input and output with zooms for five arms, no truth column: GAN Zenodo T2w (NC-ANCHOR), GAN NIST b0 (NC-EPI), ViT NIST b0 (NC-EPI), multicontrast Zenodo T2w (NC-ANCHOR), single-contrast diffusion Zenodo T1w (faithfulness computed, merges 16 and 24 mm [FP], Table 2 ). The OpenNeuro T2w GAN arm is omitted here (outputs collapse under the cross-device gap, NC-XDEV) and reported in Table 9 .

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