Super-Resolution Accuracy beyond the Cutoff Scale

Definitions and mathematical statement

Let $x$ denote the signal mentioned in the supplied record. The record does not specify its domain, codomain, function space, or admissible signal class. The terms low-pass measurements, noise, cutoff resolution, finer features, and recovery accuracy are not given mathematical definitions.

Source question. Given noisy low-pass measurements of $x$, determine how accurately its finer features can be recovered by super-resolution as the desired resolution becomes finer than the cutoff resolution.

Unresolved formulation. This is a qualitative research question, not a fully specified mathematical assertion. A precise formulation requires a measurement operator and observation domain, an admissible signal class, a noise model and noise magnitude, a definition of the features to be recovered, a resolution parameter and its relation to the cutoff, and an error criterion. It must also specify whether accuracy concerns a particular reconstruction method or optimal performance over a class of methods, together with the relevant quantifiers. None of these choices is fixed by the supplied record. Consequently, no definite recovery bound, asymptotic rate, or quantified theorem can be stated without adding hypotheses.

Short English statement

The question asks how recovery accuracy changes when super-resolution seeks details finer than the measurement cutoff. The supplied record leaves the signal model, noise, target features, and accuracy criterion unspecified, so it does not determine a precise mathematical claim. Its supplied open label is a curation status, not an independently verified mathematical conclusion.

Sources

• Local UnsolvedMath registry: supplied complete source record, permanent ID $30002095$, source problem code catalogue entry, title Super-Resolution Accuracy beyond the Cutoff Scale, in the Oberwolfach Reports Open Problems collection. The project identifies data/unsolvedmath/problems.json and catalog/problems.json as local registry files; no independent inspection is asserted here.
• Supplied report citation: Applied Harmonic Analysis and Sparse Approximation (2013), Oberwolfach Reports, DOI 10.4171/owr/2012/29, pp. 1759--1843. Supplied source URL and literature-source link, labeled "original OWR report": https://doi.org/10.4171/owr/2012/29. The background attributes the question to workshop open-problem discussions documented in Oberwolfach Reports; no individual proposer is supplied.
• Literature assessment dated 2026-08-21: the supplied curation labels the item open and states that the context-free question does not specify a model, observations, or target theorem, so no determinate solved or disproved claim can be identified. This is supplied dated curation, not independently verified literature assessment; the supplied background requests independent verification of time-sensitive status and cited claims.
• The registry labels the statement corrected_verified and reports manual semantic, typographic, and LaTeX review of the cleanup. This supplied verification claim does not resolve the missing mathematical specifications.