Dimensionality, Channels, and Observer Optimality: Conjugate Gradient Methods as a Signal-Processing Bridge in Task-Based Medical Image Quality Assessment

Task-based image quality assessment (IQA) in medical imaging demands objective figures of merit (FOMs) that faithfully reflect diagnostic utility rather than perceptual aesthetics. The theoretical gold standard — the Bayesian Ideal Observer (IO) and its linear approximation, the Hotelling Observer (HO) — provides exactly such FOMs, but their direct computation on high-dimensional image data is computationally intractable in nearly all clinically realistic scenarios. This paper synthesizes recent work on conjugate gradient (CG)-based channel construction [corpus:arxiv:2605.29415] into a broader signal-processing framework, situating the approach within the classical tension between observer optimality and computational tractability. Our thesis, stated as a candidate reading rather than a derivation, is that the CG method functions as a structured dimensionality-reduction operator whose iterative geometry — Krylov subspace expansion — is naturally aligned with the covariance structure of the signal detection task, making it a principled rather than heuristic compression step. We argue that this alignment is the mechanism distinguishing CG channels from generic basis projections, and we identify three testable falsification paths: (1) comparing CG-channel HO performance against matched-dimension PCA channels on a fixed detection task, (2) measuring how CG convergence rate scales with the condition number of the background covariance matrix, and (3) verifying that CG-derived channels yield monotonically non-decreasing AUC estimates as the channel count increases. The paper also places the approach in context relative to prior channel families (Laguerre-Gauss, PCA, etc.), discusses the methodological limits imposed by abstract-only reading, and flags where extrapolation beyond the reported abstract is required. This synthesis is intended to assist practitioners designing or optimizing medical imaging pipelines where ideal-observer analysis is desired but computationally constrained. ---

Authorship: Saluca Agentic AI Research Team (Saluca LLC). AI-drafted from arXiv preprint corpus on the date in the filename.

Cited arXiv preprints: 2605.29415