Title: FaCE: Provable Frequency-Aware Convex Enhancement for Training-Free Low-Light Images
Primary area: optimization
Keywords: Low-Light Image Enhancement (LLIE); Monogenic Fourier Transform (MFT); Frequency-domain modeling; Convex optimization; Training-free (no learned parameters); Illumination-only enhancement.

Abstract: We study training-free low-light image enhancement from a provable optimization viewpoint. Building on the Monogenic Fourier transform, we introduce Frequency-Aware Convex Enhancement (FaCE), formulating per-image enhancement as a strictly convex problem with a unique, stable minimizer. To make the frequency modeling reproducible, we (i) define the low-pass prior via the spectral centroid (u_c,v_c) and an energy–cumulative distribution radius r_τ (the smallest radius achieving cumulative spectral energy τ), and (ii) select the number of spectral clusters K with a data-driven model-selection rule. This yields a fully training-free pipeline with clear variables and no learned parameters. We prove that a unique, stable solution exists and verify the guarantees via numerical experiments. On standard benchmarks, FaCE attains competitive quality with a per-image solver, and we include in-the-wild qualitative mosaics on real images to highlight practical usefulness. Rather than competing with large learned priors, FaCE complements them with a provable, interpretable alternative that requires no training and exposes frequency-band attributions.