FaCE: Provable Frequency-Aware Convex Enhancement for Training-Free Low-Light Images

Hao Huang, Jee-Hyong Lee, Zunwei Fu

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 convex optimization viewpoint with theoretical guarantees. Building on the Monogenic Fourier Transform (MFT), we introduce Frequency-Aware Convex Enhancement (FaCE), a frequency-aware convex enhancement method for training-free low-light images with guarantees on existence, uniqueness, and stability of the per-image solution. 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 $r_\tau$ (the smallest radius achieving cumulative spectral energy $\tau$), 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 as a theoretically grounded, interpretable alternative that requires no training and exposes frequency-band attributions.

Primary Area: optimization

Submission Number: 6335