Fourier Clouds: Fast Bias Correction for Imbalanced Semi-Supervised Learning

Pseudo-label-based Semi-Supervised Learning (SSL) often suffers from classifier bias, particularly under class imbalance, as inaccurate pseudo-labels tend to exacerbate existing biases towards majority classes. Existing methods, such as \textit{CDMAD}\cite{cdmad}, utilize simplistic reference inputs—typically uniform or blank-colored images—to estimate and correct this bias. However, such simplistic references fundamentally ignore realistic statistical information inherent to real datasets, specifically typical color distributions, texture details, and frequency characteristics. This lack of \emph{statistical representativeness} can lead the model to inaccurately estimate its inherent bias, limiting the effectiveness of bias correction, particularly under severe class imbalance or substantial distribution mismatches between labeled and unlabeled datasets. To overcome these limitations, we introduce the \textbf{FARAD} (Fourier-Adapted Reference for Accurate Debiasing) System. This system utilizes random-phase images, constructed by preserving the amplitude spectrum of real data while randomizing the phase spectrum. This strategy ensures two critical properties: (1) \textbf{Semantic Irrelevance}, as randomizing phase removes any structural or recognizable semantic cues, and (2) \textbf{Statistical Representativeness}, as preserving the amplitude spectrum maintains realistic textures, color distributions, and frequency characteristics. Grounded theoretically in classical Fourier analysis, the FARAD System provides a robust, accurate estimation of per-class biases. Furthermore, computational efficiency is enhanced through optimized real-to-complex (R2C) batched Fast Fourier Transforms (FFTs). Comprehensive experiments demonstrate that our approach, significantly improves minority-class accuracy and overall SSL performance, particularly under challenging imbalance scenarios, compared with existing reference-based bias correction methods.