[Paper Review] AFSC: Adaptive Fourier Space Compression for Anomaly Detection

Haote Xu, Yunlong Zhang+4 more|ArXiv.org|Apr 17, 2022

AI in cancer detection4 citations

TL;DR

This paper proposes AFSC, a novel adaptive Fourier space compression module that enhances unsupervised anomaly detection by extracting critical healthy tissue features from the frequency domain of medical images. By jointly compressing magnitude and phase spectra in Fourier space, AFSC improves pseudo-healthy image generation, leading to state-of-the-art performance on BraTS and MS-SEG datasets, especially when integrated into existing methods like AE and DRAEM.

ABSTRACT

Anomaly Detection (AD) on medical images enables a model to recognize any type of anomaly pattern without lesion-specific supervised learning. Data augmentation based methods construct pseudo-healthy images by "pasting" fake lesions on real healthy ones, and a network is trained to predict healthy images in a supervised manner. The lesion can be found by difference between the unhealthy input and pseudo-healthy output. However, using only manually designed fake lesions fail to approximate to irregular real lesions, hence limiting the model generalization. We assume by exploring the intrinsic data property within images, we can distinguish previously unseen lesions from healthy regions in an unhealthy image. In this study, we propose an Adaptive Fourier Space Compression (AFSC) module to distill healthy feature for AD. The compression of both magnitude and phase in frequency domain addresses the hyper intensity and diverse position of lesions. Experimental results on the BraTS and MS-SEG datasets demonstrate an AFSC baseline is able to produce promising detection results, and an AFSC module can be effectively embedded into existing AD methods.

Motivation & Objective

• Address the generalization limitations of existing pseudo-healthy image generation methods in anomaly detection, which rely on manually designed or randomly generated lesions.
• Overcome the poor generalization of artificial anomalies due to distributional mismatches with real lesions.
• Explore intrinsic data properties in the frequency domain to extract robust, lesion-invariant healthy tissue representations for improved anomaly detection.
• Develop a flexible, plug-in module that enhances existing anomaly detection frameworks without requiring architectural redesign.
• Demonstrate that adaptive compression of Fourier space components (magnitude and phase) leads to more anatomically accurate pseudo-healthy reconstructions and better anomaly localization.

Proposed method

• Propose an Adaptive Fourier Space Compression module (AFSCm) that operates on the Fourier transform of input images, targeting both magnitude and phase spectra.
• Apply sparsity-based compression to retain only the most essential frequency components for healthy tissue representation, reducing lesion interference during reconstruction.
• Use a differentiable, learnable masking strategy inspired by Monte Carlo sampling to adaptively identify critical frequency components, rather than using fixed or random masks.
• Integrate AFSCm into existing anomaly detection frameworks (e.g., AE, DRAEM) as a plug-in module to improve pseudo-healthy image generation.
• Train the model end-to-end using a reconstruction loss between input and generated pseudo-healthy images, with the AFSCm module optimizing for frequency-domain sparsity.
• Utilize a discriminator in a GAN-like setup to distinguish real healthy images from generated pseudo-healthy outputs, enhancing feature quality and generalization.

Experimental results

Research questions

• RQ1 Can compressing both magnitude and phase components in the Fourier domain improve the quality and generalization of pseudo-healthy image generation in anomaly detection?
• RQ2 Does an adaptive, learnable compression mask in Fourier space outperform fixed or random masks in preserving healthy tissue structure?
• RQ3 Can the proposed AFSC module be effectively integrated into diverse existing anomaly detection frameworks to boost performance?
• RQ4 How does AFSC compare to state-of-the-art methods like AnoGAN, DRAEM, and AE in terms of anomaly localization accuracy and robustness?
• RQ5 To what extent does frequency-domain compression reduce interference from irregular or out-of-distribution lesions during reconstruction?

Key findings

• AFSC achieved state-of-the-art performance on the BraTS2017 dataset, outperforming all baselines including DRAEM and AE in DICE (0.814 ± 0.006) and APpix (0.143 ± 0.003) metrics.
• When integrated with DRAEM, the DRAEM_G w/AFSCm variant achieved the best performance on BraTS2017, with a DICE score of 0.889 ± 0.018 and APpix of 0.187 ± 0.009.
• The AE w/AFSCm variant outperformed vanilla AE on BraTS2017, demonstrating that AFSCm enhances performance even when the input is a healthy image.
• On the more challenging MS-SEG2015 dataset, AFSC achieved the highest DICE score (0.769 ± 0.016), confirming its robustness on small and subtle lesions.
• Replacing AFSCm with a random mask of the same sparsity degraded performance across all metrics, proving the discriminative value of the adaptive compression mechanism.
• Visualizations confirmed that AFSC-generated pseudo-healthy images were more anatomically accurate and better reconstructed lesion regions as healthy tissue.