Quaternion-Hadamard Network: A Novel Defense Against Adversarial Attacks with a New Dataset

Adverse-weather image restoration (e.g., rain, snow, haze) models remain highly vulnerable to gradient-based white-box adversarial attacks, wherein minimal loss-aligned perturbations cause substantial degradation in the restored output. This paper presents QHNet, a computationally efficient purification-based defense that precedes the restoration network and targets perturbation suppression in the transform and quaternion domains. QHNet incorporates a Quaternion Hadamard Polynomial Denoising Block (QHPDB) and a Quaternion Denoising Residual Block (QDRB) within an encoder-decoder framework to remove high-frequency adversarial noise while preserving fine structural details. Robustness is evaluated using PSNR and SSIM across rain, snow, and haze removal tasks, and further validated under adaptive, defense-aware white-box attacks employing Projected Gradient Descent (PGD), Backward Pass Differentiable Approximation (BPDA), and Expectation Over Transformation (EOT). Experimental results demonstrate that QHNet delivers superior restoration fidelity and significantly improved robustness compared to state-of-the-art purification baselines, confirming its effectiveness for low-level vision pipelines.