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Light-sheet fluorescence microscopy (LSFM) is a cutting-edge volumetric imaging technique that allows for three-dimensional imaging of mesoscopic samples with decoupled illumination and detection paths. Although the selective excitation scheme of such a microscope provides intrinsic optical sectioning that minimizes out-of-focus fluorescence background and sample photodamage, it is prone to light absorption and scattering effects, which results in uneven illumination and striping artifacts in the images adversely. To tackle this issue, in this paper, we propose a blind stripe artifact removal algorithm in LSFM, called DeStripe, which combines a self-supervised spatio-spectral graph neural network with unfolded Hessian prior. Specifically, inspired by the desirable properties of Fourier transform in condensing striping information into isolated values in the frequency domain, DeStripe firstly localizes the potentially corrupted Fourier coefficients by exploiting the structural difference between unidirectional stripe artifacts and more isotropic foreground images. Affected Fourier coefficients can then be fed into a graph neural network for recovery, with a Hessian regularization unrolled to further ensure structures in the standard image space are well preserved. Since in realistic, stripe-free LSFM barely exists with a standard image acquisition protocol, DeStripe is equipped with a Self2Self denoising loss term, enabling artifact elimination without access to stripe-free ground truth images. Competitive experimental results demonstrate the efficacy of DeStripe in recovering corrupted biomarkers in LSFM with both synthetic and real stripe artifacts.