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Purpose: In x‐ray radiography, the commonly used antiscatter grid for enhancing image quality causes artifacts in the form of periodic noises, such as shadows, cutoff, and Moiré fringes. Software degridding is traditionally performed via linear or homomorphic filtering in the spectral domain. These methods inevitably result in image blurring, information loss, and distortion, thus hindering detection and assessment of diseases. We seek effective and practical solutions for grid artifact correction based on spatial‐domain analysis toward high‐quality imaging. Methods: By analyzing the physical process of grid artifact formation, we track down the root of the problem associated with spectral filtering. We propose the grid regression demodulation (GRD). The degridding cost is forged as a functional of the latent x‐ray photon image and parametric grid model characterizing grid transmission property. Regularization on the grid spectra is incorporated. We devise optimization algorithms for artifact correction and grid pattern estimation. GRD decouples the partially overlapped spectra of the grid and anatomy, and removes the artifacts independently, thus restoring the underlying clinically relevant data. Results: Method efficacy is demonstrated using simulated and real data. GRD effectively preserves image edges, textures, and patterns while removing grid artifacts. For the known ground truth setting, GRD gives a near‐perfect correction. For real data, GRD is capable of correcting not only the primary grid artifacts, but also the higher grid harmonic artifacts while keeping image content unaltered, which is unachievable by the other methods. Our method has low residual errors and exhibits a successful demodulation effect without introducing additional artifacts, while ringing or cilia artifacts are present in the others. Conclusions: The proposed method outperforms the prevalent transform techniques for correcting grid artifacts in digital radiography. It is self‐sustained and self‐adaptive to a range of targets and beam quality. Our approach is advantageous in restoring the latent image while suppressing grid noises. It retrieves the true scale factor of the degridded data, which is unattainable via any spectral filtering techniques. This work unlocks a promising venue to improve and upgrade low‐dose medical radiographic imaging technology. [ABSTRACT FROM AUTHOR]