An optimization-based algorithm is introduced to achieve the subpixel resolution in x-ray imaging. In this approach, the image captured by a detector is to be considered as a degradation of a high-resolution image. The inverse problem of the degradation is formulated as an optimization program. Through solving the cost function with Chambolle–Pock (CP) algorithm, we can reconstruct the subpixel image from multiple images shifted with subpixel precision. Numerical studies indicate that the iterative algorithm can numerically accurately invert the degradation. A set of x-ray imaging experiments were performed, and some structural information can be found in the reconstruction of the high-resolution image but not existing in the original image data. It would have potential applications in x-ray high-resolution imaging and industrial detection.