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Many learning-based methods estimate ego-motion using visual sensors. However, visual sensors are prone to intense lighting variations and textureless scenarios. 4D radar, an emerging automotive sensor, complements visual sensors effectively due to its robustness in adverse weather and lighting conditions. This paper presents an end-to-end 4D radar-visual odometry (4DRVO) approach that combines sparse point cloud data from 4D radar with image information from cameras. Using the Feature Pyramid, Pose Warping, and Cost Volume (PWC) network architecture, we extract 4D radar point features and image features at multiple scales. We then employ a hierarchical iterative refinement approach to supervise the estimated pose. We propose a novel Cross-Modal Transformer (CMT) module to effectively fuse the 4D radar point modality, image modality, and 4D radar point-image connection modality at multiple scales, achieving cross-modal feature interaction and multi-modal feature fusion.