Pan-Tilt-Zoom (PTZ) cameras with wide-angle lenses are widely used in surveillance but often require image rectification due to their inherent nonlinear distortions. Current deep learning approaches typically struggle to maintain fine-grained geometric details, resulting in inaccurate rectification. This paper presents a Forward Distortion and Backward Warping Network (FDBW-Net), a novel framework for wide-angle image rectification. It begins by using a forward distortion model to synthesize barrel-distorted images, reducing pixel redundancy and preventing blur. The network employs a pyramid context encoder with attention mechanisms to generate backward warping flows containing geometric details. Then, a multi-scale decoder is used to restore distorted features and output rectified images. FDBW-Net's performance is validated on diverse datasets: public benchmarks, AirSim-rendered PTZ camera imagery, and real-scene PTZ camera datasets. It demonstrates that FDBW-Net achieves SOTA performance in distortion rectification, boosting the adaptability of PTZ cameras for practical visual applications.