Early detection of coronary artery disease (CAD) is critical for reducing mortality and improving patient treatment planning. While angiographic image analysis from X-rays is a common and cost-effective method for identifying cardiac abnormalities, including stenotic coronary arteries, poor image quality can significantly impede clinical diagnosis. We present the Coronary Artery Segmentation and Refinement Network (CASR-Net), a three-stage pipeline comprising image preprocessing, segmentation, and refinement. A novel multichannel preprocessing strategy combining CLAHE and an improved Ben Graham method provides incremental gains, increasing Dice Score Coefficient (DSC) by 0.31-0.89% and Intersection over Union (IoU) by 0.40-1.16% compared with using the techniques individually. The core innovation is a segmentation network built on a UNet with a DenseNet121 encoder and a Self-organized Operational Neural Network (Self-ONN) based decoder, which preserves the continuity of narrow and stenotic vessel branches. A final contour refinement module further suppresses false positives. Evaluated with 5-fold cross-validation on a combination of two public datasets that contain both healthy and stenotic arteries, CASR-Net outperformed several state-of-the-art models, achieving an IoU of 61.43%, a DSC of 76.10%, and clDice of 79.36%. These results highlight a robust approach to automated coronary artery segmentation, offering a valuable tool to support clinicians in diagnosis and treatment planning.