Digital subtraction angiography (DSA) in coronary imaging is fundamentally challenged by physiological motion, forcing reliance on raw angiograms cluttered with anatomical noise. Existing deep learning methods often produced images with two critical clinically unacceptable flaws: persistent boundary artifacts and a loss of native tissue grayscale fidelity that undermined diagnostic confidence. We propose a novel framework termed as CDSA-Net that for the first time explicitly decouples and jointly optimizes vascular structure preservation and realistic background restoration. CDSA-Net introduces two core innovations: (i) A hierarchical geometric prior guidance (HGPG) mechanism, embedded in our coronary structure extraction network (CSENet). It synergistically combines integrated geometric prior (IGP) with gated spatial modulation (GSM) and centerline-aware topology (CAT) loss supervision, ensuring structural continuity. (ii) An adaptive noise module (ANM) within our coronary background restoration network (CBResNet). Unlike standard restoration, ANM uniquely models the stochastic nature of clinical X-ray noise, bridging the domain gap to enable seamless background intensity estimation and the complete elimination of boundary artifacts. The final subtraction is obtained by removing the restored background from the raw angiogram. Quantitatively, it significantly outperformed state-of-the-art methods in vascular intensity correlation and perceptual quality. A 25.6% improvement in morphology assessment efficiency and a 42.9% gain in hemodynamic evaluation speed set a new benchmark for utility in interventional cardiology, while maintaining diagnostic results consistent with raw angiograms. The project code is available at https://github.com/DrThink-ai/CDSA-Net.

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