The automatic reconstruction of 3D computer-aided design (CAD) models from CAD sketches has recently gained significant attention in the computer vision community. Most existing methods, however, rely on vector CAD sketches and 3D ground truth for supervision, which are often difficult to be obtained in industrial applications and are sensitive to noise inputs. We propose viewing CAD reconstruction as a specific instance of sparse-view 3D reconstruction to overcome these limitations. While this reformulation offers a promising perspective, existing 3D reconstruction methods typically require natural images and corresponding camera poses as inputs, which introduces two major significant challenges: (1) modality discrepancy between CAD sketches and natural images, and (2) difficulty of accurate camera pose estimation for CAD sketches. To solve these issues, we first transform the CAD sketches into representations resembling natural images and extract corresponding masks. Next, we manually calculate the camera poses for the orthographic views to ensure accurate alignment within the 3D coordinate system. Finally, we employ a customized sparse-view 3D reconstruction method to achieve high-quality reconstructions from aligned orthographic views. By leveraging raster CAD sketches for self-supervision, our approach eliminates the reliance on vector CAD sketches and 3D ground truth. Experiments on the Sub-Fusion360 dataset demonstrate that our proposed method significantly outperforms previous approaches in CAD reconstruction performance and exhibits strong robustness to noisy inputs.