Robust Object Detection via Kronecker Tensor Decomposition: Theory, Algorithms, and Applications

Object detection in real-world scenarios faces significant challenges, including occlusions, sensor noise, limited training data, and computational constraints. This paper presents a comprehensive framework leveraging tensor completion methods to address these fundamental limitations. We demonstrate that tensor completion provides a mathematical foundation for handling missing and corrupted data by exploiting the multi-dimensional structure inherent in visual information. Our approach encompasses three key contributions: (1) a theoretical analysis of tensor rank properties in visual data, (2) novel algorithms integrating tensor completion with modern detection pipelines, and (3) experimental validation across multiple adversarial attacks. Results show that our methods improve detection accuracy under severe occlusion by up to 21\% (from 23 to 44 percent of mAP in the worst case) and enhance robustness to various corruption types. The proposed framework establishes tensor completion as a fundamental tool for building more robust and efficient object detection systems.