The carbon fiber reinforced polymer (CFRP) is being used frequently in the manufacturing of aerospace, rail, and other mechanical structures, where the optical pulse thermography (OPT)-based non-destructive testing (NDT) is generally used for the quality inspection, However, the output thermal sequences in OPT-based inspection suffer from uneven illumination and high-frequency thermal noise. Consequently, the inspection of defects (debonds) becomes difficult. To remedy it, post-image processing algorithms are generally carried out. The usefulness of such algorithms, however, is limited by the shape-complexity of the CFRP specimen. In this paper, we propose a tensor nuclear norm (TNN)-based low-rank and sparse total variation regularization (TVR) for CFRP debond defect detection. The integrated low-rank and sparse components are jointly and iteratively optimized. The proposed algorithm removes noise and segments/extracts the defects information from the thermal video sequences with improved resolution and contrast. Compared to the general image processing algorithm used for OPT-based NDT testing, the proposed algorithm is faster and in terms of F-score is more accurate.