In this article, we present a smooth low-rank tensor completion (SLRTC) based reconstruction algorithm to recover raw thermal image sequences from highly randomly undersampled or small numbers of available thermographic data. The presented algorithm is also fused with a temporal interpolation algorithm (to produce the SLRTCTI algorithm) to complement high frame-rate thermal image sequences with notably enhanced thermal contrast. Pulsed and lock-in thermographic data are obtained for subsurface defects in carbon fiber reinforced polymer (CFRP) to demonstrate the performance of the algorithm, and it is shown that the algorithm is data-driven and is independent of the excitation form. The algorithm enables the maximum available frame rates of thermal infrared cameras to be increased by at least ten times. To further enhance the visibility of the CFRP defects in the results reconstructed using the SLRTC algorithm, fast randomized sparse principal component thermography (FRSPCT) and 2-D principal component thermography (TDPCT) are also proposed. Results show that TDPCT remarkably enhances the thermal contrast between the defective and intact regions under highly undersampled data conditions. In addition, FRSPCT provides more easily interpretable detection results and highlights the hidden details of irregularly-shaped abnormal defects.