In ultra-high-definition active-matrix organic light-emitting diode (AMOLED) displays, the external compensation technique improves burn-in and uneven luminescence by varying the current through the driving thin-film transistors (TFTs). However, sensing the current through the driving TFT for every pixel is time-consuming because of the increased number of scanning lines. Hence, in this study, we propose a method to reduce the number of measurements and shorten the measurement time by interpolating from the current measurement data for surrounding pixels. We show that this method can be applied to a 4K flexible AMOLED display and can satisfactorily compensate degradation due to burn-in.