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In this Letter, we propose a dynamic fiber-optic white light interferometry (WLI) based on the compressed-sensing (CS) principle. The time-varying interference spectra of a Fabry-Perot cavity under vibration are considered as a two-dimensional (2D) signal with respect to both laser wavelength and time, which can be compressively sampled using a programmable semiconductor laser source during the measurement process. After CS reconstruction, the spectrum acquisition rate is equal to the random wavelength modulation rate, up to 10 MHz in thi