A new method of plasma density profile reconstruction in microwave reflectometry is proposed and implemented on anX-mode broadband reflectometer of the GAMMA 10 mirror device with an ultrafast sweep rate of 10–20 &mgr;s. The proposed method makes use of the wavelet transform of the detected signal. Excellent resolution in the time-frequency domain, inherent to wavelet analysis, allows one to obtain a radial electron density profile for every frequency sweep. The electron density reconstruction algorithm, besides the wavelet transform of the reflectometer signal, also includes the calibration, profile initialization, and the solution of an integral equation, ultimately yielding the local values of the electron density. Calibration of the measured signal phase and profile initialization is performed using the independent results of microwave interferometry. Inversion of the integral equation is implemented utilizing the gradient method, numerically stable even for plasma regions with steep density gradients and density profile plateaus. A wavelet-based profile reconstruction algorithm is especially advantageous for monitoring transient plasma phenomena and fast processes, such as in pellet injection, ultrafast swept reflectometry, and short pulsed reflectometry. ©1998 American Institute of Physics.