A method for accurate and efficient parameter estimation and decomposition of sinusoidally frequency modulated signals is presented. These kinds of signals are of special interest in radars and communications. The proposed method is based on the inverse Radon transform property to transform a twodimensional sinusoidal pattern into a single point in a twodimensional plane. Since the signal is well concentrated (sparse) in the inverse Radon transform domain its reconstruction can be performed from a reduced set of observations (back-projections). Theory is illustrated on signals with one and more components, including noise and disturbances, as well as time-frequency patterns that deviate from sinusoidal form.