Four-dimensional Fourier-based Reassignment

This article proposes four-dimensional reassignment -- an efficient tool for analyzing non-stationary two-dimensional signals. Firstly, the theoretical background is presented to constitute the considered problem. Next, the proposed approach to improve the readability of the four-dimensional signal energy concentration using the windowed two-dimensional Fourier transform (W2DFT) is defined. In general, the presented technique transforms the two-dimensional signal from the time-space domain to the time-space-frequency-spatial frequency distribution. Next, the energy is relocated according to the estimated mass centers, leading to a superior concentration in all four dimensions. The method is validated through numerical experiments with both simulated and real-life radar signals, showing its usefulness in practice.