Discrete Gabor expansions

Enhanced and Efficient Isar Image Focusing Using the Discrete Gabor Representation in an Oversampling Scheme

“…refined by the oversampling scheme can achieve both the accurate calculation of a m,n and numerical stability [26][27][28]. Note that Q should be selected in consideration of a compromise between accuracy and efficiency since Q is also related to the computation time.…”

“…Overall procedures of the TFT-based ISAR imaging are illustrated in Figure 1. The Gabor representation and its numerical implementation have been extensively investigated [26][27][28][29][30] since Gabor suggested the signal expression with a discrete set of Gaussian functions. For a discretetime signal x[k] with a length of N b , the discrete form of the Gabor representation, namely the DGR, rearranges the signal into the 2D time-frequency grid with M time samples and N frequency samples as shown in Figure 2.…”

“…For a discretetime signal x[k] with a length of N b , the discrete form of the Gabor representation, namely the DGR, rearranges the signal into the 2D time-frequency grid with M time samples and N frequency samples as shown in Figure 2. The DGR of the signal x[k] consists of the discrete Gabor expansion and the discrete Gabor transform as follows [26]:…”

“…In this paper, we propose the discrete Gabor representation (DGR) [26][27][28] as an effective approach for obtaining well-focused ISAR images. In contrast to other linear TFTs, the DGR analytically obtains the analysis window from the given synthesis window.…”

“…In contrast to other linear TFTs, the DGR analytically obtains the analysis window from the given synthesis window. With the oversampling scheme of the DGR [26,27], Gabor coefficients, derived from the analysis window frames can contain accurate information on the signal time-frequency components. In addition, the DGR compartmentally allocates the Gabor coefficients to the respective unit cells of the time-frequency grid.…”