Extrapolation and spectral estimation with iterative weighted norm modification

Aligned and Unaligned Coherence: A New Diagnostic Tool

“…5 It should also be noted that several methods are availbale to get line spectra that have higher resolution than the average periodogram procedure achieves (Cabrera, 61 Sacchi, 62 Ciuciu 5 ) and it is possible these could be used with the unaligned time histories to get the toneless cross-spectrum. Since the broadband noise has been essentially removed, it should not be necessay to use an average periodogram procedure.…”

High-Resolution Imaging Based on Coherent Processing for Distributed Multi-Band Radar Data

“…In [6], Burg algorithm is used to find the linear prediction parameters and a iterative procedure is used to improve the estimation of the parameters and the extrapolation of the data, but the gaps between subbands can not be too large. In [7,8], minimum weighted norm (MWN) method is used for optimizing one-dimensional (1-D) aperture extrapolation, but it may not suitable for multi-band data with few data samples and large gaps. In [9][10][11], the method called gappeddata APES (GAPES) is used for data fusion, which is based on an interpolation of the gapped data under certain constraints.…”

“…In [5], a data based coherent compensation method is used for coherent processing, but it is easily influenced by noise due to lack of de-noising process. For the data fusion methods, the available algorithms include nonparametric spectrum estimation [6][7][8][9][10], the parametric spectrum estimation method [1,12,13] and p-norm regularization method [14]. In [6], Burg algorithm is used to find the linear prediction parameters and a iterative procedure is used to improve the estimation of the parameters and the extrapolation of the data, but the gaps between subbands can not be too large.…”

Signal processing with the sparseness constraint

“…Unfortunately, it is evident that the FFT solution, which is the minimum 2-norm solution, does not possess representational simplicity. However, algorithms that employ the sparseness constraint can be used to obtain high resolution nonparametric spectrum estimates [15,26,16,7].…”

“…Applications include band-limited extrapolation and spectral estimation [25,26], direction of arrival estimation [15], functional approximation [27,28,29], failure diagnosis [30], sparse coding [31], and pattern recognition for medical diagnosis [32]. It is clear that an effective solution to this problem has wide ranging consequences.…”