Low-Level Sinusoidal Signal Detection From a High-Resolution Virtual Spectral Image Using Autoregressive Vector Extrapolation

A new high-resolution virtual spectral imaging technique is able to resolve a closely spaced dominant and low-level sinusoidal signal (power spread of up to 15 dB) in harsh signal-to-noise ratio environments with limited samples where a high-resolution 2-D autoregressive (AR) spectral estimation algorithm failed. This feat is accomplished by applying a 2-D fast Fourier transform to an expanded 2-D measurement data set (which consists of the original measurements extended by vector-extrapolated virtual measurements). The virtual measurement data are created from the original 2-D measurements using an innovative virtual-data vector extrapolation algorithm. A special 2-D AR model is used to model the measurements and then used to extrapolate measurements a vector at a time. Simulations compare our virtual spectral image with a high-resolution 2-D AR spectral image and a spectral image of the truth (the measurements that the extrapolation algorithm is trying to predict). The virtual measurement data are also compared with the true measurement data. We analytically show that the virtual measurements are a function of the true measurements plus some residual error terms. Mean-squared-error simulations show that the extrapolated measurements are well behaved for our problem space and provide a cost example.