Estimating two-dimensional frequencies by matrix enhancement and matrix pencil

A new method, called the matrix enhancement and matrix pencil (MEMP) method, is presented for estimating twodimensional (2-D) frequencies. The MEMP method first constructs an enhanced matrix from the data samples, and then uses the matrix pencil approach to extract out the 2-D sinusoids from the principal eigenvectors of the enhanced matrix. The MEMP method yields the estimates of the 2-D frequencies efficiently, without solving the roots of a 2-D polynomial or searching in a 2-D space. It is shown that the MEMP method can be faster than a 2-D FFT method if the number of the 2-D sinusoids is much smaller than the data set. Simulation results are provided to show that the accuracy of the MEMP method can be very close to the CramCr-Rao lower bound