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 two-dimensional (2-D) frequencies. In the MEMP method, an enhanced matrix is constructed from the data samples, and then the matrix pencil approach is used 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 Cramer-Rao lower bound