Structured covariance estimation and radar imaging with sparse linear models

The problem of the computational complexity of the structure covariance EM algorithm is considered. Ordinarily this algorithm requires O(N³) floating point operations, per iteration, for the estimation of an N-point power spectrum. However, if the linear model relating the observations to the underlying variables is sparse, the computational burden can be reduced to O(N) operations. This sparsity can be achieved approximately by a data preprocessing step that causes the effect of each underlying variable to be seen in only one component of the preprocessed observation vectors. An illustrative example involving a rotating linear array as the sensor and a Chebyshev filter bank as the preprocessor is given.