  We propose a fast sequential algorithm for the fundamental problem of
estimating frequencies and amplitudes of a noisy mixture of sinusoids. The
algorithm is a natural generalization of Orthogonal Matching Pursuit (OMP) to
the continuum using Newton refinements, and hence is termed Newtonized OMP
(NOMP). Each iteration consists of two phases: detection of a new sinusoid, and
sequential Newton refinements of the parameters of already detected sinusoids.
The refinements play a critical role in two ways: (1) sidestepping the
potential basis mismatch from discretizing a continuous parameter space, (2)
providing feedback for locally refining parameters estimated in previous
iterations. We characterize convergence, and provide a Constant False Alarm
Rate (CFAR) based termination criterion. By benchmarking against the Cramer Rao
Bound, we show that NOMP achieves near-optimal performance under a variety of
conditions. We compare the performance of NOMP with classical algorithms such
as MUSIC and more recent Atomic norm Soft Thresholding (AST) and Lasso
algorithms, both in terms of frequency estimation accuracy and run time.
