SAMV (algorithm)
SAMV (iterative sparse asymptotic minimum variance[1][2]) is a parameter-free superresolution algorithm for the linear inverse problem in spectral estimation, direction-of-arrival (DOA) estimation and tomographic reconstruction with applications in signal processing, medical imaging and remote sensing.
The name was coined in 2013[1] to emphasize its basis on the asymptotically minimum variance (AMV) criterion.
It is a powerful tool for the recovery of both the amplitude and frequency characteristics of multiple highly correlated sources in challenging environments (e.g., limited number of snapshots and low signal-to-noise ratio).
Applications include synthetic-aperture radar,[2][3] computed tomography scan, and magnetic resonance imaging (MRI).
The formulation of the SAMV algorithm is given as an inverse problem in the context of DOA estimation.
-element uniform linear array (ULA) receive
dimensional snapshot vectors are where
be a vector containing the unknown signal powers and noise variance,
is This covariance matrix can be traditionally estimated by the sample covariance matrix
After applying the vectorization operator to the matrix
is linearly related to the unknown parameter
, we develop a series of iterative SAMV approaches based on the asymptotically minimum variance criterion.
of an arbitrary consistent estimator of
based on the second-order statistic
is bounded by the real symmetric positive definite matrix where
In addition, this lower bound is attained by the covariance matrix of the asymptotic distribution of
The resolution of most compressed sensing based source localization techniques is limited by the fineness of the direction grid that covers the location parameter space.
is dependent on the distance between the adjacent element in the overcomplete dictionary
, therefore, the difficulty of choosing the optimum overcomplete dictionary arises.
The computational complexity is directly proportional to the fineness of the direction grid, a highly dense grid is not computational practical.
To overcome this resolution limitation imposed by the grid, the grid-free SAMV-SML (iterative Sparse Asymptotic Minimum Variance - Stochastic Maximum Likelihood) is proposed,[1] which refine the location estimates
by iteratively minimizing a stochastic maximum likelihood cost function with respect to a single scalar parameter
A typical application with the SAMV algorithm in SISO radar/sonar range-Doppler imaging problem.
This imaging problem is a single-snapshot application, and algorithms compatible with single-snapshot estimation are included, i.e., matched filter (MF, similar to the periodogram or backprojection, which is often efficiently implemented as fast Fourier transform (FFT)), IAA,[5] and a variant of the SAMV algorithm (SAMV-0).
-element polyphase pulse compression P3 code is employed as the transmitted pulse, and a total of nine moving targets are simulated.
The received signals are assumed to be contaminated with uniform white Gaussian noise of
The matched filter detection result suffers from severe smearing and leakage effects both in the Doppler and range domain, hence it is impossible to distinguish the
On contrary, the IAA algorithm offers enhanced imaging results with observable target range estimates and Doppler frequencies.
The SAMV-0 approach provides highly sparse result and eliminates the smearing effects completely, but it misses the weak
An open source MATLAB implementation of SAMV algorithm could be downloaded here.
