SAMV (iterative sparse asymptotic minimum variance
[) is a parameter-free superresolution algorithm for the linear ]inverse problem
An inverse problem in science is the process of calculating from a set of observations the causal factors that produced them: for example, calculating an image in X-ray computed tomography, source reconstruction in acoustics, or calculating the ...
in spectral estimation
In statistical signal processing, the goal of spectral density estimation (SDE) or simply spectral estimation is to estimate the spectral density (also known as the power spectral density) of a signal from a sequence of time samples of the signa ...
, direction-of-arrival (DOA) estimation and tomographic reconstruction
Tomographic reconstruction is a type of multidimensional inverse problem where the challenge is to yield an estimate of a specific system from a finite number of projections. The mathematical basis for tomographic imaging was laid down by Johann ...
with applications in signal processing
Signal processing is an electrical engineering subfield that focuses on analyzing, modifying and synthesizing ''signals'', such as sound, images, and scientific measurements. Signal processing techniques are used to optimize transmissions, ...
, medical imaging and remote sensing
Remote sensing is the acquisition of information about an object or phenomenon without making physical contact with the object, in contrast to in situ or on-site observation. The term is applied especially to acquiring information about Eart ...
. The name was coined in 2013[ 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
In statistics, correlation or dependence is any statistical relationship, whether causal or not, between two random variables or bivariate data. Although in the broadest sense, "correlation" may indicate any type of association, in statistic ...
sources in challenging environments (e.g., limited number of snapshots and low signal-to-noise ratio). Applications include synthetic-aperture radar,[ computed tomography scan, and magnetic resonance imaging (MRI).
]
Definition
The formulation of the SAMV algorithm is given as an inverse problem
An inverse problem in science is the process of calculating from a set of observations the causal factors that produced them: for example, calculating an image in X-ray computed tomography, source reconstruction in acoustics, or calculating the ...
in the context of DOA estimation. Suppose an -element uniform linear array
A uniform is a variety of clothing worn by members of an organization while participating in that organization's activity. Modern uniforms are most often worn by armed forces and paramilitary organizations such as police, emergency services, se ...
(ULA) receive narrow band signals emitted from sources located at locations , respectively. The sensors in the ULA accumulates snapshots over a specific time. The dimensional snapshot vectors are
:
where