# SAMV (algorithm)

**SAMViterative Sparse Asymptotic Minimum Variance**

SAMV (iterative Sparse Asymptotic Minimum Variance ) 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.wikipedia

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### Super-resolution imaging

**super-resolutionsuperresolutionsuper resolution**

SAMV (iterative Sparse Asymptotic Minimum Variance ) 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. MUltiple SIgnal Classification (MUSIC), a popular parametric superresolution method

In some radar and sonar imaging applications (e.g., magnetic resonance imaging (MRI), high-resolution computed tomography), subspace decomposition-based methods (e.g., MUSIC ) and compressed sensing-based algorithms (e.g., SAMV ) are employed to achieve SR over standard periodogram algorithm.

### Inverse problem

**inverse problemsinversioninverse method**

SAMV (iterative Sparse Asymptotic Minimum Variance ) 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.

Solutions explored include Algebraic Reconstruction Technique, filtered backprojection, and as computing power has increased, iterative reconstruction methods such as iterative Sparse Asymptotic Minimum Variance.

### Synthetic-aperture radar

**synthetic aperture radarSARsynthetic aperture**

Applications include synthetic-aperture radar, computed tomography scan, and magnetic resonance imaging (MRI).

SAMV method is a parameter-free sparse signal reconstruction based algorithm.

### Tomographic reconstruction

**reconstructedreconstruction algorithmtomography**

SAMV (iterative Sparse Asymptotic Minimum Variance ) 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.

An alternative family of recursive tomographic reconstruction algorithms are the Algebraic Reconstruction Technique s and iterative Sparse Asymptotic Minimum Variance.

### Direction of arrival

**direction-of-arrival**

SAMV (iterative Sparse Asymptotic Minimum Variance ) 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.

SAMV

### Magnetic resonance imaging

**MRImagnetic resonance imaging (MRI)magnetic resonance**

Applications include synthetic-aperture radar, computed tomography scan, and magnetic resonance imaging (MRI).

However, recent compressed sensing-based software algorithms (e.g., SAMV ) have been proposed to achieve super-resolution without requiring such high field strengths.

### Sensor array

**uniform linear array**

Suppose an M-element uniform linear array (ULA) receive K narrow band signals emitted from sources located at locations, respectively.

SAMV beamforming algorithm is a sparse signal reconstruction based algorithm which explicitly exploits the time invariant statistical characteristic of the covariance matrix.

### CT scan

**computed tomographyCTcomputerized tomography**

Applications include synthetic-aperture radar, computed tomography scan, and magnetic resonance imaging (MRI).

1) New software technology can significantly reduce the required radiation dose. New iterative tomographic reconstruction algorithms (e.g., iterative Sparse Asymptotic Minimum Variance) could offer superresolution without requiring higher radiation dose.

### Radon transform

**filtered back projectionfiltered backprojectionsinograms**

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, and a variant of the SAMV algorithm (SAMV-0).

Iterative reconstruction methods (e.g., iterative Sparse Asymptotic Minimum Variance ) could provide metal artifact reduction, noise and dose reduction for the reconstructed result that attract much research interest around the world.

### Matched filter

**matched filteringmatched-filteringNorth filters**

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, and a variant of the SAMV algorithm (SAMV-0).

SAMV

### Periodogram

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, and a variant of the SAMV algorithm (SAMV-0).

SAMV

### MUSIC (algorithm)

**MUltiple SIgnal ClassificationMUSICMUSIC (Multiple Signal Classification)**

MUltiple SIgnal Classification (MUSIC), a popular parametric superresolution method

Recent iterative semi-parametric methods offer robust superresolution despite of highly correlated sources, e.g., SAMV

### Array processing

**array signal processingarrays**

Array processing

SAMV

### Spectral density estimation

**spectral estimationfrequency estimationspectral analysis**

### Signal processing

**signal analysissignalsignal processor**

### Medical imaging

**imagingdiagnostic imagingdiagnostic radiology**

### Remote sensing

**remote-sensingremotely sensedremote sensor**

### Correlation coefficient

**correlationcorrelatedcorrelation coefficients**

It is a powerful tool for the recovery of both the amplitude and frequency characteristics of multiple highly correlated sources in challenging environment (e.g., limited number of snapshots, low signal-to-noise ratio.

### Signal-to-noise ratio

**signal to noise ratioSNRsignal-to-noise**

It is a powerful tool for the recovery of both the amplitude and frequency characteristics of multiple highly correlated sources in challenging environment (e.g., limited number of snapshots, low signal-to-noise ratio.

### Phased array

**phased array radarphased-arrayphased-array radar**

where is the steering matrix, contains the source waveforms, and {\bf e}(n) is the noise term.

### Dirac delta function

**delta functionimpulsedirac delta**

Assume that, where is the Dirac delta and it equals to 1 only if n=\bar{n} and 0 otherwise.

### Covariance matrix

**variance-covariance matrixcovariance matricescovariance**

The covariance matrix of {\bf y}(n) that contains all information about is

### Vectorization (mathematics)

**vectorizationvectorization operatorhalf-vectorization**

After applying the vectorization operator to the matrix {\bf R}, the obtained vector is linearly related to the unknown parameter as

### Compressed sensing

**compressive sensingcompressed sensing techniquesCompressed-Sensing**

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.

### Sparse dictionary learning

**dictionary learningdictionary matrixMini-batch dictionary learning**

In the sparse signal recovery model, the sparsity of the truth signal is dependent on the distance between the adjacent element in the overcomplete dictionary {\bf A}, therefore, the difficulty of choosing the optimum overcomplete dictionary arises.