Type: Package
Title: Compressive Sampling: Sparse Signal Recovery Utilities
Version: 0.3.4
Date: 2023-08-27
Maintainer: Mehmet Suzen <mehmet.suzen@physics.org>
Depends: stats, utils
Description: Utilities for sparse signal recovery suitable for compressed sensing. L1, L2 and TV penalties, DFT basis matrix, simple sparse signal generator, mutual cumulative coherence between two matrices and examples, Lp complex norm, scaling back regression coefficients.
License: GPL (≥ 3)
LazyLoad: yes
NeedsCompilation: no
Packaged: 2023-08-27 16:07:46 UTC; msuzen
Author: Mehmet Suzen [aut, cre]
Repository: CRAN
Date/Publication: 2023-08-27 16:20:02 UTC

Compare L1, L2 and TV on a sparse signal.

Description

Compare L1, L2 and TV on a sparse signal.

Usage

CompareL1_L2_TV1(N, M, per)

Arguments

N

Size of the sparse signal to generate , integer.

M

Number of measurements.

per

Percentage of spikes.

Author(s)

Mehmet Suzen

Generate Discrete Fourier Transform Matrix using DFTMatrixPlain.

Description

Generate Discrete Fourier Transform Matrix (NxN).

Usage

DFTMatrix0(N)

Arguments

N

Integer value determines the dimension of the square matrix.

Value

It returns a NxN square matrix.

Author(s)

Mehmet Suzen

See Also

DFTMatrixPlain

Examples

 DFTMatrix0(2)

Generate Plain Discrete Fourier Transform Matrix without the coefficient

Description

Generate plain Discrete Fourier Transform Matrix (NxN) without a coefficient.

Usage

DFTMatrixPlain(N)

Arguments

N

Integer value defines the dimension of the square plain DFT matrix.

Value

It returns a NxN square matrix.

Author(s)

Mehmet Suzen

Examples

DFTMatrixPlain(2)

Generate Gaussian Random Matrix

Description

Generate Gaussian Random Matrix ( zero mean and standard deviation one.)

Usage

GaussianMatrix(N, M)

Arguments

N

Integer value determines number of rows.

M

Integer value determines number of columns.

Value

Returns MxN matrix.

Author(s)

Mehmet Suzen

Examples

GaussianMatrix(3,2)

L-p norm of a given complex vector

Description

L-p norm of a given complex vector

Usage

Lnorm(X, p)

Arguments

X

a complex vector, can be real too.

p

norm value

Value

L-p norm of the complex vector

Author(s)

Mehmet Suzen

1-D total variation of a vector.

Description

1-D total variation of a vector.

Usage

TV1(x)

Arguments

x

A vector.

Author(s)

Mehmet Suzen

Cumulative mutual coherence

Description

Generate vector of cumulative mutual coherence of a given matrix up to a given order. \ Mutual Cumulative Coherence of a Matrix A at order k is defined as M(A, k) = max_{p} max_{p \ne q, q \in \Omega } \sum_{q} | <a_{p}, a_{q}> | / ( |a_{p}| |a_{q}|)

Usage

mutualCoherence(A, k)

Arguments

A

A matrix.

k

Integer value determines number of columns or the order of mutual coherence function to .

Value

Returns k-vector

Author(s)

Mehmet Suzen

References

Compressed sensing in diffuse optical tomography \ M. Suzen, A.Giannoula and T. Durduran, \ Opt. Express 18, 23676-23690 (2010) \ J. A. Tropp \ Greed is good: algorithmic results for sparse approximation, \IEEE Trans. Inf. Theory 50, 2231-2242 (2004)

Examples

set.seed(42)
B <- matrix(rnorm(100), 10, 10) # Gaussian Random Matrix
mutualCoherence(B, 3) # mutual coherence up to order k

1-D Total Variation Penalized Objective Function

Description

1-D Total Variation Penalized Objective Function

Usage

objective1TV(x, T, phi, y, lambda)

Arguments

x

Initial value of the vector to be recovered. Sparse representation of the vector ( N x 1 matrix ) X=Tx, where X is the original vector

T

sparsity bases ( N x N matrix )

phi

Measurement matrix (M x N).

y

Measurement vector (Mx1).

lambda

Penalty coefficient.

Value

Returns a vector.

Author(s)

Mehmet Suzen

Objective function for ridge L1 penalty

Description

Objective function for ridge L1 penalty

Usage

objectiveL1(x, T, phi, y, lambda)

Arguments

x

unknown vector

T

transform bases

phi

measurement matrix

y

measurement vector

lambda

penalty term

Note

Thank you Jason Xu of Washington University for pointing out complex number handling

Author(s)

Mehmet Suzen

Objective function for Tikhinov L2 penalty

Description

Objective function for Tikhinov L2 penalty

Usage

objectiveL2(x, T, phi, y, lambda)

Arguments

x

unknown vector

T

transform bases

phi

measurement matrix

y

measurement vector

lambda

penalty term

Note

Thank you Jason Xu of Washington University for pointing out complex number handling

Author(s)

Mehmet Suzen

Frequency expression for DFT

Description

Frequency expression for DFT

Usage

oo(p, omega)

Arguments

p

Exponent

omega

Omega expression for DFT

Author(s)

Mehmet Suzen

Transform back multiple regression coefficients to unscaled regression coefficients Original question posed by Mark Seeto on the R mailing list.

Description

Transform back multiple regression coefficients to unscaled regression coefficients Original question posed by Mark Seeto on the R mailing list.

Usage

scaleBack.lm(X, Y, betas.scaled)

Arguments

X

unscaled design matrix without the intercept, m by n matrix

Y

unscaled response, m by 1 matrix

betas.scaled

coefficients vector of multiple regression, first term is the intercept

Note

2015-04-10

Author(s)

M.Suzen

Examples

set.seed(4242)
 X            <- matrix(rnorm(12), 4, 3)
 Y            <- matrix(rnorm(4), 4, 1)
 betas.scaled <- matrix(rnorm(3), 3, 1)
 betas        <- scaleBack.lm(X, Y, betas.scaled)

1-D Total Variation Penalized Nonlinear Minimization

Description

1-D Total Variation Penalized Nonlinear Minimization

Usage

 solve1TV(phi,y,T,x0,lambda=0.1)

Arguments

x0

Initial value of the vector to be recovered. Sparse representation of the vector ( N x 1 matrix ) X=Tx, where X is the original vector

T

sparsity bases ( N x N matrix )

phi

Measurement matrix (M x N).

y

Measurement vector (Mx1).

lambda

Penalty coefficient. Defaults 0.1

Value

Returns nlm object.

Author(s)

Mehmet Suzen

l1 Penalized Nonlinear Minimization

Description

l1 Penalized Nonlinear Minimization

Usage

 solveL1(phi,y,T,x0,lambda=0.1)

Arguments

x0

Initial value of the vector to be recovered. Sparse representation of the vector ( N x 1 matrix ) X=Tx, where X is the original vector

T

sparsity bases ( N x N matrix )

phi

Measurement matrix (M x N).

y

Measurement vector (Mx1).

lambda

Penalty coefficient. Defaults 0.1

Value

Returns nlm object.

Author(s)

Mehmet Suzen

l2 Penalized Nonlinear Minimization

Description

l2 Penalized Nonlinear Minimization

Usage

 solveL2(phi,y,T,x0,lambda=0.1)

Arguments

x0

Initial value of the vector to be recovered. Sparse representation of the vector ( N x 1 matrix ) X=Tx, where X is the original vector

T

sparsity bases ( N x N matrix )

phi

Measurement matrix (M x N).

y

Measurement vector (Mx1).

lambda

Penalty coefficient. Defaults 0.1

Value

Returns nlm object.

Author(s)

Mehmet Suzen

Sparse digital signal Generator.

Description

Sparse digital signal Generator with given thresholds.

Usage

sparseSignal(N, s, b = 1, delta = 1e-07, nlev = 0.05, slev = 0.9)

Arguments

N

Number of signal components, vector size.

s

Number of spikes, significatn components

b

Signal bandwidth, defaults 1.

delta

Length of discrete distances among components, defaults 1e-7.

nlev

Maximum value of insignificant component, relative to b, defaults to 0.05

slev

Maximum value of significant component, relative to b, defaults to 0.9

Author(s)

Mehmet Suzen